Fanny Coumes
email: fanny.coumes@sorbonne-universite.fr

Mauricio Balarezo

Jutta Rieger

François Stoffelbach
email: francois.stoffelbach@sorbonne-universite.fr

Biobased Amphiphilic Block Copolymers by RAFT-mediated PISA in Green Solvent

Keywords: PISA, RAFT dispersion polymerization, biobased monomer, amphiphilic copolymer

Biobased amphiphilic diblock copolymers are prepared thanks to the combination of reversible addition-fragmentation transfer (RAFT) polymerization and polymerizationinduced self-assembly (PISA) in an ecofriendly solvent mixture. Firstly, the formation of a poly(acrylic acid) macroRAFT agent (PAA-TTC) is performed in water at 70 °C. Then, in a series of experiments, the PAA-TTC macroRAFT agent is used directly, without purification, as both chain transfer agent and stabilizing agent in the RAFT-PISA of menthyl acrylate (MnA) in dispersion in an ethanol/water mixture. The polymerizations of MnA are fast with high final conversions and well-controlled amphiphilic diblock copolymers are synthesized.

Stable, submicrometric spherical particles composed of the diblock copolymers are formed.

The influence of the monomer concentration and the length of the solvophobic block on the diameter of the self-assemblies is studied by means of dynamic light scattering and cryotransmission electron-microscopy.

Introduction

Thanks to the combination of reversible-deactivation radical polymerization (RDRP) techniques [START_REF] Shanmugam | Reversible Deactivation Radical Polymerization: Mechanisms and Synthetic Methodologies ACS Symposium Series[END_REF] and polymerization-induced self-assembly (PISA) [START_REF] Charleux | [END_REF][3][4][5] , it is nowadays possible to produce amphiphilic block copolymer assemblies in a straightforward way, in a large variety of solvents such as alcohols or water. This approach can be considered as a green process, as it proceeds with a minimum of compounds using environmentally safe solvents, producing the targeted copolymers in high solids contents (typically up to 40 wt%) and with high yields.

However, until now all amphiphilic block copolymers synthesized by such processes were produced from petroleum-based monomers. There is thus a need to perform investigations in order to use biobased monomers from renewable resources as an alternative solution. Hitherto, only very few examples of RDRP of biobased monomers in heterogeneous conditions have been reported. For example, Caillol et al. have managed to synthesize biobased latexes by free radical emulsion polymerization stabilized by surfactants and/or RDRP using acrylates and methacrylates derived from biobased molecules such as vanillin [6] , eugenol [7][8][9] and/or cardanol [10][11][12]. Asua et al. have also recently reported the synthesis of biobased triblock copolymers using reversible addition-fragmentation chain transfer (RAFT) [13][14][15] (co)polymerization either in homogeneous [16] or heterogeneous conditions, using conventional surfactants as stabilizers. [17,18] Nevertheless, all these synthetic approaches require the addition of free molecular surfactants to stabilize the particles produced in a heterogeneous polymerization process. Looking at hydrophilic biobased monomers, it is nowadays well known that acrylic acid can be synthesized from renewable sources. Indeed, lactic acid, which can be produced from the biomass by chemical reaction or fermentation methods [19] , can provide acrylic acid (AA) [20] by dehydration. This synthesis pathway is nowadays considered as an alternate process to the petrochemical process (obtained by oxidation of propene).

Finally, several acrylic monomers can be prepared from AA by esterification of bio-sourced alcohols. Herein, with the objective of producing diblock copolymers derived from the biomass instead of fossil resources by PISA, we decided to use the RAFT polymerization technique [13][14][15] due to its tolerance to a broad range of reaction conditions and monomer families. In that respect, a hydrophilic macromolecular chain transfer agent (macroRAFT) based on poly(acrylic acid) was chain extended with a second, less soluble monomer derived from menthol (naturally present in peppermint, for instance). In an ecofriendly solvent (here a mixture of ethanol and water was chosen) the polymerization proceeds under dispersion polymerization conditions to form an amphiphilic diblock copolymer that self-assembles in the course of the polymerization (Scheme 1). While the synthesis of poly(L-menthyl acrylate) and double hydrophobic poly(L-menthyl acrylate)-block-poly(methyl acrylate) diblock copolymers has already been reported using single electron transfer living radical polymerization (SET-LRP) in a series of alcohols [21] and atom transfer radical polymerization (ATRP) [22] respectively, to the best of our knowledge there is no example reporting the synthesis of amphiphilic menthyl acrylate based block copolymer, nor any example of entirely biobased amphiphilic copolymers in general obtained by a PISA process. As mentioned above, RAFT-mediated PISA in heterogeneous polymerization conditions was exclusively achieved in the presence of a hydrophobic petroleum-based monomer. In this communication, we describe for the first time a RAFT-mediated PISA using only bio-sourced monomers.

Results and Discussion

Menthyl acrylate (MnA) was synthesized by esterification of D,L-menthol with acryloyl chloride in the presence of triethylamine following a reported procedure. [23] The monomer was obtained as a transparent liquid and the 1 H NMR spectrum of MnA recorded in CDCl 3 displays the characteristic signals of the monomer's vinyl and cyclohexyl groups (Figure S1).

Before using the monomer in the PISA process proceeding in heterogeneous conditions, we firstly investigated its ability to be radically homopolymerized in a controlled fashion by RAFT solution polymerization using a carboxylic acid functional trithiocarbonate-type RAFT agent (HOOC-TTC) [24] (Scheme 1) well-known to control the polymerization of acrylates and acrylamides. After 6 hours of reaction in anisole at 70 °C, in the presence of 2,2'-azobis(2methylproprionitrile) (AIBN) as an initiator, the polymer was recovered by precipitation and analyzed by size exclusion chromatography (SEC). As shown in Figure S2, the RAFT homopolymerization was controlled as the polymer displayed a dispersity (Đ = M w /M n ) below 1.25 and a number-average molar mass determined by [START_REF] Shanmugam | Reversible Deactivation Radical Polymerization: Mechanisms and Synthetic Methodologies ACS Symposium Series[END_REF] H NMR, M n,NMR (41.0 kg.mol -1 ) in good agreement with the theoretical value (41.8 kg.mol -1 ) indicating that the number of chains was governed by the RAFT agent concentration. The efficiency of the transfer reaction was also confirmed by using SEC equipped with an in-line UV detector. Indeed, SEC chromatogram obtained with the UV detector at 309 nm shows the presence of the trithiocarbonate functionality which strongly absorbs at this wavelength. [25] The UV signal overlays with the RI signal, which indicates that the whole chains distribution presents the trithiocarbonate moiety. Discrepancy between SEC molar masses and theoretical one could be observed due to the use of a conventional PS calibration. In order to get more accurate values, we decided to determine the absolute M n of this homopolymer (PMnA) by using a SEC equipped with an in-line static light scattering (SLS) detector. Using the in-line RI detector of the SEC apparatus, as described previously, [26] a refractive index increment (dn/dC) of 0.085 mL.g -1 was determined in THF, providing a M n,LS of 37.9 kg.mol -1 in better correlation with theoretical value (41.8 kg.mol -1 ). Thermal analysis by differential scanning calorimetry and thermogravimetry were performed on the homopolymer showing respectively a glass transition temperature of 56 °C and a thermal degradation at about 300 °C (Figure S3), in accordance with data found in the literature. [21,22] Then, we evaluated the possibility to synthesize amphiphilic diblock copolymers possessing a hydrophilic block based on poly(acrylic acid) and a poly(menthyl acrylate) hydrophobic block using the PISA technique under dispersion polymerization conditions (in conditions where menthyl acrylate is soluble, and poly(menthyl acrylate) is not). To this end, in a first step, we performed a kinetic study on the RAFT polymerization of acrylic acid in water at 70 °C, initiated by 4,4'-azobis(4cyanovaleric acid) (ACPA), in presence of HOOC-TTC as chain transfer agent in order to reach high conversions while maintaining a good polymerization control. As depicted in Figure S4, the polymerization under these conditions proceeded rapidly exhibiting pseudofirst order kinetics with no induction period. A high monomer conversion (~92%) was reached within only 1h30. Moreover, the RAFT polymerization of acrylic acid (AA) was controlled as the growing polymer exhibited a linear increase of M n with monomer conversion and a Ð below 1.1. Throughout the polymerization, SEC traces were essentially symmetrical and narrow in shape (Figure S4b). Then, PAA macroRAFTs were synthesized in water by targeting conversions higher than 95% and directly utilized -without any purification stepsas reactive stabilizer in the dispersion polymerization of D,L-menthyl acrylate, conducted at 50 °C in a mixture of ethanol and water (80/20 in weight), in which the monomer is fully soluble, using 2,2'-azobis[2-(2-imidazolin-2-yl)propane]dihydrochloride (VA-044) as a thermal initiator. A series of polymerizations was performed, at a fixed monomer concentration (~10 wt%), varying the degree of polymerization (DP) of the hydrophobic block (DP ranging from 50 to 300), see 1a, all RAFT polymerizations reached a high monomer conversion (generally ≥ 91%) within 2 hours of reaction. The size exclusion chromatograms of the final block copolymers were narrow with a dispersity generally below 1.7 (Figure 1b and Figure S5), showing a slight tailing toward the lower molar mass side. Moreover, SEC traces showed a complete shift of the macroRAFT agent signal to higher molar masses, attesting the good blocking efficiency of the polymerizations. One may notice in Table 1, that the experimental molar masses differ significantly from the theoretical values. Such differences can be explained by the use of a conventional PS calibration which is not representative of the copolymer formed. With increasing DP of the hydrophobic block, the appearance of the solutions changed slightly towards more opaque dispersions, which remained colloidally stable. Such dispersions were diluted at 1 wt% in ethanol/water (80/20 in weight) and studied by dynamic light scattering (DLS) to determine the particle diameters. As reported in Table 1, by increasing the chain length of the hydrophobic block (DP ranging from 50 to 300), the particle diameter of the final dispersions increased from 30 to 60 nm. Thereby the particle diameter can be tuned by simply adjusting the targeted DP of the PMnA core-forming block as previously reported for spherical nanoparticles prepared via RAFT-PISA. [27][28][29][30][31][32] In addition, cryo-TEM analysis was also performed on the dispersion solution obtained in experiment 4 diluted at 1 wt% in the same mixture of solvents. While a monodisperse distribution (σ < 0.1 denoting a monodisperse sample) with an average diameter, D z , of 59 nm was obtained by DLS (Figure 2a), a smaller diameter (D n ~ 40 nm) along with particles spherical in shape was observed by cryo-TEM (Figure 2b). Such discrepancy is not unexpected considering that DLS gives a hydrodynamic diameter, while the hydrated PAA block is supposedly not visible in cryo-TEM (due to a lack of contrast).

In order to develop an even greener process by reaching higher final solids contents, we performed two other series of experiments at higher monomer concentration (at ~ 15 and 25 wt%, see Table 1, experiments 5 to 10). As depicted in Figure S6, these extensions exhibited similar polymerization behavior, yielding similar experimental molar masses when the same DP was targeted (for example in the experiments 3, 6 and 9 for a targeted DP = 150) and maintaining a high monomer conversion. Again, a significant discrepancy between theoretical and experimental molar masses determined by SEC was observed. Using the same approach as previously, we decided to determine the absolute M n values for representative copolymers by using a SEC equipped with an in-line SLS detector. After quantitative methylation of the carboxylic acid groups yielding PMeA-b-PMnA copolymers, their dn/dC was determined providing M n,LS values that were in good agreement with the theoretically ones (Table S1), confirming a good control over the polymerization. The amount of non-reacted PAA in the final copolymers exhibiting the highest dispersities (DP of 300, experiments 4, 7 and 10 in Table 1) was quantified (see details in SI). For all samples, the copolymers contain less than 5 wt% of PAA (3.4, 0.3 and 4.7 wt% for experiments 4, 7 and 10 respectively).

The particle diameter of the polymerizations performed at 15 and 25 wt% was also determined by DLS (see Table 1). An increase in particle diameter with DP was again observed, and overall no significant impact of the initial monomer concentration (10, 15 or 25 wt%) was observed, as previously reported by Quémener et al. [33] , revealing the robustness and colloidal stability of the process with regard to variations in monomer concentration at which the polymerization was performed. Cryo-TEM analyses (see Figure 2d and 2f for experiment 7 and experiment 10 respectively) showed spherical particles that were quite homogeneous in size, and no aggregates were detected. Once again, the diameters observed for both experiments 7 (D n = 30 nm) and 10 (D n = 43 nm) were slightly lower than those determined by DLS (Figure 2c and2e, Table 1). On the other hand, while spherical particles of similar diameters were obtained at 10, 15 and 25 wt%, macroscopically a significant increase in viscosity until gel formation was observed for all extensions performed at 25 wt%.

In view of the spherical morphology, we assume that this gel-like aspect of the dispersions is caused by a jamming effect. In order to know if a switching of solvent has an impact on the nanoparticle morphologies, we also tried to perform DLS and cryo-TEM analyses in water but the dispersions were unstable in pure water, without pH adjustment. However, in slightly basic conditions (pH=8.4) the dispersions remained stable and no significant change in particle morphology was observed (see for example cryo-TEM Figure S8). For all former syntheses, the racemic mixture, D,L-menthyl acrylate, was used. In order to know if the use of an enantiopure monomer could affect the self-assembly of the copolymer in PISA, we synthesized the enantiopure L-menthyl acrylate from L-menthol and polymerized it in PISA conditions comparable to experiment 10 (see Table 1 experiment 10bis). Quasi no influence on the polymerization was noticed, and the analysis of the particles by DLS and cryo-TEM revealed no significant difference in size or in shape (Figure S7). The use of enantiopure Lmenthyl acrylate did thus not influence the self-assembly of the copolymer, at least in the current experimental conditions.

Conclusions

In conclusion, a series of biobased amphiphilic block copolymer with various degrees of polymerization for the hydrophobic block was prepared by RAFT-mediated PISA in green solvent reaching solid contents up to 25 wt% and quasi quantitative monomer conversion. A considerable advantage of this PISA process relies on the one-pot/two-step process, which means that all steps can be conducted successively in the same vessel. Stable, submicrometric particles composed of self-assembled amphiphilic diblock copolymer chains were formed. No influence of the monomer concentration (from 10 to 25 wt%) or the length of the solvophobic block (DP between 50 to 300) on the morphology of the self-assemblies was observed, only spherical nanoparticles were formed which diameter increased from 30 to 60 nm with increasing DP of PMnA. The developed process paves the way for the formation of a new class of biobased copolymers for new applications. Our current work is directed towards the All polymerizations were carried out at 50 °C, in a water/ethanol mixture (20/80 in weight) using VA-044 as an initiator with an initial molar ratio, n PAA macroRAFT,0 / n VA-044,0 = 2. a)

Monomer conversion was determined by 1 H NMR. b) Theoretical number-average molar mass at the experimentally determined conversion. c) Number-average molar mass (M n ) and dispersity (M w /M n ) determined by SEC for the methylated copolymers using a polystyrene calibration and recalculated for the nonmethylated ones. d) D z is the z-average particle diameter from dynamic light scattering analysis, performed at 1 wt% in the ethanol/water mixture (the lower the polydispersity factor, , the narrower the particle size distribution).

e)

The polymerization was performed with L-menthyl acrylate.

Text for TOC

Biobased amphiphilic block copolymer with various degrees of polymerization for the

Scheme 1 .Figure 1 .

 11 Scheme 1. Reaction scheme for the synthesis of the PAA macroRAFT agent and its

Figure 2 .

 2 Figure 2. Final size distributions determined by DLS at 25 °C and representative cryo-TEM

  FIGURE FOR TOC

Table 1 ,

 1 experiments 1 to 4. As shown in Table 1 and in Figure

Table 1 .

 1 Macromolecular and colloidal characteristics of the polymer latexes prepared by dispersion polymerization of D,L-menthyl acrylate (MnA) in the presence of PAA-TTC as a

	macromolecular RAFT agent
	Entry	wt% of MnA0 in latex	Mn,PAA-TTC (kg . mol -1 )	[MnA]0/ [TTC]0	[MnA]0 (M)	Time (min)	Conv (%) a)	Mn,th (kg . mol -1 ) b)	Mn,SEC (kg . mol -1 ) c)	Ð c	Dz (nm); () d)
	1	9.9	3.8	50	0.47	72	94	13.5	8.9	1.25	28 (0.08)
	2	10	3.8	100	0.44	83	91	22.7	14.6	1.25	37 (0.19)
	3	10.5	3.8	150	0.46	77	98	36.6	16.1	1.63	44 (0.13)
	4	10.4	3.8	300	0.46	62	98	64.8	20.9	1.78	59 (0.04)
	5	14.1	3.8	100	0.67	60	96	23.3	14.9	1.28	33 (0.06)
	6	14.9	3.9	150	0.70	120	99	35.9	16.9	1.44	39 (0.10)
	7	15.2	3.9	300	0.71	120	97	64.9	27.2	1.63	54 (0.11)
	8	23.5	3.8	100	1.27	90	95	23.7	14.7	1.21	39 (0.11)
	9	25.1	3.8	150	1.37	105	96	33.6	16.1	1.49	43 (0.06)
	10	25.0	3.8	300	1.33	120	99	65.8	27.6	1.50	59 (0.09)
	10bis e)	24.7	3.8	300	1.35	107	92	62.8	27.3	1.43	59 (0.06)

Acknowledgements

We thank Jean-Michel Guigner for the cryo-TEM measurements.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff))

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author. Materials, general polymerization procedure of PAA-TTC, chain extension polymerization, characterizations, Table S1, and Figures S1-S7.


Clément François
email: clement.francois@univ-amu.fr

Alfredo Garcia-Alix

Laura Bosch

Antoni Rodriguez-Fornells

SIGNATURES OF BRAIN PLASTICITY SUPPORTING LANGUAGE RECOVERY AFTER PERINATAL ARTERIAL ISCHEMIC STROKE

Brain imaging methods such as functional Magnetic Resonance Imaging (fMRI) and Diffusion Tensor Imaging (DTI) have already been used to decipher the functional and structural brain changes occurring during normal language development. However, little is known about the differentiation of the language network after an early lesion. While in adults, stroke over the left hemisphere generally induces post-stroke aphasia, it is not always the case when a stroke occurs in the perinatal period, thus revealing a remarkable plastic power of the language network during early development. In particular, the role of perilesional tissues, as opposed to undamaged brain areas in the functional recovery of language functions after an early insult, remains unclear. In this review article, we provide an overview of the extant literature using functional and structural neuroimaging data revealing the signatures of brain plasticity underlying near-normal language development.

Introduction

In adults, language processing relies on a largely distributed network mainly involving the perisylvian areas of the left hemisphere interconnected through the dorsal and ventral pathways [START_REF] Catani | Perisylvian language networks of the human brain[END_REF][START_REF] Price | A review and synthesis of the first 20 years of PET and fMRI studies of heard speech, spoken language and reading[END_REF]. This dual-stream network for language processing includes the dorsal pathway that connects frontal, parietal and temporal areas [START_REF] Hickok | Dorsal and ventral streams: a framework for understanding aspects of the functional anatomy of language[END_REF]. This pathway mainly involves the arcuate fasciculus (AF) composed of three segments, the long, the anterior and the posterior segments [START_REF] Catani | Perisylvian language networks of the human brain[END_REF]. The dorsal stream has been shown to play a crucial role in sensory to motor transformations [START_REF] Saur | Ventral and dorsal pathways for language[END_REF][START_REF] Schmahmann | Association fibre pathways of the brain: parallel observations from diffusion spectrum imaging and autoradiography[END_REF], in verbal short-term memory [START_REF] Liberman | The motor theory of speech perception revised[END_REF], in syntactic processing [START_REF] Brauer | Neuroanatomical prerequisites for language functions in the maturing brain[END_REF][START_REF] Friederici | The brain differentiates human and non-human grammars: functional localization and structural connectivity[END_REF][START_REF] Berwick | Evolution, brain, and the nature of language[END_REF] and novel word learning [START_REF] López-Barroso | Word learning is mediated by the left arcuate fasciculus[END_REF]Rodriguez-Fornells et al., 2009;[START_REF] Cunillera | Time course and functional neuroanatomy of speech segmentation in adults[END_REF]. The ventral pathway, instead, connects the temporal, the occipital and the frontal lobes through the inferior longitudinal fasciculus, the inferior frontal-occipital fasciculus and the uncinate fasciculus (Catani & Thiebaut de Schotten, 2008). This ventral stream has been shown to mainly support speech comprehension and semantic learning by contributing to the mapping of phonological into semantic representations [START_REF] Saur | Ventral and dorsal pathways for language[END_REF][START_REF] Hickok | Dorsal and ventral streams: a framework for understanding aspects of the functional anatomy of language[END_REF]Ripollés et al., 2017).

In adults, the disruption of the dorsal part of the speech network due to stroke can induce conduction aphasia which is mainly characterized by word repetition deficits [START_REF] Wernicke | Der Aphasische Symptomencomplex. Ein Psychologische Studie auf Anatomischer Basis[END_REF][START_REF] Kümmerer | Damage to ventral and dorsal language pathways in acute aphasia[END_REF]. By contrast, stroke occurring during the perinatal period over the left hemisphere generally does not induce post-stroke aphasia thus suggesting that brain plasticity can support functional recovery [START_REF] Bates | Differential effects of unilateral lesions on language production in children and adults[END_REF][START_REF] Stiles | Cognitive development following early brain injury: evidence for neural adaptation[END_REF]. Interestingly, the speech network is still developing at the time of the insult, as recent neuroimaging studies, conducted in healthy infants, have revealed different maturational time course of grey and white matter components (see [START_REF] Dehaene-Lambertz | The human infant brain: A neural architecture able to learn language[END_REF][START_REF] Yu | Differential White Matter Maturation from Birth to 8 Years of Age[END_REF][START_REF] Ouyang | Delineation of early brain development from fetuses to infants with diffusion MRI and beyond[END_REF]. In this context, the study of children with perinatal arterial ischemic stroke (PAIS) provides a unique opportunity to show the signatures of brain reorganization and plasticity mechanisms occurring before language functions are acquired. From a biological perspective, developmental studies provide an excellent level of analysis to understand language acquisition and the gradual unfolding of language functions in the brain [START_REF] Tinbergen | On aims and methods of ethology[END_REF][START_REF] Macdougall-Shackleton | The levels of analysis revisited[END_REF][START_REF] Hladký | Was Tinbergen an Aristotelian? Comparison of Tinbergen's four whys and Aristotle's four causes[END_REF]. In this review article, we present a brief overview of the neuroimaging studies revealing the progressive maturation of the speech network during normal development. We follow by illustrating the two most prevalent hypotheses explaining the functional recovery of language functions after an early brain lesion, with a focus on studies using neuroimaging methods in children with PAIS.

Early development of the speech network

From a developmental perspective, during the first years of life, the brain is the place of very dynamic structural and functional changes that support the acquisition of increasingly complex linguistic abilities [START_REF] Dehaene-Lambertz | The human infant brain: A neural architecture able to learn language[END_REF][START_REF] Dehaene-Lambertz | The infancy of the human brain[END_REF][START_REF] Catani | A model for social communication and language evolution and development (SCALED)[END_REF]. The recent SCALED model (for "Social Communication And Language Evolution and Development") presents neuroanatomical and neurolinguistic data integrated into developmental and evolutionnary frameworks [START_REF] Catani | A model for social communication and language evolution and development (SCALED)[END_REF]. Specifically, the model describes five developmental stages of increasing linguistic complexity that may be supported by the gradual maturation of specific brain networks and their corresponding white matter pathways. Of particular interest here are the first, third and fourth developmental stages focusing on (i) early perception and production, (ii) lexical and semantic processing, and (iii) syntactic processing in language development. This model is grounded on the results of behavioural studies that have revealed that language experience modifies infants' early perceptual sensitivity to speech sounds in such a way that native sound discrimination gradually refines while nonnative speech sound perception decreases by the end of the first year of life [START_REF] Kuhl | Infants show facilitation for native language phonetic perception between 6 and 12 months[END_REF][START_REF] Kuhl | Phonetic learning as a pathway to language: New data and native language magnet theory expanded (NLM-e)[END_REF]Werker, Yeung, & Yoshida, 2012). Interestingly, language production skills also emerge and refine in the second half of the first year following a rather similar developmental trajectory. Canonical babbling, beginning around 6-8 months of age, starts to present language-specific properties by the end of the first year of life as reflected by increasing quality and tuning of speech sounds [START_REF] Kuhl | Infant vocalizations in response to speech: vocal imitation and developmental change[END_REF]. These acquisition processes may require the maturation of the the dorsal pathway connecting posterior superior temporal, inferior parietal and inferior frontal regions. Specifically, the long segment of the AF connecting speech perception to spech production brain areas seems to be crucial for the proper development of linguistic skills [START_REF] Lebel | Lateralization of the arcuate fasciculus from childhood to adulthood and its relation to cognitive abilities in children[END_REF][START_REF] Budisavljevic | Age-related differences and heritability of the perisylvian language networks[END_REF]. In adults, this pathway supports auditory-motor integration processes involved in word repetition, phonological shortterm memory and novel word learning (Rodriguez-Fornells et al., 2009;Lopez-Barroso et al., 2013). Interestingly, DTI studies in young infants show that plastic changes through fiber pruning exist at least until the end of the first postnatal year [START_REF] Dubois | Asynchrony of the early maturation of white matter bundles in healthy infants: quantitative landmarks revealed noninvasively by diffusion tensor imaging[END_REF][START_REF] Dubois | Exploring the early organization and maturation of linguistic pathways in the human infant brain[END_REF]Takahashi et al., 2012). Studies in healthy newborns even suggest a protracted growth of the long segment of the AF [START_REF] Brauer | Dorsal and ventral pathways in language development[END_REF][START_REF] Perani | Neural language networks at birth[END_REF][START_REF] Zhang | Evidence of slow maturation of the superior longitudinal fasciculus in early childhood by diffusion tensor imaging[END_REF]. These results converge with previous ones pointing to a more graded maturation of the dorsal whitematter tracts supporting language processing, particularly when compared to the maturation of the ventral pathway connecting the superior temporal, angular gyrus and inferior frontal gyri through the inferior fronto-occipital, inferior longitudinal and uncinate fasciculi [START_REF] Brauer | Dorsal and ventral pathways in language development[END_REF][START_REF] Dubois | Exploring the early organization and maturation of linguistic pathways in the human infant brain[END_REF][START_REF] Bajada | Transport for language south of the Sylvian fissure: the routes and history of the main tracts and stations in the ventral language network[END_REF]. Recent DTI results point to a similar developmental pattern for white-matter pathways connecting temporo-parietal and frontal regions via the Superior Longitudinal Fasciculus (SLF, [START_REF] Yu | Differential White Matter Maturation from Birth to 8 Years of Age[END_REF][START_REF] Ouyang | Delineation of early brain development from fetuses to infants with diffusion MRI and beyond[END_REF]. Therefore, the changes observed in the long segment of the AF, as well as those in the anterior segment of the AF (connecting frontal and inferior-parietal regions) might be crucial for early language acquisition. Finally, the SCALED model also proposes that the functional maturation of ventral temporal frontal networks, known to be involved in lexical and semantic processes [START_REF] Friederici | The brain differentiates human and non-human grammars: functional localization and structural connectivity[END_REF][START_REF] Friederici | Disentangling syntax and intelligibility in auditory language comprehension[END_REF][START_REF] Mesgarani | Phonetic feature encoding in human superior temporal gyrus[END_REF][START_REF] Price | A review and synthesis of the first 20 years of PET and fMRI studies of heard speech, spoken language and reading[END_REF][START_REF] Wilson | Syntactic processing depends on dorsal language tracts[END_REF], may support the vocabulary spurt occurring during the second year of life [START_REF] Goldfield | Early lexical acquisition: rate, content, and the vocabulary spurt[END_REF][START_REF] Schafer | Rapid word learning by fifteen-month-olds under tightly controlled conditions[END_REF].

In terms of functional activations, functional Magnetic Resonance Imaging (fMRI) has been used to show that newborns and young infants bilaterally activate fronto-temporal areas with a right predominance in the auditory cortices when presented with infant-directed speech [START_REF] Dehaene-Lambertz | Functional neuroimaging of speech perception in infants[END_REF][START_REF] Dehaene-Lambertz | Functional organization of perisylvian activation during presentation of sentences in preverbal infants[END_REF][START_REF] Perani | Neural language networks at birth[END_REF]. Older children between 5 and 6 years of age exhibit left fronto-temporal functional activations during passive story listening paradigms [START_REF] Hutton | Differences in functional brain network connectivity during stories presented in audio, illustrated, and animated format in preschool-age children[END_REF][START_REF] Romeo | Beyond the 30-Million-Word Gap: Children's Conversational Exposure Is Associated With Language-Related Brain Function[END_REF], see also Weiss-Croft & Baldeweg 2015, for a systematic review on the maturation of language networks based on fMRI studies). Taken together, these studies show that the gradual development of language abilities from early perception to word production and lexical and morphosyntactic learning is supported by the progressive development and maturation of the language brain network [START_REF] Catani | A model for social communication and language evolution and development (SCALED)[END_REF]. In this context, the study of children with perinatal brain lesions offers a good model of early brain reorganization. In the following section, we illustrate the two prevalent theories explaining near-normal development after PAIS.

Neuroimaging markers of language recovery after perinatal arterial ischemic stroke

PAIS occurs in about one in 4000 births [START_REF] Nelson | Stroke in newborn infants[END_REF]) and can have long-term negative effects on cognitive and language development. Children with unilateral PAIS often show lower academic achievement scores than typically-developing peers [START_REF] Ballantyne | Plasticity in the developing brain: intellectual, language and academic functions in children with ischaemic perinatal stroke[END_REF] and they generally present individual differences in their degree of language recovery with low to near-normal language development [START_REF] Fuentes | Determinants of cognitive outcomes of perinatal and childhood stroke: A review[END_REF][START_REF] Murias | A Review of Cognitive Outcomes in Children Following Perinatal Stroke[END_REF][START_REF] Anderson | Do children really recover better? Neurobehavioural plasticity after early brain insult[END_REF][START_REF] Bates | Differential effects of unilateral lesions on language production in children and adults[END_REF][START_REF] Stiles | Cognitive development following early brain injury: evidence for neural adaptation[END_REF]. This might be partly explained by the fact that children with PAIS present highly reorganized brain networks with language regions being consistently affected. Moreover, the presence of epileptic seizures, altered resting state networks (see Figure 1), as well as differences between early normal brain maturation and cellular mechanisms induced by the lesion may also explain the cognitive and language impairments often observed in these children. Using multimodal neuroimaging data acquired during the first week of life of 34 infants with unilateral or bilateral PAIS, it has been recently found that parietal posterior brain regions largely involved in language processing are the most affected in neonatal stroke [START_REF] Stephan-Otto | Threedimensional map of neonatal arterial ischemic stroke distribution from early multimodal brain imaging[END_REF]; see also [START_REF] Núñez | Precise neonatal arterial ischemic stroke classification with a three-dimensional map of the arterial territories of the neonatal brain[END_REF]. These early lesions seem to mainly affect the dorsal stream of language processing (especially the long segment of the AF, see Figure 2). Therefore, the question about how the developing brain compensates and reorganizes after an early lesion in order to achieve near-normal language proficiency remains open. [START_REF] Sanchez | Age-specific MRI templates for pediatric neuroimaging[END_REF]. We first linearly registered this neonatal template to the MNI152 space using FLIRT (FMRIB's Linear Image Registration Tool; Jenkinson et al., 2012). Then we used FNIRT to non-linearly register the neonatal to the adult template. The parameters obtained during these calculations were applied to the NAIS map to register it to standard space. The region in which at least 50% of the NAIS overlapped in the left hemisphere is depicted in dark blue. Probability templates for the long (in red, overlap with the lesion in pink), anterior (in green, overlap with the lesion in light blue) and posterior (yellow, overlap with the lesion in white) segments of the arcuate were extracted from the Tractotron atlas (Rojkova et al., 2015;Thiebeaut de Schotten et al., 2011) and were thresholded at a 50% (only voxels having a 50% probability of being part of the AF according to the atlas are shown). Results are overlaid over a canonical template in MNI space, with coordinates at the bottom right of each slice.

First, there is evidence showing that early left hemisphere lesions can trigger the transfer of language functions in homologous brain regions of the right hemisphere [START_REF] Tillema | Cortical reorganization of language functioning following perinatal left MCA stroke[END_REF][START_REF] Jacola | Functional magnetic resonance imaging reveals atypical language organization in children following perinatal left middle cerebral artery stroke[END_REF][START_REF] Ilves | Different plasticity patterns of language function in children with perinatal and childhood stroke[END_REF][START_REF] Guzzetta | Language organisation in left perinatal stroke[END_REF]Lidzba et al., 2017a;[START_REF] François | Language learning and brain reorganization in a 3.5-year-old child with left perinatal stroke revealed using structural and functional connectivity[END_REF][START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. For instance, Jacola and colleagues (2006) used fMRI with both a verb generation and a passive story listening task in three children aged 7, 9 and 10 years with unilateral left PAIS of the middle cerebral artery (MCA; see Table 1 for a summary of the neuroimaging studies on perinatal stroke). Compared to controls, children with PAIS showed atypical brain activations with a clear engagement of the right homologous regions [START_REF] Jacola | Functional magnetic resonance imaging reveals atypical language organization in children following perinatal left middle cerebral artery stroke[END_REF]. In another fMRI study, Tillema and collaborators (2008) evaluated ten children with unilateral left PAIS using a verb generation task and revealed a similar pattern of right-sided BOLD activation over Broca's area. These studies have brought evidence suggesting that the undamaged righthemisphere can take-over language functions probably via inter-hemispheric transfer of functions.

There is also evidence showing that the remaining of functionally active left hemisphere brain regions can be associated with better language outcomes [START_REF] Raja-Beharelle | Left hemisphere regions are critical for language in the face of early left focal brain injury[END_REF][START_REF] Dick | Inter-hemispheric functional connectivity following prenatal or perinatal brain injury predicts receptive language outcome[END_REF]. Using a category fluency task in a large sample of children with left PAIS (N=25), Raja-Beharelle and colleagues (2010) showed that preserved activation of the left frontal regions was associated with better linguistic outcomes than fully right-lateralized activations.

By contrast, in the case of children with lesions over the temporal-parietal regions, they observed that bilateral activations within these areas were associated with better outcomes than fully right-lateralized participants.

The functional recovery of language functions after PAIS may therefore depend on the type of brain mechanisms involved, in particular on the role of perilesional as opposed to homologous brain areas of the unaffected hemisphere. Several factors must be considered to explain the different outcomes observed in the case of intra vs. inter-hemispheric transfer of function. First, the type of lesion is a crucial factor. For instance, almost half of the children included in the Raja-Beharelle and collaborator's study had periventricular venous infarction (PVI) which is known to induce smaller linguistic and cognitive deficits than children with PAIS [START_REF] Kirton | Presumed perinatal ischemic stroke: vascular classification predicts outcomes[END_REF]. The presence of altered functional connectivity at rest is also an important factor. Indeed, there is recent evidence showing that children with left PAIS present altered default-mode resting-state networks [START_REF] François | Language learning and brain reorganization in a 3.5-year-old child with left perinatal stroke revealed using structural and functional connectivity[END_REF]2019) whereas children with PVI may have a preserved functional connectivity compared to controls [START_REF] Ilves | Resting-state functional connectivity and cognitive impairment in children with perinatal stroke[END_REF][START_REF] Carlson | Functional connectivity of language networks after perinatal stroke[END_REF]. The size and type of the lesions are further crucial factors. Indeed, PVI generally induces more focal sub-cortical lesions compared to PAIS of the MCA [START_REF] Kirton | Presumed perinatal ischemic stroke: vascular classification predicts outcomes[END_REF]. Taken together, these results argued against the right hemisphere take-over hypothesis and rather suggested an intra-hemispheric transfer of function that may be subsumed by perilesional tissues [START_REF] Anderson | Do children really recover better? Neurobehavioural plasticity after early brain insult[END_REF]. This pattern of results is consistent with the recovery of motor functions in adult individuals with stroke, in which the restoration of brain activity in the affected hemisphere and decreased activation in the non-affected one predicts better motor outcomes than bilateral and/or contralesional activations [START_REF] Jaillard | Vicarious function within the human primary motor cortex? A longitudinal fMRI stroke study[END_REF][START_REF] Carey | Motor impairment and recovery in the upper limb after stroke: behavioral and neuroanatomical correlates[END_REF][START_REF] Grefkes | Cortical connectivity after subcortical stroke assessed with functional magnetic resonance imaging[END_REF]. These observations in the motor domain have led to propose the bimodal balance-recovery model in which intra-, as opposed to inter-hemispheric reorganization, depends on the individual's structural reserve to support a particular function [START_REF] Pino | Modulation of brain plasticity in stroke: a novel model for neurorehabilitation[END_REF]. Importantly, most of these studies have shown a strong interaction between the size, the location, and the type of lesion as determinant factors for functional recovery (see [START_REF] Anderson | Do children really recover better? Neurobehavioural plasticity after early brain insult[END_REF]. Future research is needed to better understand the role of these factors in triggering either intra-hemispheric or inter-hemispheric plasticity mechanisms as well as in inducing functional recovery of language or not. Unfortunately, most of these studies were conducted in very heterogeneous groups of patients in terms of age-range with language functions generally evaluated after an eventual "catch-up" induced by schooling. Besides, despite an effort to thoroughly evaluate subtle language functions at the behavioural level [START_REF] Reilly | Later language development in narratives in children with perinatal stroke[END_REF][START_REF] Demir | Narrative skill in children with early unilateral brain injury: a posible limit to functional plasticity[END_REF][START_REF] Demir | Narrative processing in typically developing children and children with early unilateral brain injury: seeing gesture matters[END_REF][START_REF] Demir | Vocabulary, syntax, and narrative development in typically developing children and children with early unilateral brain injury: early parental talk about the "there-and-then" matters[END_REF][START_REF] Westmacott | Cognitive outcome following unilateral arterial ischaemic stroke in childhood: effects of age at stroke and lesion location[END_REF], combined functional and structural neuroimaging data together with fine-grained behavioral assessments are still very scarce in this population.

Diffusion tractography allows the study of the microstructural properties of white matter tracts such as the arcuate fasciculus in a non-invasive manner (see Le Bihan, 2003 for a review).

This method is particularly relevant in pediatric populations such as extremely premature infants, or children with cortical malformations. Results have suggested a link between the microstructural properties of the arcuate fasciculus and language abilities [START_REF] Salvan | Language ability in preterm children is associated with arcuate fasciculi microstructure at term[END_REF][START_REF] Paldino | Failure to identify the left arcuate fasciculus at diffusion tractography is a specific marker of language dysfunction in pediatric patients with Polymicrogyria[END_REF]. However, to our knowledge, only a few studies have gathered structural MRI together with behavioural and neuropsychological data in children with PAIS [START_REF] François | Language learning and brain reorganization in a 3.5-year-old child with left perinatal stroke revealed using structural and functional connectivity[END_REF][START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF][START_REF] Northam | Developmental conduction aphasia after neonatal stroke[END_REF], see Figure 3 for a summary of the main results of the two last studies).

In a single-case study, a 3.5-year-old boy with a unilateral left perinatal stroke of the MCA was assessed with both functional and structural MRI as well as with an exhaustive battery of language outcomes with measures of receptive vocabulary, phonological whole-word production, and linguistic complexity in spontaneous speech. In addition, word learning abilities were assessed using a fast-mapping task designed to assess the immediate and delayed recall of newly mapped words [START_REF] François | Language learning and brain reorganization in a 3.5-year-old child with left perinatal stroke revealed using structural and functional connectivity[END_REF]. Fast-mapping tasks have been originally designed to evaluate the ability to associate novel word forms with unfamiliar objects based on the observation that young children can learn and retain the names of new objects after very limited exposure to those novel labels, a process underlying vocabulary acquisition in early childhood [START_REF] Carey | Acquiring a single new word[END_REF]. Neuroimaging data of that single-case study [START_REF] François | Language learning and brain reorganization in a 3.5-year-old child with left perinatal stroke revealed using structural and functional connectivity[END_REF] revealed a right-lateralized pattern of activation during a passive story listening task and a disrupted left AF. Receptive vocabulary measured with the Peabody Picture Vocabulary Test, PPVT-III [START_REF] Dunn | PPVT-III. Peabody picture vocabulary test[END_REF], fell within normal limits but whole word production was delayed, and the child had limited spontaneous speech. Critically, the child showed clear difficulties in both the immediate and delayed recall of the words in the word learning task, significantly differing from controls in the retention of new word-referent associations. These data were in line with previous results in healthy adults [START_REF] López-Barroso | Word learning is mediated by the left arcuate fasciculus[END_REF] and suggested a crucial role of the left AF in the learning of novel word-referent associations in young children. In a further study, François and colleagues (2019) studied a group of six 4-y-o children with unilateral left PAIS who were assessed with a comprehensive battery of cognitive and linguistic outcomes with both productive and receptive aspects of language (see Table 1) as well as with a multimodal neuroimaging battery including the collection of functional activations during a passive story listening paradigm (fMRI), at rest (rs-fMRI) as well as the collection of DTI data. Despite a small sample size, the results were clear cut in showing right lateralized functional activations during the passive story listening paradigm as well as disruptions of the left AF. Importantly, the results showed significant associations between productive aspects of language functions and (i) structural reorganization of the dorsal pathway (i.e. the right lateralization of the volume of the AF) and (ii) functional reorganization of the dorsal pathway (i.e. the right lateralization of the functional connectivity at rest between the superior temporal gyrus and the inferior frontal gyrus; see Figure 3C).

Another recent study gathered functional and structural MRI data as well as various standardized neuropsychological tests evaluating perception and production of language in 21 children with left neonatal stroke [START_REF] Northam | Developmental conduction aphasia after neonatal stroke[END_REF]. Results showed that an early lesion of the dorsal pathway together with left-lateralized functional activations during a verb generation task was associated with impaired nonword and verbatim sentence repetition like conduction aphasia in adults. On the contrary, children with right-lateralized functional activations were less impaired in word repetition (see Figure 3D). Besides, atypical lateralization of cerebellar activations towards the left was also predictive of repetition performance. In adults, speech production task induces consistent cerebellar activations contralateral to the typical language dominant brain network (Jensen et al., 2005). In the study from Northam and colleagues (2018), while patients with typical activations of the left fronto-temporal language network together with right cerebellar activations showed poor speech repetition abilities, the group of patients with a mirrored pattern of activations at the cortical and cerebellar levels (i.e. activations of the right fronto-temporal network and left cerebellum) showed better outcomes. The authors suggested the possible existence of a developmental form of conduction aphasia characterized by a persistent deficit in speech repetition but occurring after neonatal stroke [START_REF] Northam | Developmental conduction aphasia after neonatal stroke[END_REF]. However, these results obtained in such a cross-sectional design did not provide information about the time course of the reorganization process. Nonetheless, they are in line with recent observations in a cohort of 4-year-old children with unilateral left PAIS in which a right-lateralized arcuate fasciculus as measured by the laterality index of the AF volume was associated with better expressive language based on utterance length (see Figure 3C; [START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. Taken together, these last studies suggest that the redundancy and bilateral organization of the language network can leave room for the functional and structural brain reorganization supporting the near-normal development of language functions. [START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. The lesion mask is shown in dark blue. Probability templates for the long (in red, overlap with the lesion in pink), anterior (in green, overlap with the lesion in light blue) and posterior (yellow, overlap with the lesion in white) segments of the AF were extracted from the Tractotron atlas (Thiebeaut de [START_REF] Thiebaut De Schotten | Atlasing location, asymmetry and inter-subject variability of white matter tracts in the human brain with MR diffusion tractography[END_REF] and are thresholded at a 50% (only voxels having a 50% probability of being part of the AF according to the atlas are shown). C) Association between the lateralization of the volume of the Arcuate Fasciculus and expressive language abilities as measures by the mean length of utterance (from [START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. D) Association between the lateralization of activations obtained during a verb generation task (laterality index) and word repetition abilities (left) with the corresponding activation maps (right) adapted from Northam et al., 2018. STG, Superior Temporal Gyrus; SMA, Supplementary Motor Area; IFG, Inferior Frontal Gyrus; SMG, Supramarginal gyrus; ANG, Angular Gyrus; STG, Superior Temporal Gyrus.

However, care must be taken when dealing with neuroimaging data obtained from lesioned brains, especially in pediatric populations. A first concern lies with the fact that group analyses, especially for fMRI but also for DTI data (see Tract-Based Spatial Statistics;[START_REF] Smith | Tractbased spatial statistics: voxelwise analysis of multi-subject diffusion data[END_REF], are computed in standard spaces. The pre-processing of MRI data can involve different normalization techniques of the individual brain data to adult atlases which are known to show several limitations (e.g., misalignments, changes in the relation between micro-and macrostructural aspects; see [START_REF] Brett | Spatial normalization of brain images with focal lesions using cost function masking[END_REF][START_REF] Crinion | Spatial normalization of lesioned brains: performance evaluation and impact on fMRI analyses[END_REF][START_REF] Altaye | Infant brain probability templates for MRI segmentation and normalization[END_REF]. While specific steps can be taken to minimize these normalization errors (e.g., cost function masking; [START_REF] Andersen | Cost function masking during normalization of brains with focal lesions: still a necessity?[END_REF]Ripollés et al., 2012), another solution is to analyze the data in native space. This latter option is very common in DTI, where laterality measures can be calculated by virtually dissecting white matter tracts in native space [START_REF] Thiebaut De Schotten | Atlasing location, asymmetry and inter-subject variability of white matter tracts in the human brain with MR diffusion tractography[END_REF], without transforming the original data. Such an approach has been successful in revealing brain to behavior relationships in children with unilateral left PAIS [START_REF] François | Language learning and brain reorganization in a 3.5-year-old child with left perinatal stroke revealed using structural and functional connectivity[END_REF][START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF].

Besides, the presence of lesioned tissues with altered microstructure can negatively impact the functioning of algorithms estimating fiber orientation which can, in turn, lead to artifacts during track reconstruction [START_REF] Ciccarelli | Diffusion based tractography in neurological disorders: concepts, applications, and future developments[END_REF][START_REF] Dell'acqua | A modified damped Richardson-Lucy algorithm to reduce isotropic background effects in spherical deconvolution[END_REF]. In this regard, an interesting approach is the development of detailed brain atlases and templates of children at different ages to compute region of interest analyses. While great advances have been made (see

Neurodevelopmental

MRI Database http://jerlab.psych.sc.edu/NeurodevelopmentalMRIDatabase/access.html; [START_REF] Almli | Brain Development Cooperative Group. The NIH MRI study of normal brain development (Objective-2): newborns, infants, toddlers, and preschoolers[END_REF][START_REF] Sanchez | Neurodevelopmental MRI brain templates for children from 2 weeks to 4 years of age[END_REF][START_REF] Richards | A database of ageappropriate average MRI templates[END_REF][START_REF] Fillmore | Stereotaxic Magnetic Resonance Imaging Brain Atlases for Infants from 3 to 12 Months[END_REF], further research is needed in order to obtain more precise atlases derived, for example, from cytoarchitectonic studies.

Conclusion

In conclusion, functional and structural neuroimaging studies in children with PAIS are of particular interest to better characterize which brain plasticity mechanisms better support the development of a complex human function such as language. The pattern of results emerging from this review indicates that two patterns of brain re-organization can be associated with good language outcomes after PAIS with (i) an inter-hemispheric re-organization with temporal and frontal language areas switching towards the right hemisphere, together with a possible reorganization of the cerebellum towards the left, and (ii) an intra-hemispheric re-organization with the involvement of functionally active perilesional brain regions. It also appears rather clear that studies including a thorough assessment of language functions are still very scarce. This is a limitation when aiming to demonstrate clinically valid linguistic recovery after early brain damage. Future studies using more complete assessments of language functions are thus needed. Finally, future research based on interventional designs or randomized clinical trials will certainly be of great help to better understand the neuroplasticity mechanisms allowing functional recovery after early brain injuries.

Figure 1 .

 1 Figure 1. (A) Structural lesions of 9 children with left or right/bilateral PAIS shown in native space using a T1-weighted axial image. The lesions are highlighted with a red circle. Neurologic convention is used. (B) Individual Default-Mode Networks obtained using Group Spatial ICA on the resting state data obtained under propofol anesthesia. Individual data is in z-scores (p < 0.05, uncorrected) and presented over each patient´s T1 registered to a common space (4-year-old MRI brain template obtained from the Neurodevelopmental MRI Database). (C) The group averaged DMN for all patients is depicted (using t-values, (p < 0.01, uncorrected) over a canonical 4-year-old MRI brain template (adapted from François et al., 2019).

Figure 2 .

 2 Figure 2. Top: Lesion maps of 34 newborns with PAIS adapted from Stephan-Otto et al., 2017 (A and B). Bottom: Overlap between the different segments of the arcuate fasciculus and the NAIS map. The probabilistic neonatal arterial ischemic stroke (NAIS) map (Stephan-Otto et al., 2017) was created by registering 34 neonatal patients to a neonatal high-resolution brain template[START_REF] Sanchez | Age-specific MRI templates for pediatric neuroimaging[END_REF]. We first linearly registered this neonatal template to the MNI152 space using FLIRT (FMRIB's Linear Image Registration Tool;Jenkinson et al., 2012). Then we used

Figure 3 .

 3 Figure 3. Examples of functional and structural reorganization after left PAIS. A) T1 image and 3D reconstructions of the AFs in a group of 4-y-o children with left MCA stroke using deterministic tractography (Adapted from[START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. B) Overlap of the different segments of the AF and the lesion mask (adapted from[START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. The lesion mask is shown in dark blue. Probability templates for the long (in red, overlap with the lesion in pink), anterior (in green, overlap with the lesion in light blue) and posterior (yellow, overlap with the lesion in white) segments of the AF were extracted from the Tractotron atlas (Thiebeaut de[START_REF] Thiebaut De Schotten | Atlasing location, asymmetry and inter-subject variability of white matter tracts in the human brain with MR diffusion tractography[END_REF] and are thresholded at a 50% (only voxels having a 50% probability of being part of the AF according to the atlas are shown). C) Association between the lateralization of the volume of the Arcuate Fasciculus and expressive language abilities as measures by the mean length of utterance (from[START_REF] François | Right structural and functional reorganization in 4-year-old children with perinatal arterial ischemic stroke predict language production[END_REF]. D) Association between the lateralization of activations obtained during a verb generation task (laterality index) and word repetition abilities (left) with the corresponding activation maps (right) adapted from[START_REF] Northam | Developmental conduction aphasia after neonatal stroke[END_REF]. STG, Superior Temporal Gyrus; SMA, Supplementary Motor Area; IFG, Inferior Frontal Gyrus; SMG, Supramarginal gyrus; ANG, Angular Gyrus; STG, Superior Temporal Gyrus.

Table 1 .

 1 Summary of the studies using neuroimaging methods (fMRI, DTI, and rs-fMRI) in groups of children with PAIS included in the present review. MCA: Middle Cerebral Artery; VG: Verb Generation task; SL: Story listening task; ICA: independent component analysis; CELF-III: Clinical Evaluation of Language Fundamentals III; CVLT-C: California Verbal Learning Test-Children; WJ-III: Woodcock-Johnson 3 rd edition; NEPSY-II: Developmental NeuroPsychological assessment 2 nd edition; CTOPP: Comprehensive test of phonological processing; BSID III: Bayley Scales of Infant and Toddler Development; PPVT-III: Peabody Picture Vocabulary test; FM: Fast-mapping task; pMLU: phonological Mean Length of Utterance; MLU: Mean Length of Utterance

		Sample	etiology	Hemisphere of	fMRI task	Main results	DTI	Resting state	Language outcomes
		size	characteristics	injury (left, right,
		age at scan		or bilateral)
	Staudt et al., 2002	N=5 18-25 y-o	Unilateral Left brain lesions periventricular	Left	Word generation	Right activation	-	-	Word chain task (number of words produced)
	Tillema et al., 2008	N=10 6-16 y-o	Unilateral Left stroke MCA perinatal ischemic	Left	VG	Right activation	-	-	-
	Raja-Beharelle et al., 2010	N=25 8-20 y-o	Unilateral Left Vascular (n=14) Periventricular (n=11)	Left	Category fluency	Right, Left or bilateral activation	-	-	Expressive vocabulary test PPVT-III CELF III (Expressive & Receptive language scores)
	Dick et al., 2013	N=14 7-10 y-o	Unilateral Left Periventricular (n=6) Vascular (n=8)	Left	Audio-visual SL	-	-	-	CELF III (receptive language & listening to paragraphs subtests) Johnson-Newport Grammaticality Judgement
									task
	Jacola et al., 2006	N=3 7, 9, 12 y-o	Unilateral Left MCA perinatal stroke	Left	VG SL	Bilateral or Right activation	-	-	-
	Lidzba et al., 2017	N=19 7-32 y-o	Unilateral Left vascular (MCA, n=8) periventricular (n=11)	Left	Beep story task (production) (comprehension) Vowel Identification task	Comprehension: right activation 16/17 patients in 7/19 patients Production: right activation in	-	-	-
	Ilves et al., 2014	N=12 6.3-13.8 y-o	Unilateral Left vascular perinatal (n=7) and childhood stroke (n=5)	Left	VG Sentence comprehension	Bilateral or Right activation for perinatal stroke	-	-	NEPSY (expressive & receptive language subtests)
	Guzzetta et al., 2008	N=10 7-19 y-o	Left perinatal arterial stroke	Left	Covert rhyme generation Right, Left or bilateral activation	-	-	-
								ICA analysis using	BSID-III
								GIFT toolbox	PPVT-III
	François et al., 2016	N=1 3.5 y-o	Unilateral Left MCA PAIS	Left	SL with anesthesia	RH activation	Deterministic tractography Disconnection of the AF	Right fronto-temporal network	Spontaneous expressive language complexity: pMLU; MLU & phonological whole-word
									proximity
									Novel label-object mapping (FM)

Acknowledgments

We would like to warmly thank Dr. Pablo Ripollés (New-York University) for helping us creating the figure 2. This work was funded by the "Plan Nacional de I+D+I and ISCIII-Subdirección General de Evaluación y Fomento de la Investigación Sanitaria", Project PI15/00846 to AGA, the European Regional Development Fund (FEDER "a Way to Build Europe"), a SLT002/16/00390 grant, funded by the Department of Health of the Generalitat de Catalunya by the call "Acció instrumental d'incorporació de científics i tecnòlegs", a grant from the Bial Foundation to ARF and a Spanish MINECO project (PSI 2014-55105P) to LB.


Marion Grzelka

Iurii Antoniuk

Eric Drockenmuller

Alexis Chennevière

Liliane Léger

Frederic Restagno
email: frederic.restagno@u-psud.fr

Viscoelasticity-Induced Onset of Slip at the Wall for Polymer Fluids

come

Viscoelasticity induced onset of slip at the wall for polymer fluids Marion Grzelka, 1 Iurii Antoniuk, 2 Eric Drockenmuller, 2 Alexis Chennevière, 3 Liliane Léger, 1 and Frédéric Restagno 1, * 1 Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France 2 Univ Lyon, Université Lyon 1, CNRS, Ingénierie des Matériaux Polymères, UMR 5223, F-69003, Lyon, France 3 Laboratoire Léon Brillouin, CEA Saclay, 91191 Gif-sur-Yvette, France (Dated: November 18, 2020)

The progressive onset of slip at the wall, which corresponds to a slip length increasing with the solicitation time before reaching a plateau, has been investigated for model viscoelastic polymer solutions, allowing one to vary the longest relaxation time while keeping constant solid -fluid interactions. A hydrodynamic model based on a Maxwell fluid and the classical Navier's hypothesis of a linear response for the friction stress at the interface fully accounts for the data. In the limit of the linear viscoelasticity of the fluid, we could postulate a Newtonian response for the interfacial friction coefficient reflecting the local character of solid-liquid friction mechanisms. Deviations between the experiments and our model are observed when the fluid is far from its linear viscoelastic behavior.

The description of liquid flows close to a surface has become a major issue during the last 10 years, due to the fast development of micro and nanofluidics, and driven by potential applications, as for example desalination [START_REF] Holt | Fast Mass Transport Through Sub-2-Nanometer Carbon Nanotubes[END_REF][START_REF] Majumder | Mass Transport through Carbon Nanotube Membranes in Three Different Regimes: Ionic Diffusion and Gas and Liquid Flow[END_REF][START_REF] Qin | Measurement of the Rate of Water Translocation through Carbon Nanotubes[END_REF][START_REF] Baek | High performance and antifouling vertically aligned carbon nanotube membrane for water purification[END_REF][START_REF] Radha | Molecular transport through capillaries made with atomic-scale precision[END_REF][START_REF] Abraham | Tunable sieving of ions using graphene oxide membranes[END_REF] or blue energy [START_REF] Ajdari | Giant Amplification of Interfacially Driven Transport by Hydrodynamic Slip: Diffusio-Osmosis and Beyond[END_REF][START_REF] Pennathur | Energy conversion in microsystems: is there a role for micro/nanofluidics?[END_REF][START_REF] Ren | Slip-enhanced electrokinetic energy conversion in nanofluidic channels[END_REF][START_REF] Bouzigues | Nanofluidics in the Debye Layer at Hydrophilic and Hydrophobic Surfaces[END_REF][START_REF] Goswami | Energy Transfer through Streaming Effects in Time-Periodic Pressure-Driven Nanochannel Flows with Interfacial Slip[END_REF].

In any fluid mechanics problem, two equations are needed: a bulk constitutive equation to describe the fluid properties, and an interfacial constitutive equation to describe the interfacial friction. For simple fluids, a single viscosity η, can be defined, assuming that the friction between two layers of fluid sliding past each other is proportional to their difference in velocity: σ visc = η γ, where σ is the viscous stress and γ the shear rate of the flow. Combined with Newton's laws this leads to the classical Navier-Stokes equation. To solve this bulk differential equation, a boundary condition needs be specified. The no slip boundary condition (equal solid and fluid velocities), has long been commonly used. In the past decades however, numerous violations of this no slip boundary condition have been reported, both experimentally [START_REF] Pit | Direct experimental evidence of slip in hexadecane: solid interfaces[END_REF][START_REF] Zhu | Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces[END_REF][START_REF] Cottin-Bizonne | Boundary Slip on Smooth Hydrophobic Surfaces: Intrinsic Effects and Possible Artifacts[END_REF][START_REF] Secchi | Massive radius-dependent flow slippage in carbon nanotubes[END_REF][START_REF] Cottin-Bizonne | Nanohydrodynamics : The Intrinsic Flow Boundary Condition on Smooth Surfaces[END_REF][START_REF] Durliat | Influence of grafting density on wall slip of a polymer melt on a polymer brush[END_REF][START_REF] Bonaccurso | Surface Roughness and Hydrodynamic Boundary Slip of a Newtonian Fluid in a Completely Wetting System[END_REF][START_REF] Boukany | Molecular Imaging of Slip in Entangled DNA Solution[END_REF][START_REF] Cuenca | Submicron Flow of Polymer Solutions: Slippage Reduction due to Confinement[END_REF][START_REF] Bäumchen | Slip effects in polymer thin films[END_REF][START_REF] Ilton | Adsorption-induced slip inhibition for polymer melts on ideal substrates[END_REF][START_REF] Cross | Wall slip of complex fluids: Interfacial friction versus slip length[END_REF][START_REF] Boukany | Interfacial stick-slip transition in simple shear of entangled melts[END_REF][START_REF] Hénot | Friction of Polymers: from PDMS Melts to PDMS Elastomers[END_REF] and numerically [START_REF] Thompson | Shear flow near solids: Epitaxial order and flow boundary conditions[END_REF][START_REF] Bocquet | Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids[END_REF][START_REF] Thompson | A general boundary condition for liquid flow at solid surfaces[END_REF][START_REF] Priezjev | Molecular Origin and Dynamic Behavior of Slip in Sheared Polymer Films[END_REF][START_REF] Chen | Determining hydrodynamic boundary conditions from equilibrium fluctuations[END_REF][START_REF] Omori | Full characterization of the hydrodynamic boundary condition at the atomic scale using an oscillating channel: Identification of the viscoelastic interfacial friction and the hydrodynamic boundary position[END_REF], especially when polymers were involved.

Navier [32] was the first to introduce the possibility of slip at the wall, assuming a linear constitutive equation at the interface: the friction stress of a layer of fluid sliding over the solid surface, σ is proportional to the slip velocity V : σ friction = kV , where k is the so-called Navier's or friction coefficient. k quantifies the ability of a given fluid to slip on a given solid surface. Balancing friction and viscous stresses, one can define the distance to the interface where the velocity profile extrapolates to zero, the so-called slip length b: b = η/k. The order of magnitude of the slip length varies from few nanometers [12, 14-16, 18, 26-28, 30] for simple fluids to micrometers [START_REF] Zhu | Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces[END_REF][START_REF] Durliat | Influence of grafting density on wall slip of a polymer melt on a polymer brush[END_REF][START_REF] Boukany | Molecular Imaging of Slip in Entangled DNA Solution[END_REF][START_REF] Cuenca | Submicron Flow of Polymer Solutions: Slippage Reduction due to Confinement[END_REF][START_REF] Bäumchen | Slip effects in polymer thin films[END_REF][START_REF] Ilton | Adsorption-induced slip inhibition for polymer melts on ideal substrates[END_REF][START_REF] Cross | Wall slip of complex fluids: Interfacial friction versus slip length[END_REF][START_REF] Boukany | Interfacial stick-slip transition in simple shear of entangled melts[END_REF][START_REF] Hénot | Friction of Polymers: from PDMS Melts to PDMS Elastomers[END_REF] for complex fluids such as entangled polymer solutions or melts. It has also been demonstrated that for soft elastic solids sliding on a solid surface, the friction stress was also obeying a Navier's equation, with a friction stress proportional to the sliding velocity, and on non adsorbing surfaces, the obtained Navier's friction coefficient was exactly the same for a crosslinked elastomer and for a sheared polymer melt of the same chemical nature, except for the crosslinks [START_REF] Hénot | Friction of Polymers: from PDMS Melts to PDMS Elastomers[END_REF]. This in turn rises a new question: when viscoelastic fluids are involved, is it sufficient to postulate a single constant friction coefficient, or, as for bulk fluid, is it necessary to introduce a viscoelastic response for the interfacial stress? Indeed, when simple or complex fluids are solicited at times smaller than their longest characteristic time, they can no longer be considered as Newtonian and the bulk fluid response presents an elastic contribution at short times, with characteristic times which strongly depend on the nature of the molecular interactions, and is in the nanosecond range for simple fluids while it can become much longer than seconds for complex fluids. The shear stress then depends on the shear time and the bulk constitutive equation has to be modified. Is it necessary to introduce a time dependent Navier coefficient, going from a solid friction coefficient at short times to the classical Navier coefficient at longer times? If so, what physico-chemical phenomena rule the characteristic time of this change in friction response of the interface? Such a time dependent Navier coefficient has rarely been reported [START_REF] Zhu | Rate-Dependent Slip of Newtonian Liquid at Smooth Surfaces[END_REF][START_REF] Cross | Wall slip of complex fluids: Interfacial friction versus slip length[END_REF][START_REF] Thompson | A general boundary condition for liquid flow at solid surfaces[END_REF][START_REF] Priezjev | Molecular Origin and Dynamic Behavior of Slip in Sheared Polymer Films[END_REF][START_REF] Omori | Full characterization of the hydrodynamic boundary condition at the atomic scale using an oscillating channel: Identification of the viscoelastic interfacial friction and the hydrodynamic boundary position[END_REF][START_REF] Craig | Shear-Dependent Boundary Slip in an Aqueous Newtonian Liquid[END_REF] in the literature and an universal interfacial constitutive equation is still lacking to pave the way to what could become solid-liquid interfacial rheology.

Inspired by model bulk rheology experiments, we present an investigation the interfacial friction for series of model complex fluid in contact with two different model surfaces, and submitted to an abrupt change of shear. To do so, we used entangled polymer solutions, for which the longest characteristic time, the terminal time, or reptation time τ rep , can easily be adjusted over a large range through the polymer volume fraction φ, while keeping constant the local fluid -solid interactions. For such fluids, the slip length, directly linked to the interfacial stress, ranges from tens to thousands of micrometers, large enough to be easily measured. We put into evidence a progressive onset of slip at the wall, char-acterized by a dependence of the slip length versus the shear time, before reaching a steady state slip regime. All characteristics of this transient slip regime are deeply affected by the polymer volume fraction. To rationalize these results, we built a model for a Maxwell-like fluid in simple shear flow, and obeying a classical Navier's time independent boundary condition. The comparison between experimental data for the time evolution of the slip length during the onset of slip and this model allows one to draw some conclusions on the locality of the fluid -solid friction mechanisms.

Experimental approach.

Velocimetry using fluorescence photobleaching is commonly used to measure slip lengths in polymer fluids (Fig. 1). A drop of fluorescent photobleachable fluid is compressed between two plane solid surfaces. The thickness h of the drop is measured by spectroscopic reflectometry. A pattern is photobleached in the fluid which is then sheared during a monitored time t by displacing the top surface at a constant velocity V shear = d shear /t, where d shear is the total displacement of the top surface. The slip length at the bottom surface is directly measured by following the evolution of the displaced photobleached pattern, as previously described [START_REF] Hénot | Friction of Polymers: from PDMS Melts to PDMS Elastomers[END_REF].

To adjust the characteristic times of the studied viscoelastic fluids, semi-dilute solutions with tunable volume fraction φ of polystyrene (PS, M n = 10.2 Mg•mol -1 , Ð = 1.08, Polymer Source Inc.) in diethyl phthalate (DEP) were used. High molar mass PS and ca. 1wt% of a photobleachable polystyrene (M n = 429 kg • mol -1 , Ð = 1.05, see Fig. S2) were dissolved in diethyl phthalate and toluene and were gently stirred for at least 3 weeks. Toluene was then evaporated at room temperature under vacuum during a week. The fluorescently labeled polystyrene contains nitro-benzoxadiazole (NBD) fluorescent groups emitting at 550 nm when excited at 458 nm at both chain ends. Synthesis protocol and characterization of PS di-NBD are detailed in Supplementary Materials. The respective viscosity η and reptation time τ rep were measured for each solution by oscillatory rheology at 22 • C using an Anton-Paar MCR 302 rheometer in a cone plate geometry (2 • cone angle, 25 mm diameter). A classical viscoelastic behavior is evidence for all polymer solutions (see Fig. S4 ).

Table I to 0.061 were measured on two model substrates: a bare silicon wafer and a dense layer of grafted-to PS brushes. Bare silicon wafer (2" diameter, 3 mm width, Si-Mat Inc.) was cleaned before each slip measurement with a UV/O 3 treatment for 30 min. The layer of dense PS brushes was prepared following a previously published protocol [START_REF] Chennevière | Direct Molecular Evidence of the Origin of Slip of Polymer Melts on Grafted Brushes[END_REF]. Briefly, a self-assembled monolayer of triethoxy(3-glycidyloxypropyl)-silane was vapor deposited on a Si wafer. The SAM was 0.9 nm thick as measured by ellipsometry. Amino end-functionalized PS (M n = 5.0 kg • mol -1 , Ð = 1.17, Polymer Source Inc.) was covalently tethered to the SAM in the melt at 140 • C for 48 hours. After through rinsing of the non-covalently tethered chains, the grafted PS layer was 2.8 nm thick and was considered as a dense polymer brush. The solutions are sheared at various shear rates in the range [2 × 10 -4 -5.7] s -1 . As shown in Figure 2 for 3 representative systems, the slip length b increases with the shear time t until it reaches a plateau. Similar results have been observed for all 5 volume fractions on the two substrates (see Supplementary Fig. S3). These data clearly evidence a transient behavior, corresponding to a progressive onset of slip before reaching a steady state regime. The characteristic time of the transient regime (dotted lines in Fig. 2) depends on φ but not on the substrate. Conversely, the plateau value obtained in the steady state regime, noted b ∞ , strongly depends on both φ and the substrate. This complex dependence is interesting by itself and highlights that the stress transmission at the interface depends on both the local structure of the interface and on the bulk properties [START_REF] Mhetar | Slip in entangled polymer solutions[END_REF][START_REF] Plucktaveesak | Interfacial Flow Behavior of Highly Entangled Polybutadiene Solutions[END_REF][START_REF] Sanchez-Reyes | Interfacial Slip Violations in Polymer Solutions: Role of Microscale Surface Roughness[END_REF]. The discussion of the influence of the concentration on the slip length will be developed in a forthcoming paper. The transient behavior appears to be independent of the shear velocity V shear , as the measurements presented in Figure 2 have been obtained for different values of V shear .

In order to gain a better understanding of the observed The polymer solution is considered as a Maxwell-like fluid, characterized by its viscosity η in the linear regime and its elastic modulus E, directly linked to its reptation time τ rep : τ rep = η/E. As the slip length b may depend on the shear time t, the real shear rate experienced by the fluid also depends on t, even for a constant shear velocity V shear = d shear /t. In the simple shear geometry illustrated in Fig. 1, one can link the shear rate dependence with t to b(t):

γ(t) = V shear -V (t) h (1)
= V shear [h + b(t)] -V shear t ḃ(t) [h + b(t)] 2 (2)
In a Maxwell-like fluid, one can write the viscous stress σ visc (t) = η γvisc (t) and the elastic stress σ elas (t) = Eγ elas (t). At the solid/liquid interface, assuming the friction coefficient to be independent of the shear time, Navier's hypothesis gives σ friction = kV (t). The stress balance at the interface and the expression of the imposed shear strain γ tot = γ visc +γ elas lead to a differential equation for the shear stress. Considering a zero shear stress at the beginning of the shear, the unique solution to this differential equation writes:

σ(t) = V shear Eτ h 1 -e -t/τ (3)
where τ = τrep 1+ b∞ h is a characteristic time depending on the steady-state slippage through b ∞ = η k . Equation (3) is the expected expression of the shear stress for a Maxwell-like fluid, except for the fact that the characteristic time τ now depends on the amount of slip at the wall.The total shear rate γ may also be calculated and the viscous and elastic parts evaluated separately (cf SI).

Pearson and Petrie [START_REF] Pearson | Polymer systems: deformation and flow[END_REF] were the first to introduce theoretically the notion of "retarded slip" due to the presence of a relaxation slip time λ s , with a model based on an analogy with a mechanical model for Maxwell-like fluids. Considering a power-law slip model, Hill et al. [START_REF] Hill | On the apparent relation between adhesive failure and melt fracture[END_REF] and Hatzikiriakos et al. [START_REF] Hatzikiriakos | Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies[END_REF] postulated a differential equation for the shear velocity: V + λ s dV dt = aσ m , where a is a slip coefficient and m is the slip power-law exponent. The origin of the introduced relaxation slip time λ s was not discussed in these papers. With our model, the postulated relaxation slip time λ s can be clearly identified as the differential equation obtained for σ may be written for the slip velocity V :

V + V τ = V shear Eτ kh .
Here the characteristic time τ = λ s is directly linked to the slip properties through b ∞ , the fluid dynamics through τ rep and the geometry of the experiment through h.

Combining equation ( 3) to the dependence of the shear rate with t (eq. ( 1) and ( 2)) allows one to solve the differential equation obtained for b(t), with the initial no slip condition:

b(T ) = h T (1 + X) T -X 1+X e -T (1+X) + X 1+X -1 (4)
where T = t τrep compares the shear time t and the reptation time τ rep . X = b∞ h is the ratio between the steady state slip length b ∞ and the thickness h of the sheared drop of fluid. Taking into account Navier's hypothesis for a Maxwell-like fluid affords a complex temporal dependence of the slip length. It is worth noting that equation ( 4) is independent of the shear velocity V shear and thus of the apparent shear rate γapp = V shear /h, in agreement with our experimental results.

As shown in Figure 3a, no matter what is the value of the parameter X, the shear stress calculated from eq. (3) increases with the shear time, before reaching a plateau. The value of X clearly affects the dynamics of the onset of slippage: the larger the thickness h compared to b ∞ (smaller X), the longer the transient slip regime. The dependence of the calculated slip length versus the shear time, presented in Figure 3b, appears however only weakly affected by the value of X.

The theoretical evolution of b(t)/b ∞ shown in Fig3b, is qualitatively similar to the trend of the experimental data: b(t) increases before reaching a steady state regime. A shear time longer than few reptation times is needed to obtain an almost constant slip length. For all X values, the slip length is larger than 0.8b ∞ at T = 5, as indicated by the dotted line in Fig3b.

To compare quantitatively the experimental data to the prediction of eq. ( 4), we used the following procedure. The thickness h of the drop, the reptation time τ rep and the slip length depending on the shear time b(t) are measured independently. We fitted the experimen- tal data with eq.( 4) with b ∞ as an adjustable parameter. Table I summarizes the fitted values for b ∞ . Figure 4 presents the measured (symbols) and calculated (lines) normalized slip lengths b/b ∞ as a function of the normalized shear time T = t/τ rep . All experimental data (five solutions and two surfaces) collapse on a master curve, indicating a universal behavior, only depending on both the volume fraction φ and the shear time t, but independent of the solid substrate. Note that in the experiments, the thickness h of the sheared drop is chosen to be as close as possible to b ∞ in order to minimize the error bars on the measured b values. Therefore experimental X values only vary within one decade (X ∈ [0.3 -3.8]). The experimental values can thus be compared with a theoretical model calculated with the corresponding X values.

The model clearly well captures the temporal evolution of b(t).

A slight difference between model and experimental data appears for T < 1. The experimental slip lengths estimated by our model seem underestimated compared to the experiments. These points correspond to large shear velocities. For these shear velocities, we enter in the shear-thinning regime of the fluid. This shear thinning regime is out of the scope of the present mechanical model, which only deals with linear viscoelastic fluids.At large T , the time of diffusion of labeled polymers becomes comparable to the shear time, leading to underestimate the error bars for b(t). The good agreement between model and experimental data in the Newtonian regime confirms that viscoelasticity combined to a linear friction fully describe the onset of slippage in these complex fluids.

No viscoelastic response of friction at the wall is needed to account for the observed dependence of the slip length on the shearing time. This confirms the idea that the interfacial friction is a local quantity, as already observed for polymer melts [START_REF] Hénot | Friction of Polymers: from PDMS Melts to PDMS Elastomers[END_REF][START_REF] De Gennes | Écoulements viscométriques de polymÃĺres enchevêtrés[END_REF][START_REF] Bãďumchen | Reduced Interfacial Entanglement Density Affects the Boundary Conditions of Polymer Flow[END_REF]. If indeed governed by phenomena at monomer or solvent molecular scales, the characteristic relaxation times associated to interfacial friction should be several orders of magnitude smaller than the relaxation times of the model viscoelastic fluids used here, and not accessible to the present experiments. The picture of a locally determined interfacial friction could be affected by chains adsorbed at the solid surface. The substrates used here have been specifically chosen to minimize adsorption: PS is known to adsorb slowly (several hours) on bare silicon wafers [START_REF] Housmans | Kinetics of Irreversible Chain Adsorption[END_REF], and we have shown (see SI) that indeed a weakly dense adsorbed layer could form on silica in conditions comparable to our experiments on bare silica, while the dense brush of short PS chains prevents adsorption of high molar mass PS chains on the other investigated surface. However, we see no evidence of any effect of the evolution of such an adsorbed layer during the slippage experiments: they were all done at random order for V shear and φ. We could not notice any effect of the time of contact of the solution with the surface on the obtained results. This is why the picture of a progressive onset of slippage controlled by the viscoelasticity of the fluid, while keeping a time independent Navier's coefficient appears fully efficient to account for experimental data.

To conclude, we have provided unambiguous experimental evidences of the existence of a progressive increase in slip length with shearing time before reaching a steady state plateau, for polymer solutions flowing on ideal surfaces. A mechanical model based on the Navier's hypothesis for Maxwell-like fluids has been built to describe this transient onset of slip, and pin point the mechanisms at stake. The good agreement between model and experiments validates the main hypothesis of the model: on ideal substrates (no adsorbed chains), the friction is driven by local phenomena and no elastic contribution to interfacial friction is needed to account for the onset of slip. The model, applicable to any linear viscoelastic fluid, provides a firm framework to identify which parameters govern the onset of slip for fluids others than polymer solutions. As the shear stress appears to be more sensitive than the slip length to details of the experimental geometry in the transient slip regime, this work highlights the importance of studying the interfa-cial rheology at a solid/liquid interface by analyzing the temporal evolution of the interfacial shear stress. The generality of the model may also lead to a better understanding of the molecular mechanisms responsible for the instabilities observed in extrusion process. We anticipate that extending this approach will contribute to understand fluid dynamics in different regimes, such as flow in nanoconfinement and turbulence in transient regimes.

FIG. 1 .

 1 FIG.1. Measurement of the slip length b of fluids by velocimetry using photobleaching. A drop of fluid, of thickness h, is sheared at a constant velocity V shear during a time t. The fluid slips with a velocity V on the bottom surface.

FIG. 3 .

 3 FIG. 3. Slippage of a Maxwell-like fluid following the Navier's boundary condition. a Normalized shear stress σ/σ∞ as a function of the normalized shear time T = t/τrep. b Normalized slip length b/b∞ as a function of the normalized shear time T = t/τrep. The dotted line represents T = 5, typically chosen to define b∞. All the calculations are made for 5 nondenationalized values X = b∞/h, with h the height of the sheared fluid.

FIG. 4 .

 4 FIG. 4. Comparison between measured slippage of polymer fluids and calculated Maxwell-like fluid slippage. Normalized slip length b/b∞ of PS in DEP solutions as a function of the normalized shear time T = t/τrep on a bare silicon wafer and on a grafted layer of PS brushes. The lines correspond to the calculation by equation (4), b∞ being the only adjustable parameters.

  summarizes the measured characteristics of the PS in DEP solutions.

	φ	τrep [s] η [Pa•s] b∞, PS [µm] b∞,Si [µm]
	0.0230 2.7	64	44 ± 1	58 ± 3
	0.0314 8.3	401	99 ± 2	184 ± 5
	0.0397 16.3	1,147	249 ± 6	327 ± 7
	0.0495 24.3	3,840	628 ± 13 1, 254 ± 37
	0.0608 50	12,000 1, 217 ± 37 2, 116 ± 31

TABLE I. Experimental characteristics of semi-dilute solutions of PS in DEP.

  Transient onset of slippage for polymer solutions. Slip length b of PS in DEP solutions as a function of the shear time t on a bare silicon wafer and on a grafted layer of PS brushes, for different PS volume fractions φ.The dotted lines represent t = 5τrep, a typical time for which the steady state regime is reached. The solid lines are guides to the eye.

			2	PS Grafted layer,
				= 0.0314
		6 8 1,000	Si Wafer, PS Grafted layer, = 0.0608
			4	= 0.0608
	b [µm]	100	8 2
			6
			4
			2
		10
			1	10	100	1,000
				t [s]
	FIG. 2.

transient regime, we built a simple mechanical model, based on the Navier's boundary condition and Maxwelllike fluids.

Table of

 of

	content graphics:
		constant velocity shearing
		viscoelastic
		fluid
	b(time)?	viscoelastic friction?

ACKNOWLEDGMENTS:

This work was supported by ANR-ENCORE program (ANR-15-CE06-005). We thank M. Corpart for experimental help. F.R. thanks J.D. McGraw and C. Derail for regular discussions.

ASSOCIATED CONTENT

Supporting Information available: Experimental methods and supporting figures.


Julius Akinyemi

Josiane Mothe

Nathalie Neptune
email: nathalie.neptune@irit.fr

AUTOMATIC DEFORESTATION DETECTION WITH DEEP LEARNING: THE CASE OF MASOALA NATIONAL PARK

published or not. The documents may come

Automatic deforestation detection with deep learning:

the case of Masoala National Park

Acknowledgements

This project is supported by the Schlumberger Foundation through the Faculty for the Future fellowship. This work also benefits support from FabSpace 2.0 project ; FabSpace 2.0 received funding from the European Union's Horizon 2020 Research and Innovation programme under the Grant Agreement number 693210.

Abstract

Large portions of territories are affected by deforestation. We aim to propose an approach based on convolutional neural networks to detect change in tropical forests. Our goal is to propose a model that requires minimal preprocessing and handcrafted features. We will test this approach with images from the Masoala National Park in Madagascar.

Conclusion

We aim to detect deforestation using free open data from satellite images. This work will be further extended with the addition of scientific documents with information on deforestation events for multimodal learning and knowledge extraction.

Introduction

Large collections of free satellite imagery are made available through the open data policies adopted by major space agencies. We aim to use both optical and radar imagery with a deep leanring approach to automatically detect change in forests.