Audrey Cochard

Garcia-Jove Navarro

Shunnichi Kashida

Michel Kress

Dominique Weil

Zoher Gueroui
email: zoher.gueroui@ens.fr

RNA at the surface of phase-separated condensates impacts their size and number

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Membrane-less organelles, by localizing and regulating complex biochemical reactions, are ubiquitous functional subunits of intracellular organization. They include a variety of nuclear and cytoplasmic ribonucleoprotein (RNP) condensates, such as nucleoli, P-bodies, germ granules and stress granules. While is it now recognized that specific RNA and protein families are critical for the biogenesis of RNP condensates, how these molecular constituents determine condensate size and morphology is unknown. To circumvent the biochemical complexity of endogenous RNP condensates, the use of programmable tools to reconstitute condensate formation with minimal constituents can be instrumental. Here we report a methodology to form RNA-containing condensates in living cells with controlled RNA and protein composition. Our bioengineered condensates are made of ArtiGranule scaffolds undergoing liquid-liquid phase separation in cells and programmed to specifically recruit a unique RNA species. We found that RNAs localized on condensate surface, either as isolated RNA molecules or as a homogenous corona of RNA molecules around the condensate. This simplified system allowed us to demonstrate that the size of the condensates scales with RNA surface density, the higher the RNA density is, the smaller and more frequent the condensates are. Our observations suggest a mechanism based on physical constraints, provided by RNAs localized on condensate surface, that limit condensate growth and coalescence.

It is increasingly recognized that biomolecular condensates contribute to organize cellular biochemistry by concentrating and compartmentalizing proteins and nucleic acids. They include a broad range of nuclear and cytoplasmic ribonucleoprotein (RNP) granules, such as nucleoli, P-bodies, germ granules and stress granules. Remarkably, abnormal condensate maturation into toxic aggregates is linked to viral infection, cancer, and neurodegenerative diseases [START_REF] Buchan | mRNP granules[END_REF] . Cellular condensates harbour a large diversity in terms of biochemical compositions as well as functions. Nevertheless, a unified model of formation via liquid-liquid phase separation (LLPS), where RNP constituents interact through multivalent and weak interactions, has been proposed to understand their biogenesis [START_REF] Brangwynne | Germline P Granules Are Liquid Droplets That Localize by Controlled Dissolution/Condensation[END_REF][START_REF] Li | Phase transitions in the assembly of multivalent signalling proteins[END_REF][START_REF] Shin | Liquid phase condensation in cell physiology and disease[END_REF][START_REF] Boeynaems | Protein Phase Separation: A New Phase in Cell Biology[END_REF][START_REF] Banani | Biomolecular condensates: organizers of cellular biochemistry[END_REF] . In addition to their diverse compositions and functions, condensates are also diverse in size.

Whereas P-bodies or PML bodies are often diffraction-limited puncta, other condensates such as germ granules, centrosomes, and nucleoli can reach few micrometres in size [START_REF] Brangwynne | Germline P Granules Are Liquid Droplets That Localize by Controlled Dissolution/Condensation[END_REF][START_REF] Standart | P-Bodies: Cytosolic Droplets for Coordinated mRNA Storage[END_REF][START_REF] Lallemand-Breitenbach | PML nuclear bodies[END_REF][START_REF] Decker | Limiting amounts of centrosome material set centrosome size in C. elegans embryos[END_REF][START_REF] Strom | The liquid nucleome -phase transitions in the nucleus at a glance[END_REF] . What sets condensate size and number in cells remains to be understood.

Mounting evidence based on in vitro reconstitutions and cellular approaches underlined the importance of multivalent interactions between RBPs and RNAs in shaping condensate biogenesis and morphology. In particular, RNA molecules have been proven to play fundamental roles in determining the structure, dynamic and biophysical properties of condensates [START_REF] Roden | RNA contributions to the form and function of biomolecular condensates[END_REF] . For instance, RNAs act as molecular seeds to nucleate phase separated-condensates and regulate their assembly in a spatiotemporal manner [START_REF] Shevtsov | Nucleation of nuclear bodies by RNA[END_REF][START_REF] Schwartz | RNA Seeds Higher-Order Assembly of FUS Protein[END_REF][START_REF] Jain | RNA phase transitions in repeat expansion disorders[END_REF][START_REF] Yamazaki | Functional Domains of NEAT1 Architectural lncRNA Induce Paraspeckle Assembly through Phase Separation Molecular Cell Article Functional Domains of NEAT1 Architectural lncRNA Induce Paraspeckle Assembly through Phase Separation[END_REF][START_REF] Saha | Polar Positioning of Phase-Separated Liquid Compartments in Cells Regulated by an mRNA Competition Mechanism[END_REF][START_REF] Falahati | Nucleation by rRNA dictates the precision of nucleolus assembly[END_REF] . On the opposite, high RNA concentration can dissolve condensates and keep prion-like RBPs soluble in cell nucleus [START_REF] Banerjee | Reentrant Phase Transition Drives Dynamic Substructure Formation in Ribonucleoprotein Droplets[END_REF][START_REF] Maharana | RNA buffers the phase separation behavior of prionlike RNA binding proteins[END_REF] . In addition to their formation or dissolution, RNA molecules can also impact the viscosity of the RNP condensates as well as the dynamics of their components in a sequence-dependent manner [START_REF] Zhang | RNA Controls PolyQ Protein Phase Transitions[END_REF][START_REF] Elbaum-Garfinkle | The disordered P granule protein LAF-1 drives phase separation into droplets with tunable viscosity and dynamics[END_REF][START_REF] Boeynaems | Spontaneous driving forces give rise to protein-RNA condensates with coexisting phases and complex material properties[END_REF] . The different structures of RNAs can determine the molecular specificity of RNP condensates and thus explain the coexistence of separate condensates with distinct molecular compositions [START_REF] Langdon | mRNA structure determines specificity of a polyQ-driven phase separation[END_REF] . Moreover, RNA-RNA interactions between unstructured RNAs can lead to the formation of non-spherical condensates [START_REF] Ma | In vivo reconstitution finds multivalent RNA-RNA interactions as drivers of mesh-like condensates[END_REF] . Finally, RNAs can take part in RNA-RBP interactions that drive the formation of multiphasic condensates, whose structure relies on RNA concentration and on RNA-RBP interaction strength [START_REF] Boeynaems | Spontaneous driving forces give rise to protein-RNA condensates with coexisting phases and complex material properties[END_REF][START_REF] Kaur | Sequence-encoded and composition-dependent protein-RNA interactions control multiphasic condensate morphologies[END_REF][START_REF] Feric | Coexisting Liquid Phases Underlie Nucleolar Subcompartments[END_REF] . In addition to the contribution of condensate constituents, extrinsic factors such as membrane, cytoskeleton and chromatin can modulate LLPS and condensate biogenesis and coarsening [START_REF] Snead | Membrane surfaces regulate assembly of a ribonucleoprotein condensate[END_REF][START_REF] Feric | A nuclear F-actin scaffold stabilizes RNP droplets against gravity in large cells HHS Public Access Author manuscript[END_REF][START_REF] Lee | Chromatin mechanics dictates subdiffusion and coarsening dynamics of embedded condensates[END_REF] .

Interestingly, the biochemical and structural heterogeneity at the surface of condensates could also influence their stability. For instance in C.elegans, the adsorption of MEG-3 on PGL droplets drives the formation of a gel-like shell around a liquid core that eventually can stabilize P granules and trap RNAs [START_REF] Putnam | A gel phase promotes condensation of liquid P granules in Caenorhabditis elegans embryos[END_REF][START_REF] Lee | Recruitment of mRNAs to P granules by condensation with intrinsically-disordered proteins[END_REF] . Moreover, using an artificial scaffold in cells named ArtiGranule (ArtiG), we previously demonstrated that the condensation of the RNA-binding domain of the P-body protein Pumilio was sufficient to attract Pumilio RNA targets and P-body proteins at the surface of the condensates, which in turn impacted the seeding and the size of the condensates [START_REF] Navarro | RNA is a critical element for the sizing and the composition of phase-separated RNA-protein condensates[END_REF] . We therefore hypothesized that the size selection of the condensates relies on the adsorption of RNP elements at their surface, which may contribute to limit coarsening by steric exclusion [START_REF] Navarro | RNA is a critical element for the sizing and the composition of phase-separated RNA-protein condensates[END_REF] . However, extracting the specific role of RNA on condensate morphology is still inaccessible since natural RNP condensates emerge from a complex combination of RNA-protein, RNA-RNA, and protein-protein interactions 33- 35 . To reduce this complexity, we developed a methodology to reconstitute the formation of RNAcontaining condensates in living cells with controlled RNA and protein composition. Our bioengineered condensates were constituted of ArtiG scaffolds undergoing LLPS in cells, which were programmed to specifically recruit a unique RNA species. We first fused ArtiG scaffolds to an orthogonal RNA binding domain chosen to interact specifically with a synthetic mRNA. We found that RNAs localized on condensate surface, either as isolated RNA molecules or as a homogenous corona of RNA molecules around the condensate. The ArtiG condensates remained distinct from endogenous condensates, which enabled us to separate the role of the recruited RNA molecules from other potential contributors. We first observed a negative correlation between the number of condensates per cell and their mean diameter. By quantifying the localization and number of individual RNA molecules, we additionally found that the higher the RNA density is, the smaller and more numerous the condensates are. Overall, our data indicate that the size of RNP condensate scales with RNA surface density, which can be explained by physical constraints limiting condensate growth and coalescence.

Reconstitution of RNA-protein condensates in human cells

Our first goal was to engineer artificial RNA-protein condensates that assemble through LLPS into cells. Our design combined two parts: a scaffold used to trigger the formation of protein condensates and a grafted RNA-binding domain to recruit specific RNA sequences (Fig. 1a). As protein scaffold, we used ArtiGs that form liquid protein condensates in a concentration-dependent manner through weak multivalent interactions [START_REF] Navarro | RNA is a critical element for the sizing and the composition of phase-separated RNA-protein condensates[END_REF] . The ArtiG scaffold developed previously was fused to a Pumilio-binding domain that recruits a large number of endogenous Pumilio RNA targets [START_REF] Navarro | RNA is a critical element for the sizing and the composition of phase-separated RNA-protein condensates[END_REF] . To restrict the targeting on ArtiGranules to one single RNA species, we chose an orthogonal RNAbinding domain, the MS2-coat protein (MCP), that recognizes specific MS2 stem-loops. The resulting plasmid construct, Fm-MCP-Ft, consisted in the fusion of an oligomeric ferritin (Ft) to MCP and a self-interacting domain F36M-FKBP (Fm) (Fig. 1a).

In order to monitor condensate formation in cells, we co-transfected HeLa cells with the multivalent MCP self-interacting scaffold Fm-MCP-Ft, and Fm-emGFP-Ft as a fluorescent tracer.

Live confocal imaging performed 8 h after transfection showed that, initially, emGFP fluorescence at low expression level was diffuse in the cytoplasm. As Fm-emGFP-Ft expression increased, several bright fluorescent bodies nucleated throughout the cytoplasm and grew to reach a micrometric size within an hour (Fig. 1b). The emGFP expressing condensates, hereafter called ArtiG emGFP/MCP , were very mobile and rapidly grew as a function of time. When two proximal condensates docked, they tended to coalesce and to relax into large spherical bodies, as generally observed for endogenous liquid-like condensates (Fig. 1b, white arrow and Fig. S1a).

To reconstitute RNA-protein condensates using ArtiG emGFP/MCP , we first generated a plasmid to express a mRNA equipped with MS2 stem-loops in its 3'UTR (RNA-MS2, Fig. 1a). We cotransfected this plasmid and the plasmids expressing the ArtiG emGFP/MCP scaffold and fixed the cells 24 h after transfection. We next monitored the intracellular localization of RNA-MS2 using singlemolecule fluorescence in situ hybridization (smFISH) [START_REF] Tsanov | smiFISH and FISH-quant -a flexible single RNA detection approach with super-resolution capability[END_REF] . The majority of cells harboured micrometric ArtiG emGFP/MCP condensates in the cytoplasm, with a striking Cy3-FISH signal around individual condensates, indicating a localization of RNA-MS2 molecules at the condensate surface (Fig. 1c, insert 1, and Fig. 1e, left panel). These RNAs were either present as isolated molecules or, when the number of recruited molecules was higher, were more homogeneously distributed around the condensates, into a corona made of a single RNA molecule layer (see other examples in Fig. S1b). Discrete Cy3 dots corresponding to individual mRNAs were also found dispersed throughout the cytosolic space (Fig. 1c, insert 2), as well as brighter spots in the nucleus corresponding to transcription foci (Fig. 1c, grey arrow). To assess the specificity of RNA recruitment on the ArtiG emGFP/MCP , we investigated the localization of RNA-MS2 in cells containing ArtiG emGFP (devoid of the MCP domain) and found a complete absence of RNA-MS2 at the condensate periphery (Fig.

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1d, upper panel, and Fig. 1e, middle panel). Experiments carried out in HEK293 cells showed the same results (Fig. S1c). Similarly, ArtiG emGFP/MCP did not show any recruitment of the endogenous mRNA ß-actin and of the NORAD lncRNA (devoid of MS2) (Fig. 1d, lower panel, Fig. 1e, right panel, and Fig. S1d), thus confirming the specificity of the RNA recruitment. When quantifying the total number of mRNA molecules dispersed in the cytoplasm and localized on ArtiG emGFP/MCP , we found that 34% ± 19% of the cytoplasmic mRNAs were specifically recruited at the condensate surface (mean of 430 recruited RNAs and 1200 dispersed RNAs per cell) (Fig. 1f). Altogether, these data show that ArtiG emGFP/MCP act as condensates localizing specific RNAs on their surfaces (ArtiG emGFP/MCP/RNA ).

Cytosolic RNAs are depleted at the vicinity of large condensates

As our data showed a robust recruitment of RNAs at the surface of ArtiG emGFP/MCP condensates, we next investigated whether this recruitment impacted the distribution of RNAs in the cytoplasm. Interestingly, we observed a depletion of cytoplasmic MS2-RNAs close to ArtiG emGFP/MCP/RNA condensates (Fig. 2a and Fig. S2a). This depletion was readily visible around large condensate clusters recruiting a high number of RNA molecules. On the examples shown in Fig. 2a and Fig. S2a, we quantified the density of RNAs as a function of the distance to the condensate edges.

RNA density was almost zero in a large area ranging from the immediate vicinity of the cluster up to 3 µm from the condensate boarder. Then, RNA density increased until reaching a plateau at a distance of about 4 µm, with a value corresponding to the mean cytoplasmic RNA concentration found in cells (Fig. 2c, blue dots, and Fig. S2b). Likewise, plotting the cumulative number of RNAs outside the condensates as a function of the distance to the condensate edges showed first a very slow increase up to 3µm from the condensate edges (Fig. 2d, blue dots, and Fig S2c). Beyond this depletion area, the increase sharpened with a steady slope corresponding to an even cytoplasmic RNA concentration, except when the area occasionally included neighbouring condensates (Fig. 2c andd, light blue dots).

For comparison, we quantified the spatial distribution of ß-actin mRNAs, which do not bind to ArtiG MCP . We found a total absence of depletion of ß-actin mRNAs around ArtiG clusters (Fig. 2b), with an even RNA density around the condensates (Fig. 2c andd, orange dots). Altogether, these results suggest that the RNA depletion was linked to the specific recruitment of RNA-MS2 on condensates and did not stem from potential non-specific steric exclusion around the condensates.

Artificial condensates are biochemically distinct from endogenous condensates

In a cellular context, biologically distinct RNP condensates that form in the same cytoplasm could interact with each other through shared proteins and RNAs, as described for P-bodies (PBs) and stress granules (SGs) [START_REF] Wilczynska | The translational regulator CPEB1 provides a link between dcp1 bodies and stress granules[END_REF] or PBs and U-bodies [START_REF] Liu | U bodies are cytoplasmic structures that contain uridine-rich small nuclear ribonucleoproteins and associate with P bodies[END_REF] . Therefore, we next sought to investigate whether the local enrichment of mRNAs on ArtiG emGFP/MCP may induce interactions with other cytoplasmic RNP granules. To this aim, we looked at the presence of PBs by immunostaining 24 h after transfection, using DDX6 as a PB marker. Our observations showed no particular physical proximity or docking between the two condensates (Fig. 3a, left panel). Similarly, there was not proximity between ArtiG emGFP/MCP and SGs. Indeed, immunostaining of ATXN2L as a SG marker showed their absence 24 h after transfection (Fig. S3a), while no docking of ArtiG emGFP/MCP/RNA with SGs was observed after SG induction with an arsenite stress (Fig. 3a, right panel). These results suggest that ArtiG emGFP/MCP/RNA are biochemically distinct and physically independent from both PBs and SGs.

Controlled dissolution of artificial condensates

Recent studies suggest that the formation and stability of biological condensates are tightly regulated by multiple stimuli, including post-translational modifications, biochemical reactions, or physical parameters such as temperature or osmotic pressure changes [START_REF] Snead | The Control Centers of Biomolecular Phase Separation: How Membrane Surfaces, PTMs, and Active Processes Regulate Condensation[END_REF][START_REF] Jalihal | Hyperosmotic phase separation: Condensates beyond inclusions, granules and organelles[END_REF] . By design, the formation and stability of the ArtiG emGFP/MCP condensates are driven by multivalent interactions mediated by the Fm-Fm homodimer, and these interactions could in principle be disrupted by the addition of a chemical competitor, FK506. We therefore assessed if FK506 addition could first prevent condensate formation and secondly dissolve already formed condensates (Fig. 3b). In the absence of FK506, the majority of transfected cells exhibited ArtiG emGFP/MCP/RNA condensates (93% after 24h of expression, Fig. 3c). This percentage dropped to 15% upon addition of FK506 at the time of transfection, with the majority of cells displaying a diffuse emGFP fluorescence and a homogeneous MS2-RNA distribution in the cytosol (Fig. 3d). Thus, FK506 efficiently inhibited the formation of the condensates. In a second experimental design, we examined the dissolution of fully formed ArtiGs by adding FK506 24h after transfection (Fig. 3b). After 2h of FK506 incubation, we found that the majority of cells lacked ArtiGs and displayed diffuse emGFP with Cy3-labelled MS2-RNAs distributed throughout the cytoplasm (70%, Fig. 3c). Thus, FK506 treatment induced the dissolution of the majority of pre-formed ArtiG emGFP/MCP/RNA condensates. To further characterize FK506 effect, we examined the time-scale of dissolution using live confocal microscopy. Upon addition of FK506, some cells exhibited condensates dissolving within few seconds (Fig. 3e and supplementary video 2), while in others dissolution took up to 30 minutes (Fig. S3b). These dissolutions were accompanied with a strong increase of the cytosolic fluorescence signal, corresponding to the release of the ArtiG scaffold (Fig. 3e). We also observed a few cells with smaller condensates and a stronger cytosolic fluorescence, corresponding to incomplete condensate dissolution, in agreement with the observation of residual condensates in fixed cells (Fig. S3c). Altogether, our data showed that pre-treatment with the FK506 binding competitor of Fm proteins provides a mean of preventing the formation of the ArtiG condensates, while it globally induces their disassembly when they are already formed. Our system thus allows for a controlled inhibition and disassembly (by adding FK506) of artificial condensates in living cells.

Linking condensate size and number of recruited RNAs

Determining how the primary constituents of condensates set the variety of condensate size and morphology naturally observed in cells remains very complex, since RNAs and proteins establish a large network of interactions. The ArtiG condensates potentially provide an important simplification to this problem, as only one RNA species is recruited to the condensates. We could therefore analyse how RNA contributes to ArtiG emGFP/MCP/RNA condensate morphology, by quantifying the recruitment of RNAs in condensates and condensate size within single cells. The size and number of ArtiG emGFP/MCP/RNA condensates were heterogenous between cells, with cells exhibiting few condensates and others a larger number (Fig. 4a). The distribution of the mean diameter of ArtiG condensates roughly ranged from 0.4 to 4 µm depending on the cell (mean ± SD = 1.1 ± 0.6 µm, coefficient of variation CV = 58%, Fig. 4b, left panel). While 75% of the cells had condensates with a mean diameter below 1.5 µm, we observed particularly large condensates, up to 4 µm in diameter, in the other cells. The number of condensates per cell was also very diverse (mean number = 33, CV = 116%, Fig. 4b, right panel). Interestingly, condensate mean size per cell was inversely proportional to their number (Fig. 4c). Indeed, cells displaying large condensates (> 1.5µm of diameter) always had a limited number of them (<25). In contrast, a higher number of condensates in a cell (>25) was correlated with a mean diameter of the condensates below 1.5 µm. As opposed to the heterogeneity of condensate size between cells, we found a homogeneity of size within a given cell (average CV=30%, Fig. 4d).

We next sought to examine whether there was a correlation between condensate number and size, and RNA recruitment. To this aim, we computed, per cell, the density of RNAs recruited at the surface of ArtiG condensates and their mean diameter (Fig. 4e). We could highlight two groups of cells. In cells displaying larger condensates (mean diameter > 1.5 µm, mean ± SD = 2.0 ± 0.6 µm), the RNA surface density was below 5 RNAs/µm² (mean = 2.0 RNAs/µm², Fig. 4e, green dots). These condensates were generally spherical with a small number of RNAs at their periphery. In contrast, a higher RNA density (> 5 RNAs/µm², mean = 16.0 RNA/µm²) was correlated with a mean diameter of ArtiG below 1.5 µm (mean ± SD = 0.79 ± 0.32 µm, Fig. 4e, orange dots). In these cells, condensates were often found in close proximity to each other, forming cluster-like patterns (more than 5 condensates docking together) with RNA patches or corona separating individual condensates (Fig. 4f). These clusters were reminiscent of coalescence events but their high number suggested that the coalescence process was arrested, so that condensates did not relax into a sphere. We even observed a few cases where ArtiG emGFP/MCP and RNA molecules seemed intertwined, with frontiers between condensates becoming blurred and ArtiG emGFP/MCP/RNA losing their round shape (Fig. 4g). To sum up, we found that all large spherical ArtiG condensates displayed few RNA molecules on their surfaces, while condensates with a high RNA surface density had a smaller size.

Evolution of condensate size and morphology as a function of RNA surface density

To refine our analysis of the role of RNA localization in the condensate morphology, we increased the expression of transcribed RNA-MS2 by transfecting a larger quantity of plasmids in cells (five-fold more). In these conditions (RNA high) the mean number of RNA-MS2 transcripts per cell rose from about 1200 to around 2400, and the mean number of RNA-MS2 recruited at the surface of the condensates from 430 to 1100. This RNA high condition did not modify the expression of the ArtiG scaffold, as indicated by Western blotting experiments (Fig. S5). Firstly, we found that experiments performed in RNA high condition led to smaller condensate size (0.70 ± 0.32 µm instead of 1.25 ± 0.69 µm) (Fig. 5a), which supports our observation that higher RNA surface localization resulted in smaller condensates. Furthermore, in the RNA high condition, almost no cells displayed large condensates (diameter > 1.5µm) (Fig. 5b) and a higher incidence of the cluster-like patterns, about 58 % of cells, was observed in regard to 42.5 % in the RNA low condition (Fig. 5c). Among the clusters, condensate intertwining, which was a rare event in the low RNA condition (5 %), became more common (17 %). Altogether these data confirm a direct relationship between RNA surface density and condensate size and number, and underlie that the average size of ArtiG condensates is influenced by the level of expression of the recruited RNA.

Discussion

RNA is more and more recognized as a driving force in cellular organization and functions.

These polymers can interact and scaffold hundreds of proteins to generate high order organizations including RNP condensates. The first high throughput biochemical studies of RNP condensates showed that their RNA and protein content is highly complex [START_REF] Saitoh | Proteomic Analysis of Interchromatin Granule Clusters[END_REF][START_REF] Hubstenberger | P-Body Purification Reveals the Condensation of Repressed mRNA Regulons[END_REF][START_REF] Khong | The Stress Granule Transcriptome Reveals Principles of mRNA Accumulation in Stress Granules[END_REF][START_REF] Jain | ATPase-Modulated Stress Granules Contain a Diverse Proteome and Substructure[END_REF] . While these studies highlight that condensates assembly is driven by the combination of multiple RNA-protein, protein-protein, and RNA-RNA interactions, the rules governing RNA and protein spatiotemporal co-assembly are still enigmatic. As a consequence, deciphering and manipulating RNP condensates in cellulo still remains a difficult task. In this context, in vitro reconstitutions using purified components have been a powerful strategy to study the diverse roles of RNAs involved in specifying the structure, composition and dynamical properties of RNP granules [START_REF] Roden | RNA contributions to the form and function of biomolecular condensates[END_REF][START_REF] Boeynaems | Spontaneous driving forces give rise to protein-RNA condensates with coexisting phases and complex material properties[END_REF][START_REF] Kaur | Sequence-encoded and composition-dependent protein-RNA interactions control multiphasic condensate morphologies[END_REF][START_REF] Tauber | Modulation of RNA Condensation by the DEAD-Box Protein eIF4A[END_REF][START_REF] Guillé | RNA-Induced Conformational Switching and Clustering of G3BP Drive Stress Granule Assembly by Condensation Article RNA-Induced Conformational Switching and Clustering of G3BP Drive Stress Granule Assembly by Condensation[END_REF] . Physicochemical parameters defining RNA polymers such as their length, chemical complexity and sequence, could thus be assessed in a reconstituted environment. Despite their obvious advantages, several limitations arose from these reductionist approaches. For instance, the physiological relevance of the concentration and composition of in vitro model condensates can be questioned, as well as their environment that lacks the physicochemical complexity present within cells. Alternatively, the over-expression of proteins, often chosen among scaffolding proteins founded to drive LLPS in test tube, was also widely used to identify the propensity of specific protein domains to undergo phase separation in a cellular environment [START_REF] Maharana | RNA buffers the phase separation behavior of prionlike RNA binding proteins[END_REF][START_REF] Banani | Compositional Control of Phase-Separated Cellular Bodies In Brief What are the general principles that define the composition of phase-separated cellular bodies?[END_REF][START_REF] Nott | Phase Transition of a Disordered Nuage Protein Generates Environmentally Responsive Membraneless Organelles[END_REF] .

To combine the level of controls provided by in vitro experiments with the possibility to study LLPS within the cellular environment, several bioengineering approaches have been developed to form, within cells, condensates with specific properties. These approaches often use optogenetic and chemical actuations based on protein-multimerization domains acting as scaffolds of artificial condensates. Being able to engineer condensates in cells with well-defined compositions, structures and dynamical properties provides novel insights to correlate condensates biochemical functions with their material states, a link that is still difficult to reach using conventional cell biology techniques.

Recent developments and applications of such engineered condensates have thus enabled the quantitative studies of the dynamical properties of phase-separated condensates within cytoplasm and nucleus. For example, light-induced strategies based on optoDroplets allowed the actuation of model condensates mimicking pathological assemblies appearing in some age-related diseases [START_REF] Shin | Spatiotemporal Control of Intracellular Phase Transitions Using Light-Activated optoDroplets[END_REF][START_REF] Mann | RNA Binding Antagonizes Neurotoxic Phase Transitions of TDP-43[END_REF] .

Alternative synthetic protein condensates were designed with programmable material properties or functions [START_REF] Watanabe | Genetic visualization of protein interactions harnessing liquid phase transitions[END_REF][START_REF] Bracha | Mapping Local and Global Liquid Phase Behavior in Living Cells Using Photo-Oligomerizable Seeds[END_REF][START_REF] Schuster | Controllable protein phase separation and modular recruitment to form responsive membraneless organelles[END_REF][START_REF] Reinkemeier | Designer membraneless organelles enable codon reassignment of selected mRNAs in eukaryotes[END_REF][START_REF] Dzuricky | De novo engineering of intracellular condensates using artificial disordered proteins[END_REF][START_REF] Heidenreich | Designer protein assemblies with tunable phase diagrams in living cells[END_REF][START_REF] Yoshikawa | Synthetic Protein Condensates That Inducibly Recruit and Release Protein Activity in Living Cells[END_REF][START_REF] Lasker | A modular platform for engineering function of natural and synthetic biomolecular condensates[END_REF] . In order to reconstitute artificial RNP condensates, iPOLYMER and ArtiGs were designed to induce condensation of RNA-binding motifs found in SGs (TIA-1) and PBs (Pumilio), respectively [START_REF] Navarro | RNA is a critical element for the sizing and the composition of phase-separated RNA-protein condensates[END_REF][START_REF] Nakamura | Intracellular production of hydrogels and synthetic RNA granules by multivalent molecular interactions[END_REF] . While these approaches provided a powerful mean to manipulate RNP condensate mimics in cells, the use of motifs from RBPs that are known to target thousands of RNA species could limit the understanding of observed effect in cells. To overcome this limitation, our approach was to reconstitute in cells the formation of artificial RNP condensates using ArtiGs modified to target a single RNA species. Remarkably, recruited RNAs localized at the condensate surface and bound as isolated RNA molecules or as homogenous RNA coronas surrounding the condensates (Fig. 1 andS1).

How these heterogenous patchy or corona-like patterns emerge from the interactions between ArtiG scaffolds and MS2-RNAs? Several in vitro studies and numerical simulations reported how multilayered organizations, such as core-shell droplets, assembled from ternary systems composed of protein-RNA interacting molecules [START_REF] Boeynaems | Spontaneous driving forces give rise to protein-RNA condensates with coexisting phases and complex material properties[END_REF][START_REF] Kaur | Sequence-encoded and composition-dependent protein-RNA interactions control multiphasic condensate morphologies[END_REF][START_REF] Feric | Coexisting Liquid Phases Underlie Nucleolar Subcompartments[END_REF][START_REF] Harmon | Differential solvation of intrinsically disordered linkers drives the formation of spatially organized droplets in ternary systems of linear multivalent proteins[END_REF][START_REF] Mountain | Formation of Multiphase Complex Coacervates and Partitioning of Biomolecules within them[END_REF][START_REF] Lu | Multiphase Complex Coacervate Droplets[END_REF] . A possible mode of formation of these multiphase droplets results from competing intermolecular interactions between macromolecular constituents that drive differences in surface tension and coexisting liquid phases. In this regard, our RNP condensates differ from co-existing liquid phases that demix into core-shell droplets, since they generally displayed a single RNA molecule layer as a shell covering ArtiG condensates. Instead, the assembly pathway controlling the formation of condensates with an RNA corona could arise from a stepwise process: first, ArtiG MCP scaffolds undergo LLPS and, subsequently, RNA molecules are recruited on the condensate surface with an efficiency that depends on the RNA expression level (Fig 5d).

The robust formation of ArtiG condensates in cells provides an efficient assay to examine basic questions such as how condensate size scales with RNA surface density. The ability to quantify individual RNA molecules on ArtiG condensate surface provides a unique mean to establish a direct link between RNA surface localization and condensate size and number. We found that the RNA density at the surface of condensates was correlated to their size and number, with large condensates displaying only a few RNAs on their surface whereas high RNA density always implied smaller and more numerous condensates. Furthermore, when we increased RNA expression in cells, and consequently RNA surface density on condensates, cells harboured smaller condensates, which supports a causal relationship between RNA surface density and condensate size.

Several examples in cell biology suggest the existence of a scaling of cellular organelles with cell volume, which could be understood if cells contain a limiting pool of structural components supporting the organelle assembly [START_REF] Decker | Limiting amounts of centrosome material set centrosome size in C. elegans embryos[END_REF][START_REF] Zwicker | Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles[END_REF][START_REF] Brangwynne | Phase transitions and size scaling of membrane-less organelles[END_REF] . In cells, native condensates such as PBs and PML nuclear bodies are generally found as sub-micrometric bodies that often do not grow over a certain size. This is generally in contradiction with the thermodynamical equilibrium picture of phase separated systems predicting an evolution towards a single condensed phase co-existing with a dilute phase. Initial growth of phase-separated condensates generally occurs through subunit addition, and coarsening through coalescence or Ostwald ripening [START_REF] Berry | RNA transcription modulates phase transition-driven nuclear body assembly[END_REF][START_REF] Berry | Physical principles of intracellular organization via active and passive phase transitions[END_REF][START_REF] Brangwynne | Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes[END_REF] . Thus, a solution to regulate condensate size would be to tune one of those three pathways (subunit addition, coalescence and Ostwald ripening), either through physicochemical parameters or by modifying interaction strengths and valences by biochemical reactions such as post-translational modifications [START_REF] Söding | Mechanisms for Active Regulation of Biomolecular Condensates Trends in Cell Biology[END_REF][START_REF] Kirschbaum | Controlling biomolecular condensates via chemical reactions[END_REF] . Recent theoretical studies suggest that both active and passive processes can be in play 70, [START_REF] Ranganathan | Dynamic metastable long-living droplets formed by stickerspacer proteins[END_REF] . For instance, it has been proposed that active processes within condensates could suppress Ostwald ripening and account for size selection [START_REF] Zwicker | Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles[END_REF][START_REF] Weber | Physics of active emulsions[END_REF][START_REF] Zwicker | Suppression of Ostwald ripening in active emulsions[END_REF][START_REF] Bressloff | Active suppression of Ostwald ripening: Beyond mean-field theory[END_REF][START_REF] Wurtz | Chemical-Reaction-Controlled Phase Separated Drops: Formation, Size Selection, and Coarsening[END_REF] . However, in the case of ArtiG emGFP/MCP/RNA , the two main formation pathways are subunit addition and coalescence (Fig. 1b). Client proteins acting like surfactants may reduce the energy required for the formation of an interface between the dense and dilute phase and lead to size-conserved multidroplet systems instead of the expected single large condensed phase, with condensate size decreasing as a result of an increase in the client concentration. [START_REF] Sanchez-Burgos | Size conservation emerges spontaneously in biomolecular condensates formed by scaffolds and surfactant clients[END_REF] In this respect, the protein Ki-67, localized at the surface of chromosomes, may for instance form a steric barrier that prevents the chromosomes from collapsing into a single entity [START_REF] Cuylen | Ki-67 acts as a biological surfactant to disperse mitotic chromosomes[END_REF] . A high surface charge density and thus a high electrostatic repulsion between biomolecular condensates may alter their propensity to fuse [START_REF] Welsh | Surface electrostatics govern the emulsion stability of biomolecular condensates[END_REF] . In vitro observations of the co-assembly between RNA homopolymers and mRNAs showed multi-phase assemblies, with RNAs localized at the droplet surface, suggesting that RNAs act as an interfacial shell stabilizing multiphasic condensates [START_REF] Tauber | Modulation of RNA Condensation by the DEAD-Box Protein eIF4A[END_REF] . Alternatively, a recent study explained how the RNA shell-forming domain of paraspeckles can modulate condensate shape and size and suggested a micellization-based model of assembly [START_REF] Yamazaki | Paraspeckles are constructed as block copolymer micelles[END_REF] . Here we propose that the RNA present at the surface of ArtiG condensates cause a steric hindrance that may prevent the growth of condensates by both subunit addition and coalescence (Fig. 5d). In this picture, RNAs could contribute to the colloidal stability of the condensates and thus regulate their size and number.

At a high RNA surface density, we found that ArtiG condensates can lose their sphericity and adopt a clustered morphology reminiscent of TIS granules [START_REF] Ma | In vivo reconstitution finds multivalent RNA-RNA interactions as drivers of mesh-like condensates[END_REF] . In contrast to TIS granules, where a skeleton made of RNA-RNA interactions between unstructured regions counterbalances the excess of surface energy generally driving fusion and relaxation, here RNAs at the condensate surface could impede coalescence by steric hindrance. We could also envision the existence of intermolecular interactions between RNAs that would bridge adjacent ArtiG condensates and consolidate their stability.

Such an impact of surface RNA on condensate morphology may be relevant for native RNP condensates. Indeed, the spatiotemporal organization of RNAs at the surface of native condensates has recently been investigated using advanced imaging tools. For example, super-resolution imaging showed that RNAs and proteins composing SGs are enriched within a main solid core surrounded by a less concentred layer [START_REF] Jain | ATPase-Modulated Stress Granules Contain a Diverse Proteome and Substructure[END_REF][START_REF] Wheeler | Distinct stages in stress granule assembly and disassembly[END_REF] . It has also been shown that RNAs exhibit diverse localization within PB core and at their surface [START_REF] Pitchiaya | Dynamic Recruitment of Single RNAs to Processing Bodies Depends on RNA Functionality[END_REF] . On SG or PB surface, RNAs can make transient contacts before stably associating inside the granules or leaving the granules for an alternative fate [START_REF] Pitchiaya | Dynamic Recruitment of Single RNAs to Processing Bodies Depends on RNA Functionality[END_REF][START_REF] Moon | Multicolour single-molecule tracking of mRNA interactions with RNP granules[END_REF] . Some of these RNAs are coding mRNAs, thus associating with ribosomes and other translation-related proteins [START_REF] Mateju | Single-Molecule Imaging Reveals Translation of mRNAs Localized to Stress Granules[END_REF] , while others are long non-coding RNAs with a regulatory function [START_REF] Pitchiaya | Dynamic Recruitment of Single RNAs to Processing Bodies Depends on RNA Functionality[END_REF] . These RNAs can partition bidirectionally between biologically different condensates [START_REF] Moon | Multicolour single-molecule tracking of mRNA interactions with RNP granules[END_REF][START_REF] Wilbertz | Single-Molecule Imaging of mRNA Localization and Regulation during the Integrated Stress Response[END_REF] . In the case of germ PBs, the association of the RNAs with the surface of the condensates can even be required for translation to happen [START_REF] Davidson | Localized Translation of gurken/TGF-α mRNA during Axis Specification Is Controlled by Access to Orb/CPEB on Processing Bodies[END_REF] . Along this line, our work suggests that localization of RNAs at the condensate surface could also feedback on condensate biogenesis.

In conclusion, our methodology to reconstitute biomolecular condensates in cells with controlled compositions and properties has proved powerful to reveal the role of RNA in condensate morphology. Not only its flexibility will enable to address other such basic biological issues in the future, but it could also be a mean to engineer novel properties within cells. More generally, our study stresses the importance of an understudied aspect of condensates, which is the role of the biomolecules present at their surface. It illustrates how chemical and physical heterogeneities on condensate surface may determine RNA granule morphogenetic properties.

MATERIALS AND METHODS

Experimental model

Human epithelioid carcinoma HeLa (ATCC, ccl-2) and embryonic kidney HEK-293 (ATCC, CRL-1573) cells were maintained in Dulbecco's modified Eagle's medium (with 4.5 g/L D-glucose, HyClone) supplemented with 10% fetal bovine serum (PAA Laboratories) and antibiotics, at 37 °C in a 5% CO2 humidified atmosphere. Cells were routinely tested for mycoplasma contamination.

Stress granules were induced with 0.5 mM sodium arsenite (Sigma) for 30 min at 37°C. For inhibition and reversibility experiments (Fig. 3b-e), 2.5 µM of FK506 was added to the cell culture medium.

Plasmids

All constructs were sub-cloned into pcDNA 3.1 plasmid (Invitrogen). The plasmids pcDNA3.1-F36M-FKBP(Fm)-emGFP-hFt and pcDNA3.1-Fm-hFt were previously described [START_REF] Navarro | RNA is a critical element for the sizing and the composition of phase-separated RNA-protein condensates[END_REF] . The plasmid pcDNA3.1-Fm-MCP-hFt was obtained by replacing the emGFP CDS between XhoI and BamHI restriction sites in pcDNA3.1-Fm-emGFP-hFt by a CDS encoding a tandem of two MS2-coat proteins (MCP). We used a tandem to improve the efficiency of binding to MS2 stem loops [START_REF] Wu | Fluorescence fluctuation spectroscopy enables quantitative imaging of single mRNAs in living cells[END_REF] . RNA-MS2 was expressed from the plasmid pcDNA3.1-4xMS2, which was obtained by inserting the iRFP CDS in the pcDNA3.1 backbone and inserting a tandem of four MS2 stem loops in the 3'UTR.

Transfection

For live experiments, HeLa cells were cultured on 35mm µ-dishes with polymer coverslip bottom (Ibidi). For other experiments, HeLa cells and HEK-293 cells were cultured on 22x22mm glass coverslips (VWR) in 6-well plates (Falcon). 24h after seeding, transient transfection using Lipofectamine 2000 (Invitrogen) was carried out according to the manufacturer's protocol. For live experiments cells were transfected with a 1:1 ratio of pcDNA3.1-Fm-MCP-hFt and pcDNA3.1-Fm-emGF -hFt (800ng total per Ibidi) and 20ng of pcDNA3.1-4xMS2. For other experiments, cells were transfected with a 1:0.7:0.3 ratio of pcDNA3.1-Fm-MCP-hFt, pcDNA3.1-Fm-emGFP-hFt and pcDNA3.1-Fm-hFt (2µg total per well) and 50ng (low RNA), 250ng (high RNA) or indicated amount (Fig. S4) of pcDNA3.1-4xMS2.

Single molecule Fluorescence In Situ Hybridization (smFISH)

Single RNA molecule detection was performed according to the previously described smiFISH method [START_REF] Tsanov | smiFISH and FISH-quant -a flexible single RNA detection approach with super-resolution capability[END_REF] . 24h after transfection, cells were fixed in 4% paraformaldehyde (PFA) for 20 min at RT, and permeabilized with 70% Ethanol in phosphate buffer saline (PBS) at 4°C overnight. For each target RNA (RNA-MS2, β-actin mRNA and NORAD lncRNA), a set of 24 primary probes, constituted of a sequence-specific part and a common FLAP sequence (TTACACTCGGACCTCGTCGACATGCATT), were designed with the Oligostan R script [START_REF] Tsanov | smiFISH and FISH-quant -a flexible single RNA detection approach with super-resolution capability[END_REF] . Genespecific probes and the Cy3 FLAP probe (sequences in the Supplementary table 1) were purchased from Integrated DNA Technologies.

Immunofluorescence

At the end of the smFISH steps, cells were permeabilized with Triton X-100 0.1% in PBS for 10 min at RT, washed twice with PBS at RT, incubated with the primary antibody, washed three times with PBS at RT for 5 min, incubated with the secondary antibody, washed three times with PBS at RT for 5 min and finally mounted with VECTASHIELD mounting medium (Vector Laboratories). Primary antibodies were rabbit antibodies against DDX6 (Bethyl, 1:1000 dilution) and rabbit antibodies against ATXN2L (Bethyl, 1:500 dilution), diluted in PBS 0.1% BSA. The secondary antibody was F(ab')2-Goat anti-Rabbit IgG conjugated with Alexa Fluor 350 dye (Invitrogen, 1:500 dilution).

Imaging

For live experiments, cells were imaged on a Zeiss LSM 710 META laser scanning confocal microscope using an ×63 oil-immersion objective (PlanApochromatic, numerical aperture (NA) 1.4), at 37 °C in a 5% CO2 humidified atmosphere, either starting 8h after transfection (ArtiG formation) or 24h after transfection (ArtiG dissolution). Microscope hardware and image acquisition were controlled with LSM Software Zen 2009. Images were analyzed using ImageJ (NIH).

For smFISH experiments, cells were imaged by epifluorescence microscopy performed on an inverted Zeiss Z1 microscope equipped with a motorized stage using a ×63 (NA 1.32) oil-immersion objective.

Images were processed with open-source software Fiji and Icy [START_REF] Schindelin | Fiji: An open-source platform for biological-image analysis[END_REF][START_REF] De Chaumont | Icy: An open bioimage informatics platform for extended reproducible research[END_REF] .

Western Blotting

24h after transfection, cells were collected using trypsin (Gibco) and resuspended in Laemmli 1X buffer. Proteins were denatured at 100°C for 5 min. Soluble proteins were retrieved after centrifugation at 15000 g at 4°C for 10 minutes and quantified using the Coomassie protein assay (Thermo Scientific). 25 µg of proteins were separated on a NuPAGE 4% -12% gel (Invitrogen, Thermo Fisher Scientific) and transferred to an Optitran BA-S83 nitrocellulose membrane (GE Healthcare Life Science). The membrane was then blocked in PBS with 5% non-fat milk for 30 min, before being incubated with the primary antibody (6x-His Tag Monoclonal Antibody, Invitrogen) overnight at 4°C. After washing the membrane five times for 5 min with PBS, it was incubated for 30 min in PBS with 5% non-fat milk and then for 1h at RT with horseradish peroxidase-conjugated secondary anti-mouse antibody (1:10000 dilution in PBS with 5% non-fat milk, Jackson Immunoresearch Laboratories), and washed again. Proteins were detected with the chemiluminescence detection reagent Perkin Western Lightning plus ECL (Perkin Elmer) and visualized using a radiology film processor (Curix 60, AGFA).

Data analysis

Detection and counting of RNA molecules was performed using version 0.4.0 of Python package Big-FISH (https://github.com/fish-quant/big-fish). A binary mask was created on the emGFP channel to detect the ArtiG emGFP/MCP condensates. To count the number of recruited RNAs in individual cells, all RNA molecules were detected, and their coordinates were compared to the binary mask.

For the analysis of RNA depletion at the vicinity of condensates, the binary mask was repeatedly expanded by 5 pixels and RNA molecules in the mask were counted at each step, which enabled the calculation of both the number and the density of RNA molecules in the last incremented area.

For the quantification of the correlation between condensates size and surface RNA density, condensates sizes were measured using Icy spot detector [START_REF] Olivo-Marin | Extraction of spots in biological images using multiscale products[END_REF] . When close condensates were not discriminated, the detected regions of interest were adjusted by hand. Clusters that were impossible to separate into individual condensates were excluded from the statistics of size. For consistency, the few large clusters included in the statistics of Figure 4 (low RNA condition) were excluded in the statistics of Figure 5, and large clusters in the high RNA condition were similarly excluded. The exterior surface was calculated for each condensate from the surface of the condensate's maximum projection. Then, for each cell, the sum of the surface of all condensates was calculated and used to determine the mean RNA density at the condensate surface (ratio of the total recruited RNAs to the sum of the condensate surface).

Formatting of cell images was performed using the open-source software Fiji 87 . For Figure 2 and S2, the RNA coordinates were first saved from the Python workflow and then opened on Fiji. Graphic were generated using the shiny app PlotsofData 90 (violin plots in Figure 4b, 4d and 5a) and OriginPro (OriginLab). For all violin plots, circles correspond to the mean. Schema (Fig. 1a and5d) were drawn with the open-source vector graphics editor Inkscape. For Figure 5a, Wilcoxon rank-sum tests (nonparametric test to compare two distributions) were performed using the ranksum Matlab function (MathWorks).

Figure 1 :

 1 Figure 1: ArtiG MCP condensates recruit a specific exogenous RNA. a. Schematic of the ArtiG emGFP/MCP formation (Fm = F36M-FKBP, MCP = MS2 coat protein, Ft = Ferritin, ArtiG = ArtiGranule). ArtiG emGFP/MCP form by LLPS driven by the homodimerization of Fm around Ferritin nanocages. MCP protein enable the recruitment of RNA-MS2 molecules to the condensates. b. Time-lapse confocal imaging of the formation of ArtiG emGFP/MCP in Hela cells starting 8 hours after transfection with plasmids Fm-emGFP-Ft and Fm-MCP-Ft (1:1 plasmid ratio). The white arrow highlights a coalescence event. Scale = 10µm. c. Epifluorescence imaging of ArtiG emGFP/MCP (green) and RNA-MS2 (red). Nuclei were stained with DAPI (blue in merge). The zoom in insert 1 shows the recruitment of RNA-MS2 around an ArtiG emGFP/MCP condensate. Insert 2 shows isolated RNA-MS2 molecules. The white arrow indicates where the intensity profile in e. (left panel) was plotted. The grey arrow highlights a transcription focus. On the right panel, greyscale images correspond to separate channels. Scale = 10µm. d. Epifluorescence imaging of ArtiG emGFP and RNA-MS2 (upper panel), and ArtiG emGFP/MCP and β-actin mRNA (lower panel). The white arrows indicate where the intensity profiles in e. (middle and right panels) were plotted. Scale = 10µm. e. Intensity profiles across ArtiG condensates (white arrows in c and d). f. Number of RNA-MS2 molecules recruited at the surface of ArtiG emGFP/MCP as a function of the total number of molecules detected in the cell, with each dot representing one cell (N = 140 from two independent experiments). Grey lines represent 20% and 60% of recruitment.

Figure S1 (

 S1 Figure S1

Figure 2 RNAFigure 2 :

 22 Figure 2

Figure S2 :

 S2 Figure S2

Figure 3 Intensity

 3 Figure 3

Figure 3 :Figure S3 :Figure 5 (

 3S35 Figure 3: Interaction of ArtiG emGFP/MCP with endogenous RNP granules, inhibition and reversibility. a. Epifluorescence imaging of ArtiG emGFP/MCP (green) and RNA-MS2 (red) in HeLa cells, after immunostaining of DDX6 as a PB marker (left panel) or ATXN2L as a SG marker panel). the right panel, SGs induced with arsenite for 30 minutes. = 10µm. b. Experimental design to test the inhibition and reversibility of ArtiG formed in the presence of RNA-MS2, using FK506 in HeLa cells. FK506 was either added right after transfection to prevent or 24h after transfection to dissolve the condensates. c. Percentage transfected cells displaying ArtiG emGFP/MCP condensates in the absence of FK506 (left), when adding FK506 at the time of transfection (middle) or 24h later for 2h (right). d. Epifluorescence imaging of ArtiG emGFP/MCP (green) and RNA-MS2 (red) after condensate dissolution with FK506. Nuclei were stained with DAPI (blue). Scale = 10µm. e. Confocal live imaging of ArtiG emGFP/MCP dissolution. FK506 was added at time zero. Colored arrows indicate where the intensity profiles in f. were plotted. Scale = 10µm. f. EmGFP intensity profile across an ArtiG emGFP/MCP condensate over time (colored arrows in e.).

Figure S4 :

 S4 Figure S4

Acknowledgments

The authors acknowledge all the members of the Biophysical Chemistry group of the École normale supérieure for fruitful discussion. We thank A. Imbert, M.A Plamont, M. Ernoult-Lange, M.N Benassy, M. Bénard, H. Saito, and S. Matsumoto for their help along the project, as well as Adham Safieddine for carefully reading the manuscript. A.C was supported by IPV-SU PhD fellowship. M.G.J.N was supported by FRM (ING20150532742). This work was supported by the CNRS, Ecole Normale Supérieure, and ARC (20181208003) to Z.G., FRM (MND202003011470) and iBio (SU) to Z.G and D.W, and ANR (ANR-19-CE12-0024-01) to D.W (ANR-19-CE12-0024-01).

Author Contributions

A.C, D.W and Z.G conceived the project and analyzed results. A.C carried out and analyzed most experiments. M.G.J.N contributed to the design of protein scaffolds and performed initial experiments. S.K and M.K contributed to the design of synthetic RNAs. A.C, D.W and Z.G wrote the manuscript and all authors were involved in revising it critically for important intellectual content.

Declaration of Interests

The authors declare that they have no competing interests.

Supporting Information

4 supplementary figures and 1 supplementary table.

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.


M Houssat

C Villeneuve-Faure

N Lahoud Dignat

M L Locatelli

J P Cambronne

Temperature influence on PI/Si3N4 nanocomposite dielectric properties: a multiscale approach

Keywords: polymer nanocomposite, interphase, multi-scale characterization, dielectric permittivity, breakdown strength, EFM, PF-QNM

In the understanding of the nanocomposites (NC) properties improvement, a major role was attributed to the interphase area between the nanoparticle and the matrix. However, the interphase properties impact on macroscale dielectric properties remains poorly understood, particularly at high temperatures. In this study, a multiscale characterization of polyimide/silicon nitride (PI/Si3N4) nanocomposite dielectric properties is performed at various temperatures. Neat PI and PI/Si3N4 NC with untreated and silane-treated nanoparticles are characterized in terms of macro/nanoscale relative dielectric permittivity (εr), breakdown strength and interphase thickness. Different behaviors are observed depending on the temperature range. At low temperatures (T<150 °C), the NC macroscale (εr) and breakdown strength are lower than the PI ones. Considering that the interphase permittivity is increasing with temperature, mixing law models manage to reproduce the macroscale (εr) value for untreated nanoparticles. At medium temperatures (150°C -200°C), NC and PI have very similar properties and the interphase (εr) remains quite constant. At high temperatures (T>200 °C) an improvement of the NC properties is observed and attributed to the reduction of ion charge carriers mobility due to the presence of the interphase. For untreated NC, an extrapolation of the mixing law indicates that the interphase (εr) could be higher than the matrix one, which could explain the breakdown strength improvement.

Introduction

Polymer dielectric materials are commonly used in advanced electronic devices and electric power systems insulation. However, even if polymer dielectrics possess excellent mechanical properties, low leakage current and high electric breakdown strength, their dielectric properties (space charge accumulation, electric breakdown field, …) at high temperature need to be improved [START_REF] Ma | A review on high temperature resistant polyimide films: Heterocyclicstructures and nanocomposites[END_REF][START_REF] Zhou | Advanced polymer dielectrics for high temperature capacitive energy storage[END_REF]. Particularly, for polyimide (PI), which is broadly used in the fields of electronic packaging and automotive applications, a degradation of its electrical resistivity [START_REF] Sessler | Electrical conduction in polyimide films[END_REF], dielectric properties [START_REF] Diaham | Conductivity spectroscopy in aromatic polyimide from 200 to 400[END_REF] and failure field [START_REF] Miyairi | Frequency dependent dielectric breakdown of thin polyimide films prepared by vapor deposition polymerization[END_REF] is observed at high temperature. According to the litterature, polymer-nanocomposites (p-NC) appear as the best candidates to improve the polymer dielectric properties at both ambiant [START_REF] Adnan | In situ synthesis of hybrid inorganic-polymer nanocomposites[END_REF] and high temperature [START_REF] Ma | A review on high temperature resistant polyimide films: Heterocyclicstructures and nanocomposites[END_REF][START_REF] Hassan | Current status of polymer nanocomposite dielectrics for high-temperature applications[END_REF]. For example, PI-based nanocomposites with a small amount of nanofillers exhibit improved mechanical, thermal [START_REF] Nikolaeva | Polyimide-Based Nanocomposites with Binary CeO2/Nanocarbon Fillers: Conjointly Enhanced Thermal and Mechanical Properties[END_REF] and dielectric properties at high temperature, as an increase of relative dielectric permittivity [START_REF] Chen | Dielectric property and space charge behavior of polyimide/silicon nitride nanocomposite films[END_REF], a limitation of space charge building [START_REF] Chen | Dielectric property and space charge behavior of polyimide/silicon nitride nanocomposite films[END_REF][START_REF] Yang | Thermal Stabilization Effect" of Al2O3 nano-dopants improves the high-temperature dielectric performance of polyimide[END_REF], an improvement of breakdown strength [START_REF] Chen | Dielectric property and space charge behavior of polyimide/silicon nitride nanocomposite films[END_REF][START_REF] Tanaka | Polymer nanocomposites as dielectric and electrical insulation -perspectives for processing technologies, materials characterization and future applications[END_REF] and/or energy density [START_REF] Li | Tuning nanofillers in in situ prepared polyimide nanocomposites for high-temperature capacitive energy storage[END_REF][START_REF] Hu | Large energy density at high-temperature and excellent thermal stability in polyimide nanocomposite contained with small loading of BaTiO3 nanofibers[END_REF] compared to the neat PI.

To explain the nanofiller influence on nanodielectric properties, T.J. Lewis has proposed in 1994 the hypothesis that a transition area named the "interphase" is created between the nanofiller and the polymeric matrix [START_REF] Lewis | Nanometric Dielectrics[END_REF]. Since then, different models have been proposed to describe the interphase morphology and structure [START_REF] Lewis | Nanometric Dielectrics[END_REF][START_REF] Tanaka | Proposal a multi-core model for polymer nanocomposite dielectrics[END_REF][START_REF] Raetzke | Role of interphase on the resistance to high-voltage arcing, on tracking and erosion of silicone/SiO2 nanocomposites[END_REF][START_REF] Kubyshkina | Impact of the interfacial structure on the charge dynamics in nanocomposite dielectric[END_REF]. In addition to these theoretical approaches, some authors have proposed to extract the interphase properties from macroscale experimental characterization methods [START_REF] Bashir | Use of dynamic mechnical analysis (DMA) for characterizing interfacial interactions in filled polymers[END_REF][START_REF] Maity | On the size and dielectric properties of the interphase in epoxy-alumina nanocomposites[END_REF][START_REF] Daily | Modeling the interphase of a polymer-based nanodielectric[END_REF][START_REF] Wang | A Transition of Interface Characteristics in LDPE/Al2O3 Nanocomposites by Permittivity Simulation[END_REF]. However, the interphase properties and its impact on p-NC ones remain poorly understood. To improve this understanding, techniques derived from the Atomic Force Microscopy (AFM) were used:

the Peak Force Quantitative Nanomechanical (PF-QNM) mode for the interphase mechanical properties and dimension determination [START_REF] Houssat | AFM Measurements of Polyimide/Silicon Nitride Nanocomposite Interphase[END_REF][START_REF] Moussa | Novel three-dimensional interphase characterization of polymer nanocomposites using nanoscalled topography[END_REF], the Electrostatic Force Microscopy (EFM) mode for the dielectric permittivity [START_REF] Khoury | Characterization of Dielectric Nanocomposites with Electrostatic Force Microscopy[END_REF][START_REF] Peng | Local Dielectric Property Detection of the Interface between Nanoparticle and Polymer in Nanocomposite Dielectrics[END_REF] or space charge probing [START_REF] Han | Study on micro interfacial charge motion of polythylene nanocomposite based on electrostatic force microscopy[END_REF] and the Kelvin Probe Force Microscopy (KPFM) for space charge measurement [START_REF] Peng | Mapping the space charge at nanoscale in dielectric polymer nanocomposites[END_REF]. All of these existing studies provide only an interphase characterization at room temperature and a partial description of dielectric properties as some assumptions are requested for their entire determination.

In this study, we propose to investigate the high temperature dielectric properties (relative dielectric permittivity and breakdown strength) of PI based nanocomposite (NC) at macro and nano scales. More particularly, our interest is focused on the relative dielectric permitivity temperature dependence of each of the PI and the interphase. To reach this goal, PI/silicon nitride (Si3N4) NC is investigated as it has demonstrated improved properties (e.g. dielectric breakdown) at high temperature [START_REF] Chen | Dielectric property and space charge behavior of polyimide/silicon nitride nanocomposite films[END_REF][START_REF] Diaham | Huge improvements of electrical conduction and dielectric breakdown in polyimide/BN nanocomposites[END_REF]. Moreover, as the interphase dimension and/or properties depend on the nanoparticles (NP)

surface treatment [START_REF] Luo | Interface design for high energy density polymer nanocomposites[END_REF][START_REF] Andritsch | Proposal of the polymer chain alignment model[END_REF][START_REF] Yang | The role of interfacial H-bonding on the electrical properties of UVcured resin filled with hydroxylated Al2O3 nanoparticles[END_REF], samples with functionalized Si3N4 were prepared and compared to samples with untreated NP.

Materials and methods

Materials processing

In this paper, a PI-based NC is investigated using a 1wt.% addition of Si3N4 spherical amorphous NP provided by SkySpring Nanomaterials Inc. (Houston, USA). The PI host matrix is processed using a mix of commercial biphenyltetracarboxilic dianhydride and p-phenylene diamine precursor monomers (BPDA-PDA) supplied as a polyamic acid (PAA) precursor solution in N-methyl-2-pyrrolidone solvent. Raw materials properties are reported in table 1. The NP surface functionalization is obtained by using (3-Aminopropyl) triethoxysilane (APTES, 98%) purchased from Sigma-Aldrich. The NC fabrication process is composed of four steps (detailed in [START_REF] Houssat | AFM Measurements of Polyimide/Silicon Nitride Nanocomposite Interphase[END_REF]). (i) 5 g of polyamic acid (PAA) are mixed, during 15 min, with 0.05 g of Si3N4-NP (treated or not with silane coupling agent) to obtain an homogeneous 1 wt.% aqueous solution. (ii) One hour of ultra-sonication process (70 °C, 300 W) and 25 min centrifugal decantation (14 400 rpm) are used to reduce the size of agglomerates formed during the mechanical dispersion. After that, only the supernatant mixture is used (1 ml). (iii) The NC solution is spin-coated (30 s at 3000 rpm), on 2-inch highly-doped Si wafers (N-type, resistivity 0.002-0.008 Ω.cm, thickness 275 ± 25 µm) to obtain a thin film with controlled thickness. (iv)

The obtained PAA/ Si3N4 NC thin films are annealled in air at 100 °C for 1 min and at 175 °C for 3 min. Finally, in order to obtain the PI imidization from PAA, the thin films are thermally cured in a SPX Blue-M convection oven in nitrogen atmosphere. Pure PI films have been elaborated as well (using the same two last process steps), for comparison. and treated (T-NC) NP respectively and a pure PI film thickness of 5.8 µm.

Density (g.cm

For macroscale characterization (dielectric spectroscopy and breakdown strength), capacitive Metal-Insulator-Semiconductor (MIS) structures are needed. To produce such structures a 150 nm-thick gold layer is deposited by sputtering over the entire top surface of the film samples. A wet etching step through a resin mask, made by photolithography, has permitted to define the top circular electrode with a diameter of 5 mm and 0.6 mm for dielectric spectroscopy and breakdown measurements respectively. Moreover, as PI is sensitive to the water absorption, a heating treatment (150 °C during 48 h) is applied to PI and NC films before macroscopic measurements.

Multiscale characterization

The dielectric properties are measured by the broadband dielectric spectroscopy (DS) using a Novocontrol Alpha-A spectrometer. Measurements are performed under a nitrogen gas flow and at a temperature range from -150 °C to 350 °C (step of 10 °C) and a frequency range from 0.1 Hz to 100 kHz. The data are obtained in the form of the dielectric complex permittivity:

𝜀 * = 𝜀 " -𝑖 𝜀" (1)
where ε' and ε" are respectively the dielectric permittivity and the dielectric loss index, and i 2 = -1.

The breakdown field measurements are carried out using a Signatone S-1160 probe station equipped with micrometric positioners and a sample holder regulated at 25, 100, 200 and 300 °C thanks to the S-1600R heating system. A DC voltage ramp of 150 V/s is supplied using a FI 9035HT source. When the breakdown occurs, the used voltage source switches into a current source applying a short-circuit limited to 1 mA. Dielectric breakdown field has been calculated as:

F #$ = 𝑉 #$ d ( 2
)
where Vbr is the measured breakdown voltage and d the insulating film thickness.

A Weibull statistical analysis on a population of 10 samples is performed to extract the scale parameter of the breakdown for each regulated temperature.

AFM measurements are performed using a Bruker Multimode 8 apparatus. PF-QNM mode is used to map the surface topography and the mechanical properties of NC films using a TAP525 tip. A contact force of 600 nN is applied to obtain a 2 nm-deformation on the bare PI. According to the stiff contact and the low adhesion observed on PI, the Young modulus is calculated using the Derjaguin-Muller-Toropov (DMT) model [START_REF] Derjaguin | Effect of contact deformations on the adhesion of particles[END_REF][START_REF] Greenwood | An Adhesion Map for the Contact of Elastic Spheres[END_REF]. To insure reliable and quantitative results a three steps calibration process is applied [START_REF] Houssat | Effect of particles surface functionalization on interphase properties of PI/Si3N4 nanocomposite[END_REF]. (i) Force Distance Curves are used to determine static and dynamic deflection sensitivity on hard sapphire sample. (ii) Scanning Electronic Microscopy (SEM) is used to determine tip geometrical parameters in order to calculate the tip spring constant k using Sader method. (iii) The effective tip radius is determined using a polystyrene (2.7 GPa modulus) reference film whose mechanical properties are close to PI ones. The measurements are done using 384x384 pixel, which corresponds to a pixel size of 5.2nm for a 2µmx2µm scanned area.

EFM mode is used to probe NC films dielectric permittivity at the nanoscale [START_REF] Khoury | Characterization of Dielectric Nanocomposites with Electrostatic Force Microscopy[END_REF][START_REF] Riedel | Nanodielectric mapping of a model plystyrene-poly(vinyl acetate) blend by electrostatic force microscopy[END_REF]. A PtIR-coated silicon tip with a resonance frequency 𝑓 % of 66.1 kHz, a spring constant k of 2.74N/m and a radius of 26nm is used. The tip frequency shift Δf0(V0) is probed for DC voltage V0 equal to 0 V and 10 V with a 50 nm-lift and the resulting frequency shift parameter aΔf is determined:

𝑎 ∆' = ∆𝑓 % (10𝑉) -∆𝑓 % (0𝑉) (10)² (3)
where Δf0(Vi) is the frequency shift measured with a DC voltage Vi applied on the tip.

To extract the relative dielectric permittivity from this measurement a 2D-axisymetric Finite Element Model on COMSOL [START_REF] Houssat | Effect of particles surface functionalization on interphase properties of PI/Si3N4 nanocomposite[END_REF] is developped, taking into account the NP (radius 10 nm), the PI matrix (NC films thickness), the interphase (relative dielctric permittivity and thickness to be determined) and the surrounding atmosphere (air box whose dimensions are fixed to avoid edge effect). As for the experiment, the DC voltage is applied on the tip and the NC/PI backside is grounded. The frequency shift parameter aΔf is computed as follows:

𝑎 ∆' = 𝑓 % 4𝑘 𝑑²𝐶 𝑑𝑧² ( 4
)
where f0 is the resonance frequency, C is the capacitance between the AFM tip and the sample, z is the vertical distance and k is the stiffness of the cantilever.

The capacitance second derivative d²C/dz² is deduced from the electrostatic force Fe gradient, as:

𝑑 ( 𝐶 𝑑𝑧 ( = 2 𝑑𝐹 ) 𝑑𝑧 ( 5
)
Results emphasize that the computed frequency shift parameter is negative and increases when the material permittivity decreases.

Results and discussion

For the PI sample (Figure 1a), an increase in the relative dielectric permittivity is observed at temperatures higher than 100 °C for different frequencies. This relaxation phenomenon is usually attributed to the electrodes polarization due to space charge accumulation [START_REF] Diaham | BPDA-PDA Polyimide: Synthesis, Characterizations, Aging and Semiconductor Device Passivation[END_REF]. Indeed, when thermally activated, positive (or negative) charge carriers can drift to the negative (or positive) polarized electrode in order to build up a space charge at the sample-electrode interface. Usually, the electrical conduction in PI films is influenced by a macroscopic migration of H+ ions (coming from unreacted PAA [START_REF] Ito | Effect of Degree of Imidization in Polyimide Thin Films Prepared by Vapor Deposition Polymerization on the Electrical Conduction[END_REF]) to the interfaces. Figures 1b and1c show the same relaxation phenomenon (relative dielectric permittivity increasing) at high temperature for PI/Si3N4 NC with untreated and treated NP respectively, whatever the frequency is.

Figure 1d emphasizes that, at low frequency, the NC relative dielectric permittivity is lower than the PI one. Moreover, this decrease is more significant for the NC with silane-treated NP. At high temperature, where ion charge carriers are highly mobile, the presence of NP seems to disturb the ions mobility. Indeed, the interphase region around nanoparticles could be a region where H+ ions are blocked and could less reach the sample-electrode interface.

Moreover, the silane coupling agent should act as a more efficient grafting link between the PI macromolecular chains and the Si3N4 improving the interphase volume where the ion charge mobility is reduced. Breakdown tests are performed on neat PI and PI/Si3N4 NC with untreated and silane-treated NP. Figure 2a shows breakdown results under 25 °C for all samples. A Weibull statistical analysis is performed giving a breakdown value at each regulated temperature for all samples and plotted in Figure 2b. At low temperature (<200 °C), PI presents a slight higher breakdown strength than both NC. However, at high temperature (>200 °C), PI presents a much lower breakdown strength compared to NC one. In comparison with neat PI, which becomes a semi-insulating material above 200 °C, it seems that PI/Si3N4 NC with treated and untreated particles are able to keep an extended insulating behavior up to 300 °C (as similarly also observed with PI/BN NC [START_REF] Diaham | Huge improvements of electrical conduction and dielectric breakdown in polyimide/BN nanocomposites[END_REF]). This phenomenon could be related to the "Thermal Stabilization Effect" introduce by Yang et al. [START_REF] Yang | The role of interfacial H-bonding on the electrical properties of UVcured resin filled with hydroxylated Al2O3 nanoparticles[END_REF] for PI/Al2O3 nanocomposite. According to this effect, the interphase region within NC contains new shallow traps compared to the neat matrix, which modifies the charge trapping and transport mainly at high temperature. Hence, the charge injection and accumulation are restrained, the local electric field is alleviated and the breakdown field is increased. From a macroscale point of view the NP (treated or not) presence decreases the relative dielectric permittivity (Figure 1c) and improves the breakdown strength (Figure 2b) at high temperature. Moreover, this effect apprears to be related to the interphase dielectric properties evolution with temperature. So, in order to identify this behaviour, the interphase properties at high temperature need to be characterized at the local scale. To reach this goal PF-QNM and EFM are used to determine the interphase dimension and relative dielectric permittivity.

The NC surface topography comparison between untreated (Figure 3a) and treated (Figure 3b) NP emphasizes that protruding isolated NP could be identified. For untreated NP, Figure 3c compares surface topography and Young modulus profiles over an isolated NP. On the topography profile, a 15 nm-height bump reveals the presence of the NP.

On Young modulus profile, two areas are identified. The first one (white area), located above and laterally far from the NP, has a Young modulus of 20 GPa and is attributed to the matrix. The second one (grey area), located around the NP, exhibits an apparent Young modulus higher than the matrix one. This area is attributed to the interphase and its width Wi is determined as the lateral dimension of this area. The interphase width is determined for at least ten NP and a mean value of 30 nm ± 2 nm is obtained. For treated NP, quite the same results are obtained. A similar bump is chosen (i.e. heigth close to 15 nm) for comparision as depicted on Figure 3d. The same Young modulus behaviour is observed.

As previously, the interphase width is determined for at least ten NP and a mean value of 42 nm ± 3 nm is obtained.

The measured interphase width is higher for treated NP than untreated ones. Indeed, the coupling agent used for the NP surface treatment increases the interaction strength between the NP and the matrix, which leads to the interphase dimension increase [START_REF] Luo | Interface design for high energy density polymer nanocomposites[END_REF][START_REF] Andritsch | Proposal of the polymer chain alignment model[END_REF][START_REF] Yang | The role of interfacial H-bonding on the electrical properties of UVcured resin filled with hydroxylated Al2O3 nanoparticles[END_REF]. 4d) and frequency shift parameter aΔf (Figures 4b and4e) maps acquired for both treated and untreated PI/Si3N4 NC in EFM mode at 25 °C. Arrows are used to identify isolated NP.

For both treated and untreated NP, the presence of an embedded NP induces a higher frequency shift parameter aΔf compared to the matrix one. This implies that the apparent relative dielectric permittivity over NP is lower than the matrix one. However, knowing that the NP dielectric permittivity is higher than PI one (Table 1), the lower permittivity value is attributed to the interphase. At room temperature, an interphase relative dielectric permittivity lower than the matrix was already observed for other NC materials [START_REF] Peng | Local Dielectric Property Detection of the Interface between Nanoparticle and Polymer in Nanocomposite Dielectrics[END_REF].

Concerning NC with untreated NP, the temperature dependence of the frequency shift profile over an isolated NP is depicted on Figure 4c. The same profile is observed for 25 °C and 50 °C, which shows that there is no real modification of the relative dielectric permittivity of both the interphase and the matrix at this temperature. For temperature higher than 50 °C the frequency shift parameter baseline, which corresponds to the matrix, decreases with temperature. This implies that the matrix relative dielectric permittivity increases with temperature. Moreover, the bump amplitude on the profile, attributed to the combined effect of the interphase and NP, tends to disappear when the temperaure increases. At 140 °C, the NP/interphase influence is no longer observable. The same behaviour is observed for NC with treated NP (Figure 4f). However, at 140 °C the NP/interphase influence is yet a little bit visible. Indeed, the hypothesis of a retarding effect of the silane treatment compared to untreated NP is addressed. To summarize, at room temperature , the interphase presents a higher Young modulus and a lower relative dielectric permittivity than the PI matrix, which indicates that polymer chains present a better organization at the interphase [START_REF] Fuse | Possible Mechanism of Superior Partial-discharge Resistance of Polyamide Nanocomposites[END_REF] and/or a restricted movement due to the nanoparticles presence [START_REF] Nelson | The Impact of Nanocomposite Formulations on Electrical Voltage Endurance[END_REF].

To go further, the matrix (𝜀 * ) and the interphase (𝜀 + ) relative dielectric permittivity values are extracted from frequency shift parameter aΔf profiles (Figure 4b and Figure 4e) using the 2D-axisymetric FEM model combined with equations ( 4) - [START_REF] Miyairi | Frequency dependent dielectric breakdown of thin polyimide films prepared by vapor deposition polymerization[END_REF]. Concerning the PI matrix, results obtained from local measurements (EFM) are plotted on Figure 5a and compared to the PI relative dielectric permittivity evolution obtained from macroscopic DS measurements. It could be noticed that the nanoscale matrix permittivity (𝜀 * ) behaviours are similar for both treated and untreated NC and are in good agreement with the PI macroscopic permittivity evolution.

For the interphase permittivity (𝜀 + ) determination, the interphase width (Wi) is fixed at 30 nm and 40 nm for untreated and treated NP respectively, according to PF-QNM results. As a first approximation, it is concidered that Wi is not modified with the temperature, as the temperature range remains lower than the glass transition one (Tg > 370 °C) [START_REF] Diaham | High Temperature Dielectric Behavior of Al/Polyimide/Al Capacitor Structures[END_REF].

Using these width values, the temperature dependence of the interphase permittivity is reported on Figure 5a. For both NC (𝜀 + ) increases with temperature. For the untreated NP, (𝜀 + ) reaches the same value as PI at 150 °C, wheareas it remains a little bit lower for treated NP.

Around 150°C, the interphase, the matrix and the NP have quite the same relative dielectric permittivity, which could explain the fact that all materials have quite the same breakdown strength at this temperature (Figure 2b).

Finally, in order to compare nano-and macro-scale approaches, the NC relative dielectric permittivity 𝜀 $ is computed using those of the matrix (𝜀 * ), the NP (𝜀 ,-) and the interphase (𝜀 + ) with two different models:

• Simple mixing law [START_REF] Praeger | A simple theoretical model for the bulk properties of nanocomposite materials[END_REF] 𝜀 $ = 𝑓 * 𝜀 * + 𝑓 ,-𝜀 ,-+ 𝑓 + 𝜀 +

where fm, fNP and fi are the matrix, the NP and the interphase volume fractions respectively.

• Interphase Power Law (IPL) model [START_REF] Todd | Complex permittivity of composite systems: A comprehensive interphase approach[END_REF] 𝜀 $ . = 𝑓 * 𝜀 * . + 𝑓 ,-𝜀 ,- . + 𝑓 + 𝜀 + .

where 𝛽 = 1/3 for spherical NP, fm, fNP and fi are the matrix, the NP and the interphase volume fractions respectively.

Table 2 summarizes the components volume fraction used for each untreated and treated NP nanocomposite. Figure 5b compares the temperature dependence of the NC relative dielectric permittivity computed by both laws and measured by DS. Concerning NC with untreated NP, a good agreement is observed between DS (UT DS) measurements and both models with a slight better fit for the IPL model. By using the PI permittivity determined by DS and by extrapolating the IPL to high temperature, we observe that the interphase permittivity remains quite constant between 150 °C and 200 °C, and becomes higher than the matrix one at T > 200 °C. This higher interphase permittivity could explain the higher breakdown strength observed at high temperature (> 200 °C). Concerning NC with treated NP, neither the simple mixing law nor the IPL model manage to fit with DS measurements. Indeed, different approaches could explain this result: (i) the interphase thickness is not constant with temperature when NP are treated with the coupling agent, (ii) a more complex model is needed for the interphase description (two layers model) and/or (iii) the silane coupling agent has an influence on the matrix properties.

Conclusion

In this paper, a multiscale investigation of NC dielectric properties is proposed. At macroscale, results emphasize that NC relative dielectric permittivity remains lower than PI one whatever the temperature is. However, the NC breakdown strength is improved for NC at high temperature. This improvement could be related to the NP "Thermal Stabilization

Effect" which is related to the modification of charge carriers transport and accumulation at high temperature due to the presence of shallow traps in the interphase area. At nanoscale, the interphase width and relative dielectric permittivity are determined using techniques derived from AFM (PF-QNM and EFM). These results emphasize that both the matrix and the interphase permittivities increase with temperature. Between 25°C and 150°C, this increase is quite the same for treated and untreated NP with a retarding effect for treated NP. The use of both EFM (nano) and DS (macro) results emphasizes that the IPL model for the NC permittivity calculation manages to reproduce macroscale results for untreated NP but fails for treated NP NC.

This study results show the strong impact of the interphase dielectric properties even at high temperature. The next step is to investigate the interphase conduction mechanisms with temperature in order to propose a more accurate description of the interphase dielectric properties.

Citation:

  Houssat M, Villeneuve-Faure C, Lahoud Dignat N, Locatelli ML and Cambronne JP Temperature influence on PI/Si3N4 nanocomposite dielectric properties: a multiscale approach. Polymers 2021, 13, x. https://doi.org/10.3390/xxxxx Academic Editor: Firstname Last-Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses /by/4.0/).

Figure 1 .

 1 Figure 1. Temperature dependence of relative dielectric permittivity for (a) neat PI, NC with (b) untreated and (c) treated NP. (d) Evolution of the relative dielectric permittivity at 10 Hz as function of temperature.

Figure 2 .

 2 Figure 2. (a) Weibull statistics for breakdown results of neat PI, PI/Si3N4 and PI/Si3N4-silane samples at 25 °C (dash lines correspond to 90% confidence bounds). (b) Temperature dependence of breakdown strength for neat PI, PI/Si3N4 and PI/Si3N4-silane samples

Figure 3 .

 3 Figure 3. PF-QNM topography map for nanocomposite with (a) untreated and (b) treated NP. Comparison of topography and young modulus profiles over protruding NP (pointed by straight line on topography map) for (c) untreated and (d) treated NP.

Figure 4

 4 Figure 4 compares surface topography (Figures4a and 4d) and frequency shift parameter aΔf (Figures4b and 4e) maps

Figure 4 .

 4 Figure 4. (a) Topography, (b) frequency shift parameter aΔf at 25 °C and (c) frequency shift parameter aΔf profiles at various temperatures for untreated Si3N4 nanoparticles. (d) Topography, (e) frequency shift parameter aΔf at 25 °C and (f) frequency shift parameter aΔf profiles at various temperatures for treated Si3N4 nanoparticles.

Figure 5 .

 5 Figure 5. (a) Evolution of the relative dielectric permittivity of the matrix (εm) and interphase (εi) as function of temperature. Comparison is done with pure PI permittivity obtained by DS (0.1 Hz). (b) Comparison of the evolution of the experimental (DS at 0.1 Hz on untreated (UT) and treated (T) NC) and computed apparent relative dielectric permittivity as function of temperature.

Table 1 .

 1 Materials properties (density, NP radius, relative dielectric permittivity εr)

-3 ) NP Radius (nm) εr

	KLA-Tencor mechanical profilometer emphasizes a NC films thickness of 2.3 µm and 3.4 µm for untreated (UT-NC)
	PI	1.48	/	3
	Si3N4	2.67	10-20	7.5

Table 2 .

 2 Matrix (fm), NP (fNP) and interphase (fi) volume fractions for untreated and treated nanocomposites.

		fm	fNP	fi
	Untreated (UT)	0.644	0.005	0.351
	Treated (T)	0.306	0.005	0.689

Author Contributions: M. Houssat (data curation, formal analysis, writing-review and editing) C. Villeneuve-Faure (data curation, formal analysis, conceptualization, writing-original draft preparation, writing-review and editing) N. Lahoud Dignat (formal analysis, conceptualization, writing-review and editing, project administration) ML. Locatelli (data curation, formal analysis) JP. Cambronne (writing-review and editing, project administration)

Conflicts of Interest: "The authors declare no conflict of interest."