Ernesto Iii Paruli

Olivier Soppera

Karsten Haupt

Carlo Gonzato

Photopolymerization and Photostructuring of Molecularly Imprinted Polymers

Keywords: Molecularly imprinted polymers, photopolymerization, photostructuring, mask lithography, maskless lithography, stereolithography, microstructures, nanostructures

Over the past few decades, molecularly imprinted polymers (MIPs) have become extremely attractive materials for biomimetic molecular recognition, thanks to their excellent affinity and specificity, combined with robustness, easy engineering and competitive costs. MIPs are synthetic antibody mimics obtained by the synthesis of 3D polymer networks around template molecules, thus generating specific binding cavities. Numerous efforts have been made to improve the performances and the versatility of MIPs, with a special focus on ways to control their size, morphology, and physical form for a given application. Gaining control over these parameters has allowed MIPs to adopt a defined micro-and nano-structure, providing access to nanocomposites and micro-/nano-systems, with fine-tuned properties, which become critical for modern

applications ranging from chemical sensing to bioimaging and medical therapy. In this rich and complex context, light as a cheap and versatile source of energy has emerged as a powerful tool for structuring MIPs. This review presents the most recent advances on structuring MIPs at the nano-/micro-scale, using light as a stimulus to trigger the polymerization process. Thus, after a general introduction on radical polymerization of MIPs, with a special emphasis on photopolymerization by UV and visible light, the reader will be presented with ways of structuring MIPs by processes that are inherently spatially confined, such a localized photopolymerization and 4cyano-4-ethyltrithiopentanoic acid; ENRO, enrofloxacin; DABP, 4,4'-bis(di-nbutylamino) SIP, surface imprinted polymer; SLA, stereolithography; SOI, silicon-on-insulator; SPE, solidphase extraction; STEM, stimulated-emission-depletion microscopy; TEA, triethylamine; TED, tetraethylthiuram disulfide; TEM, transmission electron microscopy; TPO, (2,4,6trimethylbenzoyl)phosphine oxide; TPO-L, ethyl (2,4,6-trimethylbenzoyl) phenylphosphinate;

TPS, two-photon stereolithography; UV, ultraviolet; V-50, 2,2'-azobis (2-methylpropionamidine) dihydrochloride; VIS, visible; Z-L-Phe, carbobenzyloxy-L-phenylalanine; μCP microcontact printing; μFP, microfluidic printing; μSL, microstereolithography.

I. Introduction -Molecularly imprinted polymers

Molecular recognition is an underlying phenomenon of many biochemical processes, which has also a number of important practical applications. In Nature, antibodies and enzymes are known to bear binding sites that recognize their respective antigens and substrates with high affinity and selectivity, thus ensuring their physiological functions. [START_REF] Haupt | Molecularly Imprinted Polymers[END_REF][START_REF] Turiel | Molecularly Imprinted Polymers[END_REF][START_REF] Parisi | Molecularly Imprinted Polymers for Selective Recognition in Regenerative Medicine[END_REF][START_REF] Cegłowski | Molecularly Imprinted Polymers as Adsorbents in Mass Spectrometry Techniques[END_REF] These "high-precision" host-guest interactions have inspired the design of many synthetic recognition systems (e.g. aptamers, metal organic frameworks, dendrimers, crown ethers), including molecularly imprinted polymers (MIPs), which are considered one of the simplest though elegant ways to generate synthetic molecular recognition systems. MIPs have been dubbed "plastic antibodies" as they mimic in artificial polymeric matrices the recognition phenomena occurring in natural biomolecules, thus they are an excellent example of biomimicry at the molecular level. Although the first evidence of imprinting was serendipity reported in the early '30s by Polyakov while attempting to modify silica for chromatographic purposes, [START_REF] Polyakov | Adsorption Properties and Structure of Silica Gel[END_REF] the "modern era" of molecular imprinting was launched with the seminal works of Wulff [START_REF] Wulff | The Use of Polymers with Enzyme-Analogous Structures for the Resolution of Racemates[END_REF] and Mosbach 7 in the '70s and '80s.

MIPs are synthetic polymers displaying high affinity and selectivity for analytes ranging from ions, [START_REF] Erdem | Molecularly Imprinted Polymers for Removal of Metal Ions: An Alternative Treatment Method[END_REF][START_REF] Ardestani | Synthesis and Characterization of Nanopore MoVI -Imprinted Polymer and Its Application as Solid Phase for Extraction, Separation and Preconcentration of Molybdenum Ions from Water Samples Fatemeh[END_REF][START_REF] Perera | The Binding of Metal Ions to Molecularly-Imprinted Polymers[END_REF] to small organic molecules, [START_REF] Diliën | Label-Free Detection of Small Organic Molecules by Molecularly Imprinted Polymer Functionalized Thermocouples: Toward in Vivo Applications[END_REF][START_REF] Lu | Visual Detection of 2,4,6-Trinitrotolune by Molecularly Imprinted Colloidal Array Photonic Crystal[END_REF][START_REF] Anirudhan | Extraction of Melamine from Milk Using a Magnetic Molecularly Imprinted Polymer[END_REF] peptides, [START_REF] Rossetti | Exploring the Peptide Retention Mechanism in Molecularly Imprinted Polymers[END_REF][START_REF] Nakamura | Molecularly Imprinted Polymer for Glutathione by Modified Precipitation Polymerization and Its Application to Determination of Glutathione in Supplements[END_REF][START_REF] Sharma | Synthesis and Application of a "Plastic Antibody" in Electrochemical Microfluidic Platform for Oxytocin Determination[END_REF] biomolecules [START_REF] Saylan | Molecular Imprinting of Macromolecules for Sensor Applications[END_REF][START_REF] Tchinda | Recognition of Protein Biomarkers Using Epitope-Mediated Molecularly Imprinted Films: Histidine or Cysteine Modified Epitopes? Biosens[END_REF][START_REF] Ying | Preparation and Specific Recognition of Protein Macromolecularly Imprinted Polyampholyte Hydrogel[END_REF] , up to viruses [START_REF] Gast | Advances in Imprinting Strategies for Selective Virus Recognition a Review[END_REF][START_REF] Graham | Evaluation of Molecularly Imprinted Polymers as Synthetic Virus Neutralizing Antibody Mimics[END_REF][START_REF] Liang | A Virus-MIPs Fluorescent Sensor Based on FRET for Highly Sensitive Detection of JEV[END_REF] and whole cells. [START_REF] Ait Lahcen | Label-Free Electrochemical Sensor Based on Spore-Imprinted Polymer for Bacillus Cereus Spore Detection[END_REF][START_REF] Idil | Imprinting of Microorganisms for Biosensor Applications[END_REF] In the majority of the reports, a template polymerization approach is used, that is, a polymer is synthesized in the presence of a molecular template, which results in the generation of specific 'cavities'. There are a few examples, though, where MIPs have been obtained from preformed polymers which are molded around the template. [START_REF] Hayden | Artificial Antibodies for Bioanalyte Detection -Sensing Viruses and Proteins[END_REF][START_REF] Dmitrienko | A Simple Approach to Prepare Molecularly Imprinted Polymers from Nylon-6[END_REF] In the template polymerization approach, the crucial step in the preparation of a MIP involves the formation of a prepolymerization complex based on non-covalent interactions [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF][START_REF] Włoch | Synthesis and Polymerisation Techniques of Molecularly Imprinted Polymers[END_REF] (or in some cases, reversible covalent bonds [START_REF] Wulff | The Use of Polymers with Enzyme-Analogous Structures for the Resolution of Racemates[END_REF] ) between functional monomers and a target molecule, or a derivative thereof, which serves as the template (Figure 1). This pre-polymerization complex is then polymerized with an excess of cross-linker in order to "freeze" its structure into a three-dimensional rigid matrix. Thus, after polymerization and template removal, cavities are created in the polymer network that are complementary to the template in terms of size, shape and spatial distribution of functional groups. As such, the polymer is effectively "imprinted" and its binding sites locally display a "ligands sphere" able to host the template with affinities comparable to those of antibodies. At the same time, MIPs surpass their natural counterparts in terms of physical stability, physico-chemical and biochemical resistance, robustness and low-cost due to their synthetic polymeric nature. Thanks to these advantages, MIPs have been exploited in diverse applications requiring molecular recognition such as affinity separation, [START_REF] Xie | Magnetic Molecularly Imprinted Polymer Combined with High-Performance Liquid Chromatography for the Selective Separation and Determination of Glutathione in Various Wild Edible Boletes[END_REF][START_REF] Hroboňová | Molecularly Imprinted Polymer as Stationary Phase for HPLC Separation of Phenylalanine Enantiomers[END_REF][START_REF] Boysen | Advances in the Development of Molecularly Imprinted Polymers for the Separation and Analysis of Proteins with Liquid Chromatography[END_REF][START_REF] Sánchez-González | Development of a Micro-Solid-Phase Extraction Molecularly Imprinted Polymer Technique for Synthetic Cannabinoids Assessment in Urine Followed by Liquid Chromatography-Tandem Mass Spectrometry[END_REF] drug delivery, [START_REF] Kurczewska | Molecularly Imprinted Polymer as Drug Delivery Carrier in Alginate Dressing[END_REF][START_REF] Luliński | Molecularly Imprinted Polymers Based Drug Delivery Devices: A Way to Application in Modern Pharmacotherapy[END_REF][START_REF] Bodoki | Perspectives of Molecularly Imprinted Polymer-Based Drug Delivery Systems in Cancer Therapy[END_REF] drugs, [START_REF] Haupt | Molecularly Imprinted Polymers: Antibody Mimics for Bioimaging and Therapy[END_REF] bioimaging, [START_REF] Medina Rangel | Solid-Phase Synthesis of Molecularly Imprinted Polymer Nanolabels: Affinity Tools for Cellular Bioimaging of Glycans[END_REF][START_REF] Wang | Targeted Imaging and Targeted Therapy of Breast Cancer Cells: Via Fluorescent Double Template-Imprinted Polymer Coated Silicon Nanoparticles by an Epitope Approach[END_REF][START_REF] Panagiotopoulou | Fluorescent Molecularly Imprinted Polymers as Plastic Antibodies for Selective Labeling and Imaging of Hyaluronan and Sialic Acid on Fixed and Living Cells[END_REF] cosmetics, 40 catalysis [START_REF] Wang | Molecularly Imprinted Nanocapsule Mimicking Phosphotriesterase for the Catalytic Hydrolysis of Organophosphorus Pesticides[END_REF][START_REF] Mohamed | A Versatile and Recyclable Molecularly Imprinted Polymer as an Oxidative Catalyst of Sulfur Derivatives: A New Possible Method for Mustard Gas and v Nerve Agent Decontamination[END_REF][START_REF] Mathew | Synthesis and Characterization of Enzyme-Analogue-Built Polymer Catalysts as Artificial Hydrolases[END_REF] and chemical sensing. [START_REF] Rico-Yuste | Molecularly Imprinted Polymer-Based Hybrid Materials for the Development of Optical Sensors[END_REF][START_REF] Saylan | Molecularly Imprinted Polymer Based Sensors for Medical Applications[END_REF][START_REF] Uzun | Molecularly-Imprinted Polymer Sensors: Realising Their Potential[END_REF][START_REF] Chiappini | Molecular Imprinted Polymers Coupled to Photonic Structures in Biosensors: The State of Art[END_REF] Figure 1. General scheme for the molecular imprinting of polymers: Functional monomers (FM)

self-assemble around a template (T) to form a pre-polymerization complex which undergoes polymerization in the presence of a cross-linker (CL). Upon template extraction, binding sites become available for the template uptake.

An important aspect to consider when synthesizing a MIP is the way of triggering its polymerization, as this choice affects the reaction conditions and thus the resulting MIP properties.

Except for silica-based MIPs made by sol-gel chemistry (i.e. obtained by hydrolysispolycondensation), imprinted polymers are usually synthesized by electrochemically, thermally, photochemically or redox-initiated chain-reaction. Electropolymerization of electroactive monomers such as pyrrole, aniline or dopamine is a technique based on a redox process or a potential sweep [START_REF] Sharma | Electrochemically Synthesized Polymers in Molecular Imprinting for Chemical Sensing[END_REF] which is especially suited for depositing polymer films directly on electrodes for electrochemical sensors, since it allows controlling the rate of polymer growth, film thickness and film morphology. Unfortunately, this technique is limited to a restricted number of functional monomers, which in turn limits the functionalities available for molecular imprinting. Redoxinitiated radical polymerization is also used for MIPs synthesis, and thanks to its ability to generate radicals under mild conditions, it is especially suited for the imprinting of proteins [START_REF] Ambrosini | Solid-Phase Synthesis of Molecularly Imprinted Nanoparticles for Protein Recognition[END_REF] or peptides [START_REF] Hoshino | Peptide Imprinted Polymer Nanoparticles: A Plastic Antibody[END_REF] in aqueous media.

Conversely to electrochemical and redox polymerization, thermal polymerizations use thermal initiators to generate radicals and initiate the polymerization. Mostly based on azobis-or peroxyderivatives, [START_REF] Székely | Molecular Radical Chain Initiators for Ambient-to Low-Temperature Applications[END_REF][START_REF] Ehlers | Kinetics and Thermodynamics of Radical Polymerization[END_REF] such initiators cover a large range of temperatures thanks to the possibility of modulating their half-lives at a given temperature with changes in their chemical structure.

Thermal polymerization accounts for a great majority of (meth)acrylic and styrenic MIPs, with reaction temperatures usually spanning from room temperature to roughly 60°C.

Photopolymerization is another very common technique for MIPs, wherein radicals are generated upon photo-induced or photo-promoted dissociation of suitable initiating species. This approach has over the recent years gained much importance and is today often the method of choice. So why photopolymerization? There are two main reasons: Firstly, since light is directly responsible for radical generation, the temperature can be set to low values, which protects temperature-sensitive, non-covalent interactions between template and functional monomers, thus improving the imprinting efficiency and the MIP's affinity for its target. [START_REF] O'shannessy | Molecular Imprinting of Amino Acid Derivatives at Low Temperature (0°C) Using Photolytic Homolysis of Azobisnitriles[END_REF] Also, the use of low temperatures (e.g. 0°C to 20°C) [START_REF] Söylemez | Preparation and Detailed Structural Characterization of Penicillin G Imprinted Polymers by PALS and XPS[END_REF][START_REF] Lu | Influence of Polymerization Temperature on the Molecular Recognition of Imprinted Polymers[END_REF] is preferred to avoid degradation of sensitive analytes such as proteins [START_REF] Piletsky | Polymer Cookery: Influence of Polymerization Conditions on the Performance of Molecularly Imprinted Polymers[END_REF] and in some cases, to suppress undesired side reactions. [START_REF] Quinn | The Application of Ionizing Radiation in Reversible Addition-Fragmentation Chain Transfer (RAFT) Polymerization: Renaissance of a Key Synthetic and Kinetic Tool[END_REF] Secondly, owing to their nature, photochemical processes allow spatiotemporal and intensity control over the polymerization reaction. By simply turning on or off the light source, the radical generation can instantaneously be "switched on" or "off" in a much more efficient way compared to the other approaches such as thermal polymerization. This is especially useful in photo-induced controlled radical polymerizations, officially referred to as reversible-deactivation radical polymerizations (RDRP), wherein the molecular weight of growing polymers directly relates to monomer conversion [START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF] and can thus be controlled by the irradiation time. RDRPs are wellestablished in the imprinting field thanks to their ability to easily chain-extend with consecutive blocks and to inherently boost the binding properties of MIPs compared to free radical polymerization (FRP). The reader who is interested in this topic is invited to refer to the following representative review and research articles. [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF][START_REF] Zhang | Recent Advances in Macromolecularly Imprinted Polymers by Controlled Radical Polymerization Techniques[END_REF][START_REF] Zhang | Controlled/"living" Radical Precipitation Polymerization: A Versatile Polymerization Technique for Advanced Functional Polymers[END_REF][START_REF] Salian | The Role of Living/Controlled Radical Polymerization in the Formation of Improved Imprinted Polymers[END_REF] Light can also be confined into limited volumes to arbitrarily initiate localized polymerizations in restricted regions, as seen in various photolithographic and 3D printing techniques (i.e. spatial control). Adjusting the wavelength and the intensity of light sources allows the manipulation of the polymerization rate via controlling the number of generated radicals, similarly to variating the temperature in a thermal polymerization. [START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF]62 All these features, which also include relatively low costs and availability of a range of light sources (i.e. lamps, LED, lasers, UV plasma sources, sunlight), 62,63 make photopolymerization a convenient strategy for precise, hierarchical structuring and even automation in the design and fabrication of MIPs.

II. Photopolymerization of MIPs

II.1. Introduction to photopolymerization

Photoinitiation is a process wherein a light-sensitive system (called a photoinitiator) achieves, upon absorption of a suitable photon, an excited state that leads to a reactive species capable of initiating the polymerization of monomers (i.e. photopolymerization). [START_REF] Frick | Toward a Quantitative Description of Radical Photoinitiator Structure-Reactivity Correlations[END_REF][START_REF] Michaudel | Cationic Polymerization: From Photoinitiation to Photocontrol[END_REF] Depending on the nature of the photogenerated reactive species and on the chosen monomers, the polymerization can follow radical, cationic or anionic acid/base growing mechanism. If this variety provides the user with a wide choice of experimental setups, the reader should be aware that not all previously mentioned techniques are suited to the synthesis of MIPs. Indeed, in order to promote a strong interaction between the template and the functional monomers, the photoinitiating system should not interfere with them. If this can normally be achieved by formulating the photoinitiator in low molar amounts, this requirement can also be met by selecting initiating species that show poor reactivity toward common chemical functionalities in both their fundamental and excited state. Among the cited polymerization pathways (i.e. radical, cationic or anionic), the radical mechanism exhibits the best compatibility with the chemical functionalities borne by the different components of a MIP pre-polymerization mixture, which can be rather complex. Thus, over the years, radical polymerization has become the most viable solution for MIPs, due to its tolerance for many common functional groups as well as to the commercial availability of a wide range of (meth)acrylic and styrenic monomers. [START_REF] Salian | Molecularly Imprinted Polymers via Living Radical Polymerization: Relating Increased Structural Homogeneity to Improved Template Binding Parameters[END_REF][START_REF] Bompart | Molecularly Imprinted Polymers and Controlled/Living Radical Polymerization[END_REF]

II.2. Radical photoinitiators

From the physico-chemical point of view, free radical photoinitiators are divided into two main categories: Type I and Type II photoinitiators. Type I photoinitiators undergo unimolecular homolytic bond cleavage upon excitation, to generate radicals (Figure 2A). They vary considerably in structure but prominent examples are aromatic carbonyl compounds such as acetophenone derivatives, benzoin derivatives, benzylketals, hydroxyalkylphenones and acyl (TPO) and diacyl (BAPO) phosphines. [START_REF] Székely | Molecular Radical Chain Initiators for Ambient-to Low-Temperature Applications[END_REF][START_REF] Karaca | Preparation of Hydrogels by Photopolymerization of Acrylates in the Presence of Type I and One-Component Type II Photoinitiators[END_REF] Azoinitiators, notably AIBN, can also act as photoinitiators beyond being thermal initiators. From a general standpoint, ideal Type I photoinitiators should: (1) feature a high extinction coefficient at the selected (irradiation) wavelength to efficiently generate excited states (singlets), ( 2) provide a high internal conversion from singlets to (dissociative) triplet states, which in turn afford radicals by bond scission and (3) generate highly reactive radicals capable of triggering the polymerization of monomers. [START_REF] Ehlers | Kinetics and Thermodynamics of Radical Polymerization[END_REF][START_REF] Frick | Toward a Quantitative Description of Radical Photoinitiator Structure-Reactivity Correlations[END_REF][START_REF] Barner-Kowollik | The Kinetics of Free-Radical Polymerization[END_REF]

DMPA

Type II photoinitiators on the other hand, do not undergo bond cleavage; instead, they get excited to a triplet state and proceed to hydrogen abstraction from a donor (also known as a co-initiator, usually an alcohol or amine) thus generating an initiating radical (Figure 2B). Since this process involves a bimolecular reaction, Type II activation occurs more slowly than Type I activation and their efficiency is diffusion-controlled. Camphorquinones, benzophenones, thioxanthones and many visible-light-activated initiators are representative examples of this second category. [START_REF] Ehlers | Kinetics and Thermodynamics of Radical Polymerization[END_REF][START_REF] Bagheri | Photopolymerization in 3D Printing[END_REF][START_REF] Esen | One-Component Thioxanthone Acetic Acid Derivative Photoinitiator for Free Radical Polymerization[END_REF] One of the advantages of these systems is to allow extending the wavelength range by the choice of the suitable photosensitizer from the high UV up to the near infrared (NIR) (300 nm -1064 nm). [START_REF] Shao | Polymer Chemistry Photopolymerization : Status , Development And[END_REF][START_REF] Tar | Panchromatic Type II Photoinitiator for Free Radical Polymerization Based on Thioxanthone Derivative[END_REF][START_REF] Allushi | Conventional Type II Photoinitiators as Activators for Photoinduced Metal-Free Atom Transfer Radical Polymerization[END_REF][START_REF] Mokbel | NIR Sensitizer Operating under Long Wavelength (1064 Nm) for Free Radical Photopolymerization Processes[END_REF] On the other hand, the need for one, or more, coinitiators makes Type II photoinitiating systems less suitable than Type I for MIPs. Indeed, the increased number of chemicals required for a Type II photoinitiation, may interfere with the self-assembly process between template and functional monomer(s). A list of Type I and Type II photoinitiators widely used for radical polymerization, together with their excitation wavelengths, has recently been published by Lalevée and coworkers. 63

II.3. Photo-induced controlled/living radical polymerization

FRP has proven over the years to be an extremely versatile and convenient way of synthesizing polymers in general, and also MIPs. However, it suffers from some limitations. For instance, it does not allow controlling the length of polymer chains, the size of polymer nanospheres, or the thickness of polymer layers in composite materials. Also, fine-tuning the surface properties of, and attachment of special functional groups to polymer materials through extension with polymer blocks is difficult. These limitations are inherently related to the reaction mechanism of FRP, wherein 'dead' polymer chains are created by irreversible termination, and where the strong competition between chain growth, irreversible termination and chain transfer, does not allow to control the molecular weight of polymers.

These limitations have been overcome thanks to the development of reversible-deactivation radical polymerizations (RDRPs), previously referred to as 'controlled/living radical polymerizations', which introduced reversible dormant forms for propagating species. Having a high number of such species and only a low number of active radicals, which can quickly and reversibly switch into dormant species, is of capital importance in order to decrease the probability of irreversible termination and uncontrolled chain-transfer. [START_REF] Odian | Principles of Polymerization[END_REF] This has been achieved mainly by two different approaches, namely (1) reversible termination and (2) reversible transfer.

RDRPs thus allow controlling the molecular weight of growing species via the extent of monomer conversion, while simultaneously ensuring low polydispersity on polymer chains (i.e. < 1.3). Various techniques are currently available to perform RDRPs, which will not be detailed here. The reader is invited to refer to the following representative reviews for a wider introduction and deeper discussion on different RDRPs. [START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF][START_REF] Perrier | 50th Anniversary Perspective: RAFT Polymerization -A User Guide[END_REF][START_REF] Corrigan | Reversible-Deactivation Radical Polymerization (Controlled/Living Radical Polymerization): From Discovery to Materials Design and Applications[END_REF] In the case of MIPs, the most frequently applied RDRPs are ATRP, RAFT and Iniferter polymerizations. [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF] Atom Transfer Radical Polymerisation (ATRP) (Figure 3A), which belongs to the family of 'reversible termination', relies on alkyl-halide initiators that are reversibly activated into propagating radicals via a catalyst-mediated redox process (usually a ligated metal complex [START_REF] Sasaki | Highly Selective Bisphenol A -Imprinted Polymers Prepared by Atom Transfer Radical Polymerization[END_REF][START_REF] Adali-Kaya | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites: Atom-Transfer Radical Polymerization with Acidic Monomers[END_REF][START_REF] Zu | Preparation of Molecularly Imprinted Polymer Microspheres via Atom Transfer Radical Precipitation Polymerization[END_REF] or an organo catalyst). [START_REF] Matyjaszewski | Atom Transfer Radical Polymerization (ATRP): Current Status and Future Perspectives[END_REF][START_REF] Ramakers | Laser-Grafted Molecularly Imprinted Polymers for the Detection of Histamine from Organocatalyzed Atom Transfer Radical Polymerization[END_REF] A chain-transfer mechanism operating faster than chain propagation is at the basis of Reversible Addition-Fragmentation chain-Transfer radical polymerization (RAFT) (Figure 3B), wherein dithioesters and trithiocarbonates are used as chain transfer agents ('RAFT agents'). [START_REF] Titirici | Thin Molecularly Imprinted Polymer Films via Reversible Addition-Fragmentation Chain Transfer Polymerization[END_REF][START_REF] Pan | Preparation of Molecularly Imprinted Polymer Microspheres via Reversible Addition-Fragmentation Chain Transfer Precipitation Polymerization[END_REF][START_REF] Gonzato | On the Effect of Using RAFT and FRP for the Bulk Synthesis of Acrylic and Methacrylic Molecularly Imprinted Polymers[END_REF][START_REF] Vaughan | Enhancing Therapeutic Loading and Delaying Transport via Molecular Imprinting and Living/ Controlled Polymerization[END_REF] Conversely to iniferter polymerization (see below), RAFT polymerization requires both a RAFT agent and an exogenous source of radicals (conventional radical initiator) and does not control the termination step.

Iniferters (the term stands for initiator, transfer agent and terminator) (Figure 3C) are situated between these two approaches since they operate through reversible termination and reversible transfer. [START_REF] Otsu | Iniferter Concept and Living Radical Polymerization[END_REF] They can control a polymerization in either a photo-or heat-driven context. Introduced in the early '80s, iniferter polymerization usually involves dithiocarbamates which, irradiated with near-visible UV light, [START_REF] Li | One-Pot Synthesis of Surface-Functionalized Molecularly Imprinted Polymer Microspheres by Iniferter-Induced '"Living"' Radical Precipitation Polymerization[END_REF][START_REF] Pérez-Moral | Molecularly Imprinted Multi-Layer Core-Shell Nanoparticles -A Surface Grafting Approach[END_REF][START_REF] Çakir | Protein-Size Molecularly Imprinted Polymer Nanogels as Synthetic Antibodies, by Localized Polymerization with Multi-Initiators[END_REF][START_REF] Bonomi | A New Versatile Water-Soluble Iniferter Platform for the Preparation of Molecularly Imprinted Nanoparticles by Photopolymerisation in Aqueous Media[END_REF] simultaneously behave as initiator, transfer agent and terminator.

Recently, trithiocarbonates have also been included among (photo)iniferters, since their dissociation can be triggered with visible light. [START_REF] Xu | Catalyst-Free Visible Light-Induced RAFT Photopolymerization[END_REF][START_REF] Garcia-Soto | Synthesis of Molecularly Imprinted Polymers by Photo-Iniferter Polymerization under Visible Light[END_REF] Other examples are thiocarbonylthio, thiuram disulfides, peroxides, tetraphenylethanes, sulfides, phenylazo compounds, amines, alkoxyamines and halides. [START_REF] Otsu | Iniferter Concept and Living Radical Polymerization[END_REF] Overall, the use of RDRPs for the synthesis of polymers and also MIPs has allowed controlling feature size such as the thickness of the polymer layers or the particle diameter, and also tuning their surface-chemistry. In some cases, controlled polymerization also allowed to increase the affinity of the MIP for its target compared to MIPs synthesized by FRP, by favoring a more regular network structure. 27

II.4. The photopolymerization wavelength

While UV light remains a mainstay because many organic species generate radicals upon UV absorption, it also requires caution as absorption by the template and/or functional monomers may result in template degradation and/or monomer self-initiation. [START_REF] Garcia-Soto | Synthesis of Molecularly Imprinted Polymers by Photo-Iniferter Polymerization under Visible Light[END_REF][START_REF] Urraca | Molecular Recognition with Nanostructures Fabricated by Photopolymerization within Metallic Subwavelength Apertures[END_REF] For this reason, visible light has recently risen as an interesting alternative: applying initiators that specifically absorb in the visible spectrum allows to preserve sensitive molecules in solution by specifically triggering a single chemical species. This applies to conventional as well as to controlled radical polymerization, with the latter recently drawing great attention due to the possibility of easily tuning the polymer's features as detailed for instance by Johnson and co-workers. [START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF] Various kinds of initiators exist for visible light photopolymerization such as some organic dyes and many organometallic compounds. Some initiators such as anthraquinone derivatives are actually Type II UV photoinitiators modified with auxochromes and extended π-π bond conjugation to shift their absorption range from the UV to the visible region. [START_REF] Shao | Polymer Chemistry Photopolymerization : Status , Development And[END_REF] The recent use of trithiocarbonates, 97 benzyl tellurides [START_REF] Benedikt | Benzoyl Phenyltelluride as Highly Reactive Visible-Light TERP-Reagent for Controlled Radical Polymerization[END_REF] and diselenide compounds [START_REF] Ding | Diselenide Mediated Controlled Radical Polymerization under Visible Light Irradiation: Mechanism Investigation and α,ω-Ditelechelic Polymers[END_REF] as visibleactive photoiniferters has considerably expanded the use of higher wavelengths for controlled/living polymerizations as well. [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF][START_REF] Chen | Light-Controlled Radical Polymerization: Mechanisms, Methods, and Applications[END_REF][START_REF] Zhang | Recent Advances in Macromolecularly Imprinted Polymers by Controlled Radical Polymerization Techniques[END_REF][START_REF] Bonomi | A New Versatile Water-Soluble Iniferter Platform for the Preparation of Molecularly Imprinted Nanoparticles by Photopolymerisation in Aqueous Media[END_REF] Also, the use of catalysts allowing for photoelectron transfer (PET) processes, as reported for instance by Hawker and co-workers, 100-102 and Boyer and co-workers, 103-107 has helped the application of longer wavelengths in photo-induced controlled radical polymerizations. During PET, light absorption causes a photo-redox catalyst to enter an excited state, which allows oxidizing or reducing a photoinitiator that in turn forms a radical able to start the polymerization. 108,109 The first successful attempt to control polymerization by means of activation/deactivation cycles mediated by blue light was reported by Fors and

Hawker who used fac-[Ir(ppy)3] as a catalyst for the atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA), with ethyl-a-bromophenylacetate as an initiator. 100 Subsequently, Boyer and his team used fac-[Ir(ppy)3] as PET catalyst to thiocarbonyl compounds and thus to reversible addition-fragmentation chain-transfer (RAFT) polymerization. 103,107 Different kinds of catalysts have so far been applied to PET-RAFT polymerization, which have progressively allowed moving from blue to green 110 and red light (e.g. zinc porphyrins 104 ) and up to the nearinfrared (NIR) light thanks to the use of some pigments such as bacteriochlorophylls. 105 NIR is particularly interesting for in vivo applications, as it is known to deeply penetrate biological tissues 111,112 thanks to the so called "biological window", 113 which preserves cells from photodamage and holds great promise for in vivo polymerizations. [START_REF] Bagheri | Photopolymerization in 3D Printing[END_REF] NIR photopolymers have been initially developed for graphic industry 114 and holography. 115 The recent interest for NIR photopolymer systems is due to the potential applications in the field of in-depth photocuring. 116,117 Indeed, as light penetration is higher in the NIR region than in the UV, NIR appears as a good solution to improve the penetration depth and polymerization of thick objects and composites.

Other examples of photopolymerization and photostructuration using NIR lights have also been proposed. [118][119][120] Typical photoinitiator systems contain an NIR dye and a co-initiator.

Carbocyanines (Indocyanine Green) associated to amines have shown their efficiency for polymerization in the 780-850 nm range. Indeed, due to its low energy content, NIR cannot excite a Type I photoinitiator upon a single absorption, conversely to UV or visible light. 121 NIR can also trigger photopolymerization through two-photon absorption, where the simultaneous absorption of two photons allows matching the energy associated with a single UV or visible photon. This phenomenon, similar to photon "upconversion" in the field of fluorescence, thus allows triggering conventional UV or visible photoinitiators via NIR excitation. From the chemical point of view, multiple photon absorption can occur directly on suitable photoinitiators, such as Type I Lucirin TPO 122 and Type 123 or be mediated by exogenous species absorbing multiple NIR photons and returning this energy as UV or visible radiation, like upconverting phosphors. [START_REF] Beyazit | Versatile Synthetic Strategy for Coating Upconverting Nanoparticles with Polymer Shells through Localized Photopolymerization by Using the Particles as Internal Light Sources[END_REF] A compelling example of photopolymerization mediated by NIR light was reported by Torgensen et al. who photopolymerized via two-photon polymerization a hydrogel which partially trapped the roundworm Caenorhabditis elegans as a model living organism. 124 C. elegans kept moving during the photopolymerization, while a short segment of its body was progressively immobilized into the growing hydrogel. This remarkable result proved that it was possible to drive a photopolymerization with NIR light in the presence of and through a living sample. The application of two-photon polymerization to the synthesis and structuring of MIPs will be discussed later in this review.

An interesting route for visible-light driven photopolymerization consists in using the emission of fluorescent nanoparticles upon excitation with shorter or longer wavelengths. For example, quantum dots (QDs) are fluorescent semiconductor nanocrystals able to emit visible light of a certain wavelength (depending on the size of the QDs) upon excitation by UV light. [125][126][127] Polymerization can thus be initiated by the emitted fluorescence light by using a suitable initiator that is activated by visible but not by UV light. 128 On the other hand, visible light-driven photopolymerization can also be achieved upon upconversion. Upconverting phosphors (UCPs) are lanthanide-or actinide-based nanoparticles capable of converting low-energy radiation (such as infrared) into high-energy radiation (such as visible light) through absorption of multiple photons or through energy transfer. 129,130 Again, a suitable initiator activated by visible light is needed to start the polymerization. 70

II.5. Photopolymerization of MIPs

As previously mentioned, photopolymerization is an attractive technique for the synthesis of MIPs. Table 1 shows a selection of examples of photopolymerized MIPs with their monomers, initiators, and polymerization conditions, and imprinting template. Despite an increasing interest over the recent years in exploring different controlled photopolymerization mechanisms as outlined in the next section, free-radical polymerization (FRP) continues to be the most widely used polymerization approach to MIPs. [START_REF] Salian | Molecularly Imprinted Polymers via Living Radical Polymerization: Relating Increased Structural Homogeneity to Improved Template Binding Parameters[END_REF] Its regular setup includes a light source, a photoinitiator and a solution of template and monomers. Light sources can be lamps, LEDs or lasers that emit at specific wavelengths in the UV or the visible range depending on the activation wavelength of the initiator. UV-A photopolymerization of MIPs can also proceed via controlled radical polymerization. As mentioned above, controlled radical polymerization allows controlling the molecular weight of growing chains, and provides access to block copolymers via chain-extension of polymers, which behave as macro-initiators ('living character'). It has also been shown that binding capacity and binding affinity may be improved compared to classical FRP, through an improved network structure. [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF] Nevertheless, its main advantage over the latter technique is the chain-extension capability, which allows tuning the chemistry and reactivity of the MIP surface. [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF] Photoiniferter polymerization was the first controlled polymerization technique applied to the synthesis of MIPs in 1997 by Wang et al. [START_REF] Beyazit | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites by Controlled/Living Radical Polymerization[END_REF] A great majority of photoiniferters used for MIPs rely on benzyl-derived dithiocarbamates and require an excitation near 365 nm. [START_REF] Çakir | Protein-Size Molecularly Imprinted Polymer Nanogels as Synthetic Antibodies, by Localized Polymerization with Multi-Initiators[END_REF][START_REF] Bonomi | A New Versatile Water-Soluble Iniferter Platform for the Preparation of Molecularly Imprinted Nanoparticles by Photopolymerisation in Aqueous Media[END_REF][146][147][148] For instance, the iniferter diethyldithiocarbamate (DEDTC) was exploited by Kidakova et al. to Some papers still refer to photo-RAFT even though no external radical source is involved: in these cases, a RAFT agent is irradiated with UV light thus triggering its own decomposition which should be rather described as photoiniferter synthesis. [149][150][151] ATRP is another widely used technique for the controlled radical polymerization of MIPs.

Despite its wide success, this technique historically suffered the catalyst's incompatibility with acidic monomers such as MAA (which is arguably the most commonly used functional monomer for MIPs), which greatly limited its applicability to the molecular imprinting field. However, a breakthrough was reported in 2012, when

II.5.2. Visible and NIR light mediated photopolymerization of MIPs

There is currently a growing interest in the use of visible light for photopolymerization in the MIP field due to its considerable advantages over conventional UV polymerization. The lower energy of visible light allows for more specific light-induced processes. As opposed to UV radiation, visible light is less likely to alter the ingredients of the MIP precursor mixture other than to initiate polymerization. Moreover, the now widely available LEDs as visible-light sources generate less heat and thus help avoiding thermal effects on polymerization.

Urraca and co-workers exploited for instance a system composed of Eosin Y and methyldiethanolamine as a Type II initiator to synthesize a MIP using a 532-nm green laser. To do that, they coated an aluminum film featuring nanoholes laid on top of a glass substrate with a precursor mixture containing the initiating system, the template rhodamine 123, MAA, the crosslinker EGDMA and acetonitrile (ACN). The laser beam was then directed onto the glass slide to synthesize sub-micron MIP dots for the fluorescent assay of rhodamine 123. [START_REF] Urraca | Molecular Recognition with Nanostructures Fabricated by Photopolymerization within Metallic Subwavelength Apertures[END_REF] Wei's group chose a photo-redox couple sensitive to red light based on methylene blue/p-toluenesulfinate for the surface functionalization of SPR chips with theophylline-imprinted polymers. The aqueous pre-polymerization mixture composed of the template, MAA, MBAAm and the photo-redox initiator system was sandwiched between an SPR gold chip and a cover glass which was peeled off after polymerization. Irradiating with a red laser beam of 633-nm wavelength resulted in the formation of a MIP for theophylline. 152 There are only very few Type I visible-light photoinitiators with wavelengths above the blue region, one of them being the titanocene initiator at 532 nm (Table 1). 138 As mentioned above, an interesting route for visible-light driven photopolymerization consists In this way, the AB monomer included in the first shell was used to anchor the template for the synthesis of a second, imprinted shell. Measurements with fluorescein isothiocyanate-labelled trypsin showed that the UCP-MIPs were selective for trypsin over other serine proteases such as kallikrein and thrombin. [START_REF] Beyazit | Versatile Synthetic Strategy for Coating Upconverting Nanoparticles with Polymer Shells through Localized Photopolymerization by Using the Particles as Internal Light Sources[END_REF] In a similar context, NIR can be upconverted to blue and even near UV light and used to locally trigger photopolymerization (see previous section). [START_REF] Beyazit | Versatile Synthetic Strategy for Coating Upconverting Nanoparticles with Polymer Shells through Localized Photopolymerization by Using the Particles as Internal Light Sources[END_REF] In this perspective, Gou's team reported using a 'bioink' consisting of UV-sensitive photoinitiator-coated UCPs and gelatin methacryloyl for the subcutaneous in vivo polymerization of projected NIR constructs. 155 The NaYF4:Yb,Tm-based UCPs upconverted 980-nm NIR into UV light between 340 nm and 375 nm allowing the photoexcitation of lithium phenyl-2,4,6-trimethylbenzoylphosphinate that was previously electrostatically adsorbed on the positively charged UCPs. Since NIR can penetrate the skin tissue, subcutaneous injection of the bioink into mice and the subsequent exposure of the injected area to NIR constructs resulted in the polymerization of triangular, cross-shaped and double-layered microstructures. The application was further extended to the in vivo polymerization of ear-like tissue and scaffold for muscle defect repair by adding chondrocytes and adipose-derived stem cells, respectively, to the bioink formulation. In all cases, there were no apparent adverse effects to the surrounding tissues nor to the vital organs studied for a period up to a month. The work served as a proof-of-concept for non-invasive in vivo 3D bioprinting with the aid of UCPs. 155 In another example, Tang et al. fabricated core-shell MIP nanoparticles based on the UCP NaYF4:Yb 3+ ,Er 3+ that would serve as fluorescent probes for sensing quinolones in fish samples (Figure 6). The UCPs were first coated with an ultrathin silica shell doped with Fe3O4 to render it magnetic for easy handling.

II.6. Limitations of photopolymerization of MIPs

Despite the obvious advantages mentioned above, photopolymerization has also a number of limitations, both in general and from a MIP point of view. General limitations are more of the technical kind, such as the limited penetration depth of light into bulk solutions and suspensions (physical barrier). This is dependent on the wavelength (visible light usually penetrates better than UV), and may require special reactor designs to ensure homogeneous irradiation and high polymerization yields. As a result, photopolymerization has been more widely adopted to the synthesis of micro and nanostructures and to the patterning of polymers, than to the synthesis of bulk materials.

Specifically in the MIP field, there are a number of additional factors to be taken into account.

Since most organic molecules absorb at least UV light, the template molecule used to generate the MIP may be sensitive to the irradiation during photopolymerization, in particular with UV initiators. On the other hand, photopolymerization at higher wavelengths of the visible spectrum mostly use Type II photoinitiators (a notable exception being the titanocene initiator at 532 nm 138 , see Table 1). These require a co-initiator (often an amine), which renders the polymerization solution more complex and may even interfere with the template-monomer assembly.

III. Photostructuring MIPs

The different means of tuning a photopolymerization (i.e. spatiotemporal, wavelength, intensity, pulsating) make this process a favorable strategy for the structuration of polymers and their intelligent design and engineering into arbitrary patterns. Adding photostructuration to molecular imprinting opens the possibility for non-contact high-resolution fabrication of micro-and nanostructures, [START_REF] Saylan | Molecularly Imprinted Polymer Based Sensors for Medical Applications[END_REF][START_REF] Söylemez | Preparation and Detailed Structural Characterization of Penicillin G Imprinted Polymers by PALS and XPS[END_REF] with applications ranging from microelectromechanical systems (MEMS), to microfluidic channels, to transducers in sensors, etc. When MIPs are structured to have dimensions in the micro-/nano-range, their effective surface-to-volume ratio increases. This allows providing a high number of binding sites with only a limited mass of MIP, which in turn improves their sensitivity, binding kinetics and binding site regeneration. [159][160][161] Furthermore, since light can be projected onto a surface, it also allows for an easy in situ polymerization of structures on substrates. 162 Thanks to these advantages, one of the obvious applications of photo-structured MIPs deals with chemical sensing. A chemical sensor, as defined by the IUPAC, is a "device that transforms chemical information, ranging from the concentration of a specific sample component to total composition analysis, into an analytically useful signal. The chemical information, mentioned above, may originate from a chemical reaction of the analyte or from a physical property of the system investigated." 163 Chemical sensors are usually composed of two main functional units: a sensing element in charge of transforming the chemical information into a form of energy, and a transducer, which is responsible for translating this energy into an analytical signal. In the context of chemical sensing, it is desirable that the recognition element be optimally exposed to the sample while remaining well attached to the transducer, to effectively generate a signal upon interaction with its target. Assembling the recognition element into a structure, whether simple or hierarchical, thus needs to take into account the above requirements and is therefore a crucial step. MIPs as recognition elements offer several advantages over their biological counterparts, as they can be easily synthesized in a wide range of physical forms (e.g. bulk, micro-/nano-particles, membranes, films, complex 2.5D and 3D elements, etc.) and interfaced on a wide variety of substrates, owing to their "synthetic" nature which also comes with superior physico-chemical properties.

III.1. Introduction to photolithography

Photolithography is a powerful technology for the fabrication of sophisticated 2D and 3D

structures at the micro-and the nanoscale with the aid of light. 164 There exists a myriad of photolithographic techniques, which can be categorized into either "mask" or "maskless" techniques (Figure 7A). Conventional photolithography uses masks to transfer a pattern onto a given surface, by selectively allowing the transmission of light from a source onto a photosensitive material which is usually spread on top of a substrate. Depending on the nature of the material, the illuminated areas will either cross-link and harden, or become susceptible to removal. This is often followed by an etching step that eliminates the exceeding parts and reveals the actual pattern. Such techniques are grouped according to the placement of the mask between the light source and the photoresist into: (i) contact photolithography, (ii) proximity lithography and (iii) projection lithography (Figure 7B). Conventional photolithography is known as a "parallel" process, as it fully transfers the pattern of a mask onto a photoresist upon a single light exposure. 165,166 As such, it guarantees high throughput and high resolutions, which makes it the dominant fabrication method in microelectronics. 165,167,168 Unfortunately, photolithography can be costly as its setup often requires the use of clean rooms to prevent contamination from particulates and guarantee the quality of printed structures. 169 The main drawback of photolithography is its diffraction-limited resolution. For proximity lithography for instance, which is carried out within the near-field (Fresnel) diffraction regime, the achievable resolution (R) is (Equation 1):

𝑅 ≈ √𝜆𝐿

(Equation 1)

where λ is the wavelength of the source and L is the distance between the mask and the resist (usually 2-4 μm). This means that the lateral resolution for proximity lithography can be several times the used wavelength. In contact photolithography on the other hand, the mask directly touches the resist, thus bringing the resolution to the order of magnitude of the wavelength. The resolution (R) of projection lithography (and of all other lens-based lithographies) is governed by far-field (Fraunhofer) diffraction and constrained by the Rayleigh equation (Equation 2): 2) where "k1" is a process-dependent factor (with values typically between 0.25 and 0.8), "n" is the refractive index of the medium, "q" is the half-aperture angle of the lens or optical imaging system used and "NA" corresponds to its numerical aperture. This places the resolution around half the wavelength of the source. [170][171][172] Many approaches have been developed by specifically targeting the different parameters of Equation 2to improve lateral resolution, which afforded techniques such as deep and extreme UV lithography, phase-shift lithography or immersion lithography. As a result, resolutions down to 10 nm can now be achieved. 168,173 Deep and extreme UV lithography utilize for instance short wavelengths (193 nm and 13.5 nm, respectively). Phase-shift lithography on the other hand relies on lowering the k1 parameter by using optically transparent masks which are micro-/nanostructured on their surface. 171,173 Such masks modify the light optical path via destructive interference, thus enhancing the sharpness of the replicated image. Immersing the mask projection system in a fluid with a refractive index higher than 1 (i.e. higher than air) also improves resolution as it occurs for immersion lithography. 171,174 In contrast to the previous techniques, maskless lithography does not require any physical mask, as it relies on focusing a beam of photons or charged particles within a photoresist in order to construct patterns. Interference lithography, a photon-based technique, exploits the interference patterns of coherent optical beams incident at various angles within a photoresist. The resulting pattern may extend in 2D or 3D depending on the thickness of the reactive layer and it is generally further developed by thermal or chemical treatment in order to remove the unreacted photoresist.

𝑅 = 𝑘 1 𝑘 𝑛𝑠𝑖𝑛𝜃 = 𝑘 1 𝜆 𝑁𝐴 (Equation
Also considered a "parallel" process, interference lithography represents a fast, straightforward and accurate approach for quasiperiodic structures with resolution below 10-nm, making it attractive for fabricating photonic crystals and metamaterials. 175 Another photon-based, maskless technique is stereolithography (SLA). In SLA, a computer-generated 3D design is "directly written" into a photoresist by focusing a laser beam of appropriate wavelength while following a sequence of stacked 2D layers which are thus photoprinted successively on top of each other by moving a "z" stage. SLA can operate via one-photon or multiphoton absorption. In one-photon stereolithography, a laser source (usually UV) is used to induce a cross-linking based on simple, one-photon absorption, as it occurs in ordinary photopolymerizations. On the other hand, multiphoton SLA (MSLA) involves the simultaneous absorption of multiple photons of low energy, which virtually matches a "single", high-energy photon absorption. A prominent example of multiphoton SLA is the two-photon stereolithography (TPS) (Figure 8). In this technique, the use of a femtosecond laser (usually with wavelengths in the NIR around 800 nm) allows for a twophoton absorption, which corresponds to the mono-absorption of a 400-nm photon. Such twophoton absorption thus allows reaching the energy threshold required to trigger the dissociation of an ordinary, near UV-active photoinitiator such as TPO-L. Many works have been dedicated to develop specific photoinitiators exhibiting a high two-photon absorption cross-section. Unlike one-photon stereolithography, MSLA has the advantage of being exclusively confined within the (small) focal point of the beam (i.e. less than 1 μm 3 ) where high intensities promote a two-photon absorption process (Figure 8B). Thus, multiphoton SLA enables a highly localized polymerization of the photoresist, which is essential for the direct writing of elaborate 3D geometries (Figure 8D).

However, multiphoton SLA only affords a resolution of a few hundred nanometers and provides a low throughput as it belongs to "serial" processes, which operate with a multi-exposure to light for the voxel-to-voxel printing of the resist. 165,166 Nevertheless, MSLA is compatible with a wide variety of photoresists including (meth)acrylates, epoxides, organically modified silica and organically modified ceramics. [175][176][177] While the lateral resolution for traditional TPS can be as small as a few hundred nanometers, reduced the resolution based on the Rayleigh equation (Equation 2) by using a 520-nm laser source whose dosage had been optimized against a resist containing the photoinitiator DABP. 180 Jiang et al. took advantage of polythiols to provide a photoresist with oxygen tolerance as well as to expand the writing range, while enabling the use of near-threshold laser dosages for the production of mechanically stable fine lines. 181 A different approach was instead used by Liu and co-workers, who deliberately fabricated photonic woodpiles with an intralayer rod distance of 1.57 μm which decreased to 350 nm by thermal-shrinking at 450°C, resulting in the appearance of a visible color due to the woodpiles. 182 Defying the diffraction limit, near-field-assisted optical lithography may also be included among light-based lithography techniques, which can be used in different configurations, including mask and maskless approaches. This technique triggers a polymerization using the evanescent wave which can be generated in different configurations. By its nature, the optical near-field is not governed by the classical diffraction limit, which permits to reach high resolution (down to the lower nm scale using visible light). Total internal reflection of light at the interphase between two media with different refractive indices and which propagates into the medium of lower index can be used to generate near-field irradiation. 183 This technique allows for a highly confined polymerization (i.e. few tens of nm), as the energy of the evanescent wave which tails from the interphase decays exponentially. 184,185 Metal nanostructures excited in their resonance plasmonic bands are also very interesting to generate near-field excitation with nanoscale resolution, as described in several examples. [186][187][188] The near-field being generated at the surface of the metal structure, in hot-spots, this method is quite efficient to couple polymer materials with metal nanostructures, with a precise control of the polymer position in proximity of the nanostructure. 189 Finally, maskless techniques can also rely on charged particles, such as electron-beam lithography (EBL) and focused-ion-beam lithography (FIBL). In EBL, a beam of accelerated electrons is scanned on the surface of a resist, such as polymethylmethacrylate (PMMA), in order to alter its solubility. Upon development, a pattern is created in the resist, which can in turn be transferred to a substrate upon further etching. FIBL is analogous to EBL but it applies an accelerated beam of ions, such as He + and Ga + . FIBL can also be used to deposit materials such as tungsten, platinum and carbon on a surface. This is typically achieved upon interaction between a focused ion beam and a gaseous precursor in proximity to a surface, wherein the precursor decomposes. 190 EBL and FIBL can achieve high resolutions, with features below 10 nm, but they remain costly and rather difficult to miniaturize. Similarly to SLAs, they also have low throughputs. 168,171 Representative examples of the above techniques triggered by light and applied to the synthesis or functionalization of MIPs will be discussed in the following paragraphs.

III.2. Mask lithography of MIPs

III.2.1. Contact and proximity photolithography

A straightforward technique for photostructuring MIPs is contact lithography. Contact photolithography involves the use of a photomask touching the surface of a photoresist. Upon irradiation with a suitable wavelength, the exposed zones of the resist undergo polymerization, which results in transferring a pattern from the mask to the underlying polymer (i.e. MIP). This approach involves the use of what is called a negative tone resist, which upon washing with a "developing" solution affords polymeric structure features as the inverse pattern of the mask.

Similarly, positive tone resists also exist, which work in the opposite way, i.e. the exposed zones become soluble and can be removed with the developing solution. Despite being conceptually simple, contact photolithography requires a complete and direct contact between the resist and the photomask to avoid defects and contamination, but this can sometimes be particularly tricky. To avoid such mishaps, proximity printing can be used, which overcomes the above limitations by including a small gap between the resist and the mask during the photostructuring step (Figure 7B). The gap must be as small as possible to preserve the resolution but big enough to prevent defects and contamination. in both cases. The spin-coated formulations were both cured at 365 nm, but only for the second one a 300-mesh TEM gold grid was used as a mask, which resulted in a double layered MIP system consisting of a series of patterned squares (MIP2) on top of a continuous film (MIP1). Upon incubation with N-dansyl-L-phenylalanine, fluorescent microscopy images revealed that the squares had a much higher fluorescent intensity than the underlying film (Figure 9B), thus suggesting that 4-VP had a higher affinity for the target, as supported by molecular modelling and In another work, Liu's group fabricated thin-film arrays on a pre-treated glass slide or filter membrane by light-curing a pre-polymerization solution while covering it with a patterned photomask. The MIP was based on boronic acid as functional monomer, which is known to interact with cis-diols such as present in certain sugars via reversible covalent bonds. These imprinted arrays were used for the colorimetric detection and chemiluminescent assay of five glycoproteins, with the test exhibiting a limit of detection as low as 1 ng mL -1 for one of the glycoproteins. 193 More recently, Nicu and his team integrated MIPs into arrays of nanocantilevers (Figure 10) for a label-free detection via functionalized resonators. 194 To achieve this, a 100-mm silicon-on-insulator (SOI) wafer was dry-etched to shape a cantilever and silanized with 3-(trimethoxysilyl)propyl methacrylate to anchor an organic MIP. The cantilever was then spincoated with a monomer mixture and placed under an automatic mask aligner for photolithography.

Upon photopolymerization and wet etching of the sacrificial oxide layer, a MIP coated cantilever was obtained which worked as a nanoelectromechanical system (NEMS) for sensing the fluorescent N-dansyl-L-phenylalanine. Preliminary results showed that while the mechanical sensing on cantilevers required further optimization due to the damping by the polymer, a direct fluorescence measurement of the target confirmed a successful imprinting, with the MIP cantilever emitting about 3.5 times stronger fluorescence intensity than the corresponding NIP cantilever.

III.2.2. Projection photolithography

In projection photolithography, the photomask is placed at a certain distance from the resist while an optical system is located in between to focus the pattern image from the mask onto the resist (Figure 7B). In this way, it is possible to overcome the mechanical and diffraction issues encountered in contact and proximity photolithography, which improves the whole resolution. For instance, Haupt's group combined microscope projection photolithography with nanomolding to prepare arrays of MIP nanofilaments (Figure 11A-B) by inserting a photomask into the fielddiagram plane of a microscope. In this way, UV light from the mercury lamp of the microscope could pass through the unmarked areas of the mask and polymerize 70 nm-dots from a methacrylate-based precursor solution. The light was also filtered with an IR mirror to prevent thermal polymerization. Since the precursor was deposited on a nanoporous alumina substrate, the polymerized spots were composed of upright MIP nanofilaments (Figure 11C-E) whose structure provided a large surface area and an easy diffusion of the targets fluorescein or myoglobin. This approach also allows decreasing the size of the projected pattern (i.e. the size of the dots) by simply using higher magnification objectives, as well as improving the whole resolution by using higher numerical apertures. 195

III.3.2. One-photon stereolithography

Microstereolithography (µSL) is another approach for fabricating 3D structures by localized photopolymerization using a sharply focused laser beam. A 3D model of the desired shape is initially sliced into consecutive 2D layers by a computer-aided design (CAD) program. A laser beam of the appropriate wavelength is then focused in a precursor solution a few micrometers above a microscope slide to write the first 2D layer. This allows minimizing light scattering, for an improved resolution, while also preventing a premature polymerization of the second 2D layer. 177,197,198 The motion of the substrate along the z-axis then allows the structure to grow to 3D.

Shea and co-workers were the first to use this technique for MIPs, manufacturing 600 µm x 600 µm 2D and 3D (today considered 2.5D) grids (Figure 13) imprinted with 9-ethyladenine using a 364-nm Ar+ laser and an x-y-z motorized stage to explore the possibilities of miniaturization, which is important in sensing and diagnostics as it limits both energy consumption and production costs. Recognition of the target 9-dansyladenine was evaluated through a fluorescence assay which showed that the MIP grids had affinity for the target comparable to bulk MIPs. 162,199

III.3.3. Multiphoton stereolithography

The MIP photostructuring methods described so far were based on single-photon absorption.

However, as outlined in section 3.1, fabrication of 3D structures by multiphoton stereolithography has recently gained great attention. Multiphoton stereolithography (MSLA) relies on a multiphoton absorption process highly confined within the focal volume of a laser beam passing through a microscope objective. It is therefore a true 3D fabrication approach since complex structures can be manufactured by moving the laser focus in three dimensions. The best-known example is twophoton stereolithography (TPS). The use of TPS in molecular imprinting is relatively new, even though the technique has already been reported in several different applications such as scaffolding for cells, 200,201 shape-shifting of microstructures for proteins, 202 biocompatible hybrid materials, 203 tomography, 204 and optics. 205,206 This technique was first applied to the synthesis of MIPs by Chia Gomez et al., who showed its versatility by fabricating different structures such as grids, dot arrays and cantilevers smaller than 60 µm (Figure 14). Lucirin TPO was used as a photoinitiator for a laser wavelength of 800 nm. An array of dots forming the words MIP (imprinted dots, with Z-L-Phe as template) and NIP (non-imprinted dots) were for instance printed, which upon incubation with a fluorescent template analogue (i.e. dansyl-L-Phe) only emitted green light in the case of the MIP (Figure 14B). Interestingly, MIP cantilevers, a format which normally requires timeconsuming and multi-step processes to be made, were also conveniently fabricated by TPS and allowed the straightforward sensing of their target Z-L-Phe as shown by a frequency shift exquisitely limited to the MIP (Figure 14D). 122,179,196,207 carrying a prism of the same index (Figure 15A). An actinic laser of 405 nm was internally reflected within the prism-slab system, allowing for the evanescent wave at the slab-precursor interface to initiate polymerization, leading to microdots of sub-100 nm thickness (Figure 15B-E).

The MIP microdots showed selectivity and some degree of enantiospecificity toward their target, dansyl-D-phenylalanine. The method allowed for quick fabrication (within tens of seconds) of MIPs as thin as <100 nm. 183

IV. Conclusions

From the synthetic point of view, MIPs are compatible with a variety of structuring techniques, particularly with photon-based lithographic approaches as we presented in detail in this review.

These techniques allow not only fabricating micro-and nano-structures with high capacity and sensitivity, due to favorable surface-to-volume ratios, but also shaping and pattering MIPs for generating a direct, analytical signal upon binding, which is essential for some applications such as sensing.

Each photon-based lithographic technique has its own strengths and weaknesses and this review is intended to help the reader to make his choice depending on his purpose. With its highthroughput and the different possibilities of improving resolution, conventional photopolymerization and photolithography are expected to continue flourishing in MIP fabrication. Focusing on the light sources associated with these techniques, a great majority of them use UV light to trigger the polymerization, but longer wavelengths such as visible and NIR are gaining attention in MIP synthesis, as they are more suited for processing mixtures containing sensitive templates such as bio(macro)molecules and are inherently safer.

Finally, stereolithographic techniques offer the most convenient solution to the direct writing of sophisticated architectures. Although limited by a low-throughput and rather expensive setups, stereolithography allows for direct, one-step prototyping of 2.5D and 3D structures. Among these techniques, TPS has risen as a "high-precision" technique which allows confining the polymerization to the focal point (voxel) of the used laser. Due to the multi-photon absorption process involved in TPS, NIR lasers can be used as sources to trigger near-UV or visible photoinitiators, which is advantageous when working with bio-based mixtures or even with living cells. More importantly, if strategies to improve the current TPS resolution can be standardized, it will be possible to shape materials with structural features able to rise optical properties falling directly in the visible spectrum, for a systematic tuning of molecularly imprinted optical sensors.

  ABBREVIATIONS

Figure 2 .

 2 Figure 2. The initiating mechanism of a representative (A) Type I photoinitiator (dimethoxy-2-

Figure 3 .

 3 Figure 3. Mechanisms of various kinds of RDRP: (A) ATRP, (B) RAFT, and (C) iniferter polymerization.

1 .

 1 photopolymerization (i.e. wavelength around 365 nm), as many photoinitiators are active in this region, while monomers such as acrylates absorb weakly and are therefore relatively stable.139

Figure 4 .

 4 Figure 4. The fabrication process of an imprinted microtip by guiding UV through an optical fiber

  control the thickness of MIP growth in combination with microcontact printing for the imprinting of bovine serum albumin (BSA). A chlorinated diazonium salt was electrochemically reduced onto a gold substrate for grafting DEDTC on the surface. Meanwhile, BSA was immobilized on a separate glass slide via an epoxy-silane linker. An aqueous precursor solution consisting of 2-(diethylamino)ethylmethacrylate (DEAEM) and MBAAm was sandwiched between the DEDTCmodified gold substrate and the BSA-modified glass slide before exposure to 365-nm UV light.After peeling off the glass slide bearing the BSA molecules, the resulting thin MIP on the gold substrate allowed sensing the protein by surface plasmon resonance (SPR). The sensor displayed a rather narrow dynamic range between 2.5 nM and 25 nM and an adsorption capacity for BSA only twice that of similar proteins (i.e. human serum albumin and the Fc fragment of immunoglobulin G), indicating limited selectivity.131 RAFT polymerization is one of the most popular controlled radical polymerizations and operates with a chain transfer mechanism similar to that of iniferter. There are no examples on photo-RAFT polymerization of MIPs in the UV range, most examples using visible light, as outlined below.

  in using the emission of fluorescent nanoparticles upon excitation with shorter or longer wavelengths.Panagiotopoulou et al. used two kinds of QDs to locally grow a MIP shell around them by excitation with UV in the presence of visible-light-active, Type II photoinitiators (Figure5) set off by the fluorescent light of the QDs. Since the light intensity emitted by the QDs decreases with distance, polymerization only took place in close proximity to the QDs. In their experiment, they used InP/ZnS QDs (red and green emitting QDs) combined with two photo-initiating systems: respectively a methylene blue/trimethylamine (TEA) and an Eosin Y/TEA tandem. Thus, after growing a first hydrophilic shell based on poly[2-hydroxyethylmethacrylate-co-N,N'-ethylene bis(acrylamide)] by irradiating with 365-nm UV light, they then synthesized thin MIP shells imprinted with N-acetylneuraminic acid (NANA) on red emitting QDs and glucuronic acid (GlcA) on green emitting QDs as a second layer. Thanks to the embedded emission properties of the resulting imprinted composites, both red and green MIP-coated QDs were applied as biocompatible imaging agents for the multiplexed detection of glycosylations in cells.128 The same principle was employed to synthesize thin MIP shells directly around carbon dots (CDs),153 and very recently, around individual protein molecules. The latter was possible by using proteins (myoglobin, lactoferrin) surface-derivatized with Eosin, as macroinitiators. After removal of the template protein, the resulting nanogel particles contained on average one binding site and specifically recognized their target protein.154

Figure 5 .

 5 Figure 5. General scheme for the synthesis of a polymer shell around red and green InP/ZnS emitting

  They were then added to a MIP precursor composed of the template enrofloxacin (ENRO), MAA, EGDMA and benzophenone in dichloromethane (DCM)/TEA. The setup was exposed to a 980-nm infrared radiation, upon which the UCPs emitted light mainly at 405-nm, triggering the formation of the MIP layer on the surface. The resulting MIP UCPs were able to detect and measure ENRO together with other quinolones since these target molecules, through their hydrogen bond with the functional groups found in the binding sites, could quench the fluorescence of the MIP UCPs when exposed to 980-nm NIR. The MIP UCPs exhibited fast response, high selectivity and specificity towards five quinolones.132

Figure 6 .

 6 Figure 6. Schematic representation of the fabrication of the MIP magnetic upconverting

Figure 7 .

 7 Figure 7. A: Classification of different photolithographic techniques. B: Comparison of different

Figure 8 .

 8 Figure 8. (A) Jablonski diagram showing electronic excitation via two-photon absorption. (B-C)

  Ayela's group has pioneered contact photolithography of MIPs, at the wafer scale, fabricating consecutively multiplexed patterns of different MIPs on the same silicon wafer, with a µm resolution. This was done by UV photopolymerization of spin-coated monomer films under nitrogen atmosphere, using standard photolithography equipment with a mask aligner.191 More recently, Hearn and co-workers applied contact lithography to the synthesis of a double-layered MIP thin film in the form of a grid-patterned surface, with the aim of developing a tool for the direct and visual comparison of different functional monomers toward the binding of the fluorescent target N-dansyl-L-phenylalanine (Figure9A).192 Their strategy relied on the spincoating and curing of two consecutive prepolymerization mixtures based on different functional monomers: first, a formulation based on methacrylic acid (MAA, i.e. MIP1), then a second based on 4-vinyl pyridine (4-VP), with N-boc-L-phenylalanine as a non-fluorescent template analogue

Figure 9 .

 9 Figure 9. (A) Schematic representation for the preparation of a grid-patterned double-layered

Figure 10 .

 10 Figure 10. SEM images of (A) a MIP-coated silicon cantilever obtained by photolithography and

Figure 11 .

 11 Figure 11. Schematic representation of the preparation of (A) porous microdot arrays and (B)

Figure 12 .

 12 Figure 12. (A) Scheme showing the in situ MIP microstructuring process by interference lithography

Figure 13 .

 13 Figure 13. (A) SEM image of a 3D imprinted microstructure (600 μm x 600 μm x 100 μm) fabricated

Figure 14 .III. 3 . 4 .

 1434 Figure 14. (A-B) Multiplexed NIP and MIP dots polymerized on the same sample by two-photon

Figure 15 .

 15 Figure 15. (A) Schematic representation of the setup for the polymerization of MIP microdots by

Table 1 .

 1 Non-exhaustive list of recent examples (from 2013 to 2018) of MIPs synthesized via photopolymerization.

	Mechanism of Polymerization	Initiator	Initiator type Light Source (nm)	Monomer Composition	Template	Solvent	Use	Ref
	RDRP: SFRP		I	UV (365)	DEAEM, MBAAm	BSA	Ultrapure water	Surface film	131
		Grafted DEDTC (iniferter)
	FRP	Benzophenone (TEA as	II	NIR (980) upconverted to VIS (405)	MAA, EGDMA	Enrofloxacin	DCM	Core-shell nanoparticles
		hydrogen donor)

  Fors and Hawker noticed that the photocatalyst fac-[Ir(ppy)3] could tolerate MAA much better than previous catalysts, making possible the synthesis of PMAA of around 30 000 kDa with a PDI as low as 1.61. 100 Taking advantage of the robustness of fac-[Ir(ppy)3], Adali-Kaya et al. thus reported on the synthesis of MIPs specific for S-

propranolol and testosterone, both formulated using MAA as functional monomer. Two different formats were tested (i.e. bulk and nanoparticles) which in both cases afforded MIPs with affinities and selectivities comparable to those of similar MIPs obtained by FRP. In addition, the halidecapped chain-ends allowed for chain-extension and grafting of polyacrylamide p(AAm) brushes onto MIP nanoparticles.

[START_REF] Adali-Kaya | Molecularly Imprinted Polymer Nanomaterials and Nanocomposites: Atom-Transfer Radical Polymerization with Acidic Monomers[END_REF]

H NMR spectroscopy titrations.

ACKNOWLEDGMENT

The authors acknowledge the Hauts-de-France Region and the European Regional Development Fund (ERDF) (CPER 2014/2020) for the funding of equipment. EP wishes to thank the Embassy of France in the Philippines and the Commission on Higher Education of the Philippines (CHED) for granting his fellowship. KH acknowledges financial support from Institut Universitaire de France. KH and OS thank the French National Research Agency (ANR) for funding (DYNABIO grant). The authors thank Dr. Damien Thuau from the Laboratoire de L'Intégration du Matériau au Système, Université de Bordeaux, France, for help with creating the

Table of Content graphics.

AUTHOR INFORMATION

Corresponding Authors

* E-mails: karsten.haupt@utc.fr, carlo.gonzato@utc.fr

Author Contributions

All authors have given approval to the final version of the manuscript. These authors contributed equally.

Notes

There are no conflicts of interest to declare.


Fernanda Vendrame
email: fernanda.vendrame@safrangroup.com

Christophe Forgez

Marie Sayegh

Reduced Model for Fast Simulation of a Lithium-Ion Battery Pack Taking Into Account

come   L'archive ouverte pluridisciplinaire

Introduction

When a battery pack is operating, each cell in the pack has a slightly dierent behavior. For this reason, they have dierent voltages, currents and states of charge (SOC). Quantifying these dispersions is important to monitor the limiting cells, to get better estimations of each individual cell, to evaluate the need for a balancing system or even to rethink the pack design.

Several authors have worked on the electrical modeling of battery packs. Li et al. [START_REF] Li | Optimization of charging strategy for lithium-ion battery packs based on complete battery pack model[END_REF] combined the electrical, thermal and aging models in order to nd an optimal recharging strategy. He et al. [START_REF] He | Reduced-order thermal modeling of liquid-cooled lithium-ion battery pack for evs and hevs[END_REF] also proposed an electrothermal model to predict the temperature of each cell in the pack. Huang et al. [START_REF] Huang | Estimating battery pack soc using a cell-to-pack gain updating algorithm[END_REF] developed a method to estimate the SOC of the pack from the SOC of the cells, taking into account capacity dispersion. Kim et al. [START_REF] Kim | Online soc and soh estimation for multicell lithium-ion batteries based on an adaptive hybrid battery model and sliding-mode observer[END_REF] proposed a combined SOC and SOH real time estimator. However, all mentioned works present only packs with cells in series. So, the eect of current dispersion between cells in parallel cannot be studied. Other authors studied the case of cells connected in parallel. Ye et al. [START_REF] Ye | A novel dynamic performance analysis and evaluation model of series-parallel connected battery pack for electric vehicles[END_REF] compared the performance of two connection types of battery packs, whether they were connected rst in parallel and then in series or rst in series and then in parallel. Zhang et al. [START_REF] Zhang | Investigation of current sharing and heat dissipation in parallel-connected lithium-ion battery packs[END_REF] modeled a battery pack in order to explain the impact of temperature on current unbalance. Gong et al. [START_REF] Gong | Study of the characteristics of battery packs in electric vehicles with parallel-connected lithium-ion battery cells[END_REF] investigated the inuence of cell inconsistency due to heterogeneous aging in cells connected in parallel. In these three works, the authors show a concern similar to ours, i.e. the cell to cell dispersion, and they propose very relevant models to simulate it.

1

The main contribution of our work compared to the existing literature is an algorithm that reduces computation time. Indeed, in the mentioned works, each cell of the pack has to be simulated in detail, which is not necessarily desirable if we want to simulate a pack composed of a large number of cells and even less desirable in the perspective of implementing the pack model in real time applications. To reduce computation time, our method requires only a few cells in the pack to be simulated in detail. For all the other cells, a simplied calculation of their resistances based on their temperatures allows the current distribution to be calculated, so that we can estimate current and SOC dispersion.

In this paper, our goal is to validate the proposed method through simulation. In the future, we intend to implement it on a BMS (Battery Management System) to run it in real time. In section 2, we present the electrical model of the cell and the pack, explaining how to obtain the cell parameters as well.

In section 3, we explain how to estimate the temperature distribution from a few measurement points in the pack. In section 4, we present our simulation algorithm, step by step. In section 5, we validate our method (only a few cells simulated in detail) by comparing its performances in terms of computation time and accuracy with those obtained when all the cells of the pack are simulated in detail.

2

Proposed modeling method

Cell model

The electrical behavior of the pack depends on the electrical behavior of the cells that constitute it, so the starting point for modeling the pack is modeling the cells. For that, we chose an equivalent electrical circuit model [START_REF] Damay | Separation of the charge transfers and solid electrolyte interphase contributions to a battery voltage by modeling their non-linearities regarding current and temperature[END_REF] (see the cell zoom in Fig. 3), composed of: R dif f : a diusion resistance related to the phenomena of lithium ions diusion in the electrolyte and lithium atoms in both electrodes; All these parameters are obtained from previously determined look-up tables as a function of temperature, SOC and current.

τ dif f = R dif f • C dif f

Parameters identication

To identify the look-up tables, two tests were performed:

EIS (Electrochemical Impedance Spectroscopy): consists in applying a sine current wave to the cell and measuring its voltage variation in order to compute its impedance [START_REF] Huet | A review of impedance measurements for determination of the state-of-charge or state-ofhealth of secondary batteries[END_REF].

Frequencies: 10 kHz to 10 mHz Current : sinus with a peak value of ±500mA SOC: 100% to 0%, every 10% Temperatures: 0°C, 10°C, 25°C, 50°C

GITT (Galvanostatic Intermittent Titration Technique): combines transient and steadystate measurements, by applying small current steps followed by a relaxation period [START_REF] Weppner | Determination of the kinetic parameters of mixed-conducting electrodes and application to the system li3sb[END_REF].

Current : +1C, +C/2, -1C, -3C, -5C SOC: 100% to 0%, every 10% Temperatures: 0°C, 10°C, 25°C, 50°C

From EIS tests, we directly identify R surf at a near-zero current and R s , which is assumed not to depend on the current, as shown in Fig. 1. From GITT tests, we directly identify U oc , which is the voltage when the cell is relaxed. Once U oc is identied, we t the voltage response to obtain the surface and diusion parameters (R surf , τ surf , R dif f , τ dif f ). Fig. 2 shows the GITT protocol, as well as the contribution of each parameter on the voltage response.

𝑹 𝒔 𝑹 𝒔𝒖𝒓𝒇 (~0𝐴)

Pack model

The pack is modeled as shown in Fig.

r T (i, j) = T (i, j) -T min T max -T min , i ∈ [1, n s ], j ∈ [1, n p ] (1)
Since the internal resistance of the cells decreases as temperature increases, we assume that a resistance ratio can be dened as follows:

r R (i, j) = 1 -r T (i, j) (2)
At any given moment, the temperature of all the cells in the pack can then be estimated from the measurements (T ref ) as:

T (i, j) = T ref,min + r T (i, j) (T ref,max -T ref,min ) (3)
During experimental tests, we found that the hottest cell at a given moment tended to remain the hottest throughout the test and was also the hottest or second hottest during other tests. The same was found for the coldest cells. Based on this observation, we assumed that the temperature ratios r T remained constant throughout the mission prole, i.e. the hottest cell is always the hottest, the coldest is always the coldest and the temperatures of all cells change at the same rate. This assumption allows the temperature ratios to be calculated only once, in a pre-simulation step, which reduces the calculation time. However, if one wishes to be more precise and take into account the dierent heating and cooling dynamics of the cells, it is also possible to perform a temperature interpolation every few seconds or minutes.

Simulation algorithm

Once a temperature ratio r T has been assigned to each cell, the algorithm presented in the end of this section is used to compute the current and the SOC of each cell.

Through step 1, we obtain the highest and lowest cell resistances. In step 2, we obtain the total resistance (internal resistance plus connection) related to each cell in the pack by using the ratios calculated in (2), their temperature with the ratio determined in (1) and the temperature measurements (T ref ), as well as their OCV. In step 3, we simulate in detail one cell per group of parallel cells, which is necessary to calculate the pack voltage and current in step 4. To have a good estimation of the global behavior of the pack, we recommend choosing the cells to be simulated in detail so that their temperature distribution is representative to that of all the cells in the pack. In step 5, we use the total resistances and the OCVs from step 2 and the pack current from step 4 to calculate the current distribution within each group of parallel cells and update the SOC of each cell in the pack.

The equations of the equivalent open-circuit voltage U oc,eq and the cell current I in step 5 were presented by Juston [11, p. 31-34]. The calculation of the current at cell level must take into account not only the distribution of the pack current between the cells in parallel according to their resistances, but also the eect of rebalancing between the cells, which is present even in the absence of external current.

STEP 1: Obtain highest and lowest cell resistances.

R max = f (T min , I min , SOC max ) ▷ From look-up tables R min = f (T max , I max , SOC min )
▷ From look-up tables ▷ R max/min is the sum of R s,max/min , R surf,max/min and R dif f,max/min STEP 2: Estimate one global resistance for each cell and its connections. Estimate its temperature and its OCV.

for i = 1, n s do for j = 1, n p do

▷ Index t-1 indicates the previous time step R(i, j) = R min + r R (i, j) • (R max -R min ) + R connec (i, j) G(i, j) = 1/R(i, j) T (i, j) = T ref,min + r T (i, j) • (T ref,max -T ref,min ) U oc (i, j) = f Uoc (T (i, j) t-1 , SOC(i, j) t-1 )
end for end for STEP 3: For one cell per group, calculate its resistance and voltage in detail.

for i = selectedCells do R s (i) = f (T (i) t-1 , SOC(i) t-1 ) R surf (i) = f Rs (T (i) t-1 , I(i) t-1 , SOC(i) t-1 ) R dif f (i) = f R dif f (T (i) t-1 , I(i) t-1 , SOC(i) t-1 ) τ dif f (i) = f τ dif f (T (i) t-1 , I(i) t-1 , SOC(i) t-1 ) U dif f (i) = U dif f (i) t-1 1 -∆t τ dif f (i) + R dif f (i)I(i) t-1 ∆t τ dif f (i)/R dif f (i) U (i) = U oc (i) + (R s (i) + R surf (i)) • I(i) t-1 + U dif f (i) U cell+connec (i) = U (i) + R connec (i) • I(i) t-
U oc,eq (i) = np k=1 Uoc(i,k)•G(i,k) np k=1 G(i,k) for j = 1, n p do ▷ Each cell in the group I(i, j) = I pack • G(i,j) np k=1 G(i,k) + G(i, j) • (U oc,eq (i) -U oc (i, j)) ▷ G = 1/R SOC(i, j) = SOC(i, j) t-1 + I(i, j) • ∆t 3600
end for end for [START_REF] Ye | A novel dynamic performance analysis and evaluation model of series-parallel connected battery pack for electric vehicles[END_REF] Validation

Experimental and simulation setup

We validated the proposed method using a battery pack (see Fig. 5) composed of 66 Samsung 18650-25R cylindrical cells (NCA+NMC/graphite+SiO, nominal capacity of 2.5 Ah, nominal voltage of 3.6 V). The pack is equipped with voltage sensors at the terminals of each cell and on the metal strips connecting the cells (one per group of cells in parallel, measuring the voltage over the cells and the connection resistance) and 18 temperature sensors on cells distributed over dierent areas of the pack. Although there is not an ideal number of sensors, there should be enough to measure extreme temperatures. In our case, it is the center for the hottest cells and the edges for the coldest. Other sensors are distributed over intermediate areas. To allow for good interpolation of the measurements, as described in section 3, it is better to scatter the sensors instead of aligning them.

For charging and discharging the pack, we used a power emulator composed of a power supply Regatron TCP 32.200.400S with 32 kW and an electronic load H&H ZS21030 with 21 kW. Both were connected to a dSPACE system, that sends the control input to the emulator and gathers the output values.

The results of the experimental tests were then used as a reference for our simulations. These simulations were performed on Matlab 2021a with the following PC conguration:

Operating system: Windows 10 Pro

Processor: Intel Core i5-7300U (base frequency of 2.60 GHz)

Simulation results

To validate the performances of our method, the pack was submitted to the mission prole of an aircraft presented in Fig. 6. This prole represents the following phases of the ight of a VTOL (vertical take-o and landing) aircraft: (1) ground, (2) climb, (3) hover, (4) cruise, (5) hover, (6) descent and ( 7) ground. The ability to correctly estimate current and SOC dispersion. The reference is the method where each cell is simulated in detail.

The ability to correctly estimate the voltage (cells and pack). The reference is the measured voltage.

The required computation time. The reference is the method where each cell is simulated in detail.

Current and SOC dispersion

Cell current and SOC cannot be directly measured. However, we need a reference to judge the consistency of our method. For this reason, we simulated the mission prole in Fig. 6 with two methods:

1. A full model, where all cells are simulated in detail (as presented in step 3 of our algorithm) to have maximum accuracy.

2. A reduced model, the method we propose in the present paper, where only one cell per group of cells in parallel is simulated in detail and all others are simulated using approximations of their resistance as a function of the temperature distribution.

Accuracy of voltage estimation

Another performance indicator that is very important to evaluate our method is voltage, since it is the only indicator that can be compared to experimental measurements. Fig. 8a presents the measurements and simulated values of the voltages over the cells and the connection resistances (U cell +U connec ), showing a good consistency between simulation and measurements for both full and reduced models.

To compare the estimation errors of the two models, we can compare the measured and simulated pack voltages. Fig. 8b shows that the accuracy of the model is preserved, since the voltage errors obtained with the reduced model are very close to the errors obtained with the full model.

Computation time

The simulation with the full model took 7.2 seconds to run, while it took only 2.9 seconds with the reduced model, a 60% reduction in computation time.

Conclusion

In this paper, we proposed a method to estimate the dispersion of current and SOC among all the cells of a battery pack, taking into account the temperature measured in dierent zones of the pack. First, we estimated the temperature of all cells in the pack from measurements of a few sensors. Then, we simulated in detail one cell per group of parallel cells to have an accurate estimation of pack voltage. To Our method reduces computation time by 60% compared to the case where all cells are simulated in detail, while preserving the accuracy of the model.

The next step would be to implement the proposed model on a BMS to perform real-time estimation of current and SOC dispersion, which would improve battery safety.

U

  oc : a voltage source representing the OCV (open-circuit voltage), which is the voltage measured when the cell is as rest and completely relaxed;R s : a series resistance representing all purely resistive contributions (electrolyte, current collectors and contact resistances); R surf : a surface resistance related to the voltage drop between the surface of the active material and the electrolyte due to charge transfer and SEI (Solid Electrolyte Interphase); τ surf = R surf • C surf : a time constant related to the surface phenomena, which are associated with charge transfer, double layers and SEI. It represents a very quick dynamic, of the order of a few milliseconds;

  : a time constant related to the diusion phenomena. It represents a slower dynamic, of the order of a few seconds or minutes.

Figure 1 :

 1 Figure 1: Parameters identication from EIS test

3 .Figure 2 :

 32 Figure 2: Parameters identication from GITT test

Figure 3 :

 3 Figure 3: Cell and pack models

Figure 4 :

 4 Figure 4: Example of a 2D interpolation of temperatures measured by the sensors

  selectedCells = [cell group1 , ..., cell groupns ]

Figure 5

 5 Figure 5: Battery pack

Figure 6 :

 6 Figure 6: Validation prole

Fig. 7a and

  Fig.7a and 7bshow the current and the SOC, respectively, simulated for each cell in the pack with both models. Considering the full model as the reference, the comparison between the two models leads to a RMSE (Root Squared Mean Error) of 102 mA for a current dispersion going up to 2500 mAh, and a RMSE of 3.3 mAh for a SOC dispersion going up to 160 mAh. There is a good consistency between the two models, which shows that we can use the reduced model to obtain very similar results to what we could obtain with a more detailed but time-consuming model (see "Computation time" in the end of this section).

Figure 7 :

 7 Figure 7: Simulation results : current and state of charge

Figure 8 :

 8 Figure 8: Simulation results : voltage