Catherine Tom

Venkata Tanuku

Erwan Paineau

Ravi Kumar Pujala

Venkata M S Ganesh Tanuku

Binary Mixtures of Colloidal Cellulose Nanocrystals and Laponite for Preparation of Functional Nanocomposites

Keywords: Cellulose nanocrystals, Laponite nanoclay, phase behavior, birefringent gels, aerogels, thin films, dye removal, flame retardants

published or not. The documents may come

INTRODUCTION

Driven by concerns about the depleting resources and the environmental hazards, the researchers are now focusing on the implementation of renewable resources for the production of highly performing, sustainable materials. Recently, scientists are excited by the tremendous properties and applications of Cellulose Nanocrystals (CNCs) as it is renewable, biodegradable and non-toxic [START_REF] Roman | Toxicity of Cellulose Nanocrystals: A Review[END_REF][START_REF] Endes | A Critical Review of the Current Knowledge Regarding the Biological Impact of Nanocellulose[END_REF] , which have attracted a lot of attention due to its ability in forming liquid crystals [START_REF] Andrienko | Introduction to Liquid Crystals[END_REF][START_REF] Buffa | Cellulose Nanocrystals in Aqueous Suspensions: Rheology of Lyotropic Chiral Liquid Crystals[END_REF] , its application in nanocomposites [START_REF] Chee | Rheological Properties of Cellulose Nanocrystal-Embedded Polymer Composites : A Review[END_REF][START_REF] Younas | A Review on Versatile Applications of Blends and Composites of CNC with Natural and Synthetic Polymers with Mathematical Modeling[END_REF][START_REF] Mariano | Cellulose Nanocrystals and Related Nanocomposites: Review of Some Properties and Challenges[END_REF][START_REF] Gray | Nanocellulose: From Nature to High Performance Tailored Material[END_REF] and photonic metamaterials [START_REF] Giese | Functional Materials from Cellulose-Derived Liquid-Crystal Templates[END_REF][START_REF] Wang | A Sol-Gel Biotemplating Route with Cellulose Nanocrystals to Design a Photocatalyst for Improving Hydrogen Generation[END_REF] . CNCs are crystalline nanomaterials and obtained typically from wood, bacteria, tunicate and linen by hydrolysis with sulfuric acid [START_REF] Siqueira | Cellulosic Bionanocomposites: A Review of Preparation, Properties and Applications[END_REF][START_REF] Pech-Cohuo | Production and Modification of Cellulose Nanocrystals from Agave Tequilana Weber Waste and Its Effect on the Melt Rheology of PLA[END_REF] . This results in nanocrystals possessing rod shape, which bear sulfate ester groups rendering the surface of CNC negatively charged (Scheme 1).

Even though Marchessault et al. [START_REF] Marchessault | Liquid Crystal Systems from Fibrillar Polysaccharides[END_REF] reported the formation of colloidal dispersions of CNCs since 1952, it took another forty years to understand the ordering in chiral nematic structure of CNC, proposed by Revol et al. [START_REF] Revol | Helicoidal Self-Ordering of Cellulose Microfibrils in Aqueous Suspension[END_REF] in 1992. The formation of self-organized chiral nematic domains depends on several parameters such as the aspect ratio of CNCs, the surface chemistry or the ionic strength of the medium [START_REF] Habibi | Cellulose Nanocrystals: Chemistry, Self-Assembly, and Applications[END_REF] . As the concentration is increased, aqueous suspensions of CNCs may undergo a first order transition from isotropic to pure liquid crystalline phase [START_REF] Shafiei-Sabet | Ionic Strength Effects on the Microstructure and Shear Rheology of Cellulose Nanocrystal Suspensions[END_REF] , typically above 6.0 wt% for CNCs from wood pulp [START_REF] Orts | Enhanced Ordering of Liquid Crystalline Suspensions of Cellulose Microfibrils: A Small Angle Neutron Scattering Study[END_REF][START_REF] Lagerwall | Cellulose Nanocrystal-Based Materials: From Liquid Crystal Self-Assembly and Glass Formation to Multifunctional Thin Films[END_REF][START_REF] Klemm | Nanocellulose as a Natural Source for Groundbreaking Applications in Materials Science : Today's State[END_REF][START_REF] Beck-Candanedo | Effect of Reaction Conditions on the Properties and Behavior of Wood Cellulose Nanocrystal Suspensions[END_REF] . At higher concentration, the liquid Scheme 1. Crystal structures of (left) cellulose nanocrystals (CNCs) with sulfate ester group and (right) Laponite clay nanosheets. Illustration of the procedure used to prepare composite films and aerogels from binary colloidal mixtures of CNC and Laponite.

As the larger CNC particles form the liquid crystalline phase, the smaller particles remain in the isotropic phase, at critical concentration when isotropic to biphasic transition takes place [START_REF] Dong | Effect of Microcrystallite Preparation Conditions on the Formation of Colloid Crystals of Cellulose[END_REF] . Thus, size distribution plays an important role in the phase behavior exhibited by the CNC dispersions. From an application point of view, CNCs can be shaped in the form of fibers [START_REF] Emerton | Electron-Microscopy of Degraded Cellulose Fibres[END_REF] and films [START_REF] Gençer | Control of the Colloidal Deposition of Cellulose Nanocrystal Films[END_REF][START_REF] Wu | Transparent Cellulose / Laponite Nanocomposite Films[END_REF] and these regenerated cellulose materials are suitable for wrapping cardboard boxes or for packaging drugs [START_REF] Roman | Cellulose Nanocrystals for Drug Delivery[END_REF][START_REF] Sheikhi | Recent Advances in Nanoengineering Cellulose for Cargo Delivery[END_REF] and food items [START_REF] Criado | Cellulose Nanocrystals in Food Packaging[END_REF] . The high aspect ratio, high specific moduli and stiffness makes CNCs suitable as nanofillers in polymer matrices [START_REF] Kumar | Mechanically Viscoelastic Nanoreinforced Hybrid Hydrogels Composed of Polyacrylamide, Sodium Carboxymethylcellulose, Graphene Oxide, and Cellulose Nanocrystals[END_REF][START_REF] Nagalakshmaiah | Melt Extrusion of Polystyrene Reinforced with Cellulose Nanocrystals Modi Fi Ed Using Poly [( Styrene ) -Co -( 2-Ethylhexyl Acrylate )] Latex Particles[END_REF] , so that the mechanical, optical and rheological properties of the obtained nanocomposites can be enhanced [START_REF] Cheung | Iridescent Chiral Nematic Cellulose Nanocrystal/Polymer Composites Assembled in Organic Solvents[END_REF][START_REF] Beuguel | Rheological Behavior of Cellulose Nanocrystal Suspensions in Polyethylene Glycol[END_REF][START_REF] Qiao | Structure and Rheological Properties of Cellulose Nanocrystals Suspension[END_REF] .

Meanwhile, inorganic nanofillers have gained prominence nowadays, especially layered aluminosilicates used extensively in polymer nanocomposites [START_REF] Alexandre | Polymer-Layered Silicate Nanocomposites: Preparation, Properties and Uses of a New Class of Materials[END_REF][START_REF] Krishnamoorti | Structure and Dynamics of Polymer-Layered Silicate Nanocomposites[END_REF] . Among them, Laponite, a synthetic clay mineral having a disk shape morphology, possesses appealing properties like biocompatibility [START_REF] Grüner | Reaching Biocompatibility with Nanoclays: Eliminating the Cytotoxicity of Ir(III) Complexes[END_REF] , hydrophilicity [START_REF] Li | The Mechanical Properties and Hydrophilicity of Poly (L-Lactide) /Laponite Composite Film[END_REF] and biodegradability [START_REF] Liu | Biodegradable Poly(Lactic-Acid)/Poly(Trimethylene-Carbonate)/Laponite Composite Film: Development and Application to the Packaging of Mushrooms ( Agaricus Bisporus )[END_REF] . A positive charge deficiency is created in the Laponite sheet by substituting lithium atoms in place of few magnesium atoms in the octahedral layer (Scheme 1) [START_REF] Bonn | Laponite : What Is the Difference between a Gel and a Glass ?[END_REF][START_REF] Balnois | Probing the Morphology of Laponite Clay Colloids by Atomic Force Microscopy[END_REF][START_REF] Saunders | A Small-Angle X-Ray Scattering Study of the Structure of Aqueous Laponite Dispersions[END_REF] . The anisometric shape of the Laponite nanoparticle has a different charge contribution between the surface (negative) and the rims (pH dependent).

Hence, the phase diagram of aqueous dispersions of Laponite is rather complex, exhibiting a variety of phase behaviors ranging from isotropic fluid to kinetically arrested phases [START_REF] Jabbari-Farouji | Multiple Nonergodic Disordered States in Laponite Suspensions: A Phase Diagram[END_REF][START_REF] Ruzicka | Observation of Empty Liquids and Equilibrium Gels in a Colloidal Clay[END_REF] .

Laponite dispersions exhibit an improvement in its physical properties like relaxation time and mechanical properties with increasing time and is an obvious consequence of physical aging in spin and molecular glasses [START_REF] Jabbari-Farouji | Multiple Nonergodic Disordered States in Laponite Suspensions: A Phase Diagram[END_REF][START_REF] Ruzicka | Observation of Empty Liquids and Equilibrium Gels in a Colloidal Clay[END_REF][START_REF] Dhavale | Thermally Activated Asymmetric Structural Recovery in a Soft Glassy Nano-Clay Suspension[END_REF][START_REF] Pujala | Slow Dynamics and Equilibrium Gelation in Fractionated Montmorillonite Nanoplatelet Dispersions[END_REF][START_REF] Ruzicka | A Fresh Look at the Laponite Phase Diagram[END_REF] . The colloidal and rheological behaviour of aqueous suspensions of Laponite has been extensively addressed in the scientific literature [START_REF] Ruzicka | A Fresh Look at the Laponite Phase Diagram[END_REF] . Depending on the waiting time, at concentration lower than 1 wt%, it is observed that aqueous dispersions undergo a slow phase separation process into clay-rich and clay-poor phases. Above this threshold, Laponite dispersion forms a repulsive arrested phase.

CNC nanorods would easily be blended with Laponite without doing organic modification beforehand, in order to obtain favorable nanofiller-matrix compatibility and interaction.

Electrostatic interactions between Laponite and CNC surfaces as well as hydrogen bonding between the hydroxyl groups present on their surfaces should promote the formation of complex self-assembled structures. CNC included composite systems are of great importance today as they enhance the rheological properties by forming complex network structures within the system. Trindade et al. reported that CNCs could be developed into excellent fire-retardant material by adding sodium fluorohectorite (NaFH) clays [START_REF] Trindade | Photonic Composite Materials from Cellulose Nanorods and Clay Nanolayers[END_REF] . In that case, NaFH nanolayer provides a planar anchoring to rod shaped CNCs and the evaporation of water leads to the formation of colored films, which could exhibit the property of fire retardancy. Recently, it has been proposed that aerogels of amine-modified CNCs are excellent absorbers of CO 2 [START_REF] Zhu | Preparation of an Amine-Modified Cellulose Nanocrystal Aerogel by Chemical Vapor Deposition and Its Application in CO2Capture[END_REF] .

In this work, we propose a systematic analysis of the optical, structural and rheological properties of the composite gels and proposed a phase diagram. We observed a drastic change in the microscopic properties of the composite when clay nanosheets are added to CNC aqueous dispersions. To this end, we demonstrate the realization of functional thin-films and aerogels from CNC/L mixtures. We investigate the efficiency of the nanocomposite films for the removal of pollutants such as dyes (Rhodamine B and Nile blue) as well as the kinetics of dye adsorption. In parallel, we investigate the enhancement of fire-retardant property of CNC aerogels with the incorporation of clay particles Our results should be useful for the applications, where there requires an increase in properties like yield stress, viscosity and elastic modulus and for which the organic modification of CNC particles is not needed in preparing composites.

MATERIALS AND METHODS

Sample preparation

CNC powder was purchased from CelluForce (Canada). Laponite ® RD was procured from BYK

Additives & Instruments (Germany) and was used as received. The purity of both samples was determined by Wide Angle X-ray scattering measurements (Figure S1). Particle size and zeta potential of both samples were measured using Anton-paar Litesizer 500. The main physical properties of CNCs and Laponite are summarized in Table 1. Milli-Q purified water was used to prepare the CNC/L composite suspensions. To this end, stock solutions of Laponite (0.1-3.0 wt%) were prepared by dilution in water and appropriate amount of CNC powder (1.0-3.0 wt%) was added slowly during stirring.

Preparation of nanocomposites

Thin-films were obtained by pouring CNC and CNC/L composite samples into 6 cm diameter petridish. Solid flexible films were recovered and stored after solvent evaporation (Scheme 1).

For aerogels, CNC/L composite samples and the pure CNC samples were frozen by dipping the vials containing the samples in liquid nitrogen. The caps of the vials containing samples were removed and were covered it using kim wipes. The frozen samples were kept immediately in Virtis S P Scientific (Bench top lyophilizer with a temperature of -104 0 C and pressure of 23 mT)

for freeze-drying overnight (Scheme 1).

Rheological measurements

Rheological properties of CNC/L composite system were studied using AntonPaar MCR302

rheometer with cone-plate geometry having a nominal angle of 2 °. All the experiments were conducted at room temperature. The composite system of CNC/L was investigated with loading and trimming the samples in the rheometer following a standardized procedure. In order to avoid the evaporation of samples, a thin layer of silicone oil was applied on the edges of the samples and an evaporation trap was used to cover the samples placed on the rheometer. Sol/gel transition and yield stress values were extracted by fitting the flow curves describing the shear viscosity versus shear stress. These experiments were completed with oscillation sweep measurements.

We first performed amplitude sweep measurements at 0.1 rad/s frequency. The constant linear region observed in the variation of storage modulus (G') and loss modulus (G'') with oscillation stress allowed determining the linear viscoelastic region (LVR) of each sample. In order to evaluate the viscoelastic properties of the system, small deformation oscillatory measurements were carried out by choosing the stress value from LVR. In that case, G' and G'' moduli were recorded in an oscillatory frequency sweep using angular frequency ranging from 0.1 to 100 rad s -1 .

X-Ray Scattering experiments

All X-ray scattering experiments were performed on the MORPHEUS platform of Laboratoire de Physique des Solides. Small Angle X-ray Scattering (SAXS) measurements were carried on an in-house SAXS setup using a rotating anode generator (Rigaku Corp., Japan) at a wavelength of Cu K α = 1.542 Å delivered by a multilayer Ni/C focusing optic (Osmic) [START_REF] Paineau | Liquid-Crystalline Nematic Phase in Aqueous Suspensions of a Disk-Shaped Natural Beidellite Clay[END_REF]

Dye removal and kinetics

The prepared CNC/L films of different concentrations (3.0 wt% CNC with 0, 0.3, 0.7, 1.0 and 2.0 wt% Laponite) having dimensions 1.5 cm x 1.5 cm and mass of 28 mg were dipped in 7 ml of Rhodamine B dye (S D Fine Chem Limited) and Nile Blue dye solutions of initial concentrations 0.01253 mmol L -1 and 0.00787 mmol L -1 respectively. Without disturbing the films, 2 ml of dye solution was taken out at different intervals over 24h. The aliquots were analyzed by UV-vis spectroscopy using a Cary 4000 UV-Vis spectrophotometer. The amount of dye adsorbed by CNC/L films at equilibrium is calculated by: where q is the amount of dye adsorbed on the film at equilibrium (mmolg -1 ), C 0 and C correspond respectively to the initial and equilibrium concentrations of dye solutions (mmolL -1 ),

V is the volume of solution and W the mass of the films.

Preparation of aerogel:

CNC/L composite samples and the pure CNC samples were frozen by dipping the vials containing the samples in liquid nitrogen. The caps of the vials containing samples were removed and were covered it using kim wipes. The frozen samples were kept immediately in Virtis S P Scientific (Bench top lyophilizer with a temperature of -104 0 C and pressure of 23 mT)

and was freeze dried overnight in order to obtain CNC/L aerogels and flame test was conducted.

Prepared aerogels in the nose cone shape were ignited using a torch lighter and observed the time taken for the samples to put off the flame.

RESULTS

Optical properties of gels

Having prepared CNC/L composites, we investigated the evolution of birefringence by nakedeye observations between crossed polarizers at one week, and ten months after sample preparation (Figure 1a, b and Figure S2). As mentioned before, pure CNC aqueous dispersions remain isotropic for concentration lower than 3.0 wt%, i.e., the highest concentration used in this work. Conversely, pure Laponite presents a complex phase diagram that has been largely debated [START_REF] Mourchid | On Viscoelastic, Birefringent, and Swelling Properties of Laponite Clay Suspensions: Revisited Phase Diagram[END_REF][START_REF] Jabbari-Farouji | Multiple Nonergodic Disordered States in Laponite Suspensions: A Phase Diagram[END_REF][START_REF] Ruzicka | A Fresh Look at the Laponite Phase Diagram[END_REF][START_REF] Gabriel | Observation of Nematic Liquid-Crystal Textures in Aqueous Gels of Smectite Clays[END_REF][START_REF] Tanaka | Nonergodic States of Charged Colloidal Suspensions: Repulsive and Attractive Glasses and Gels[END_REF][START_REF] Pujala | Hierarchical Self-Assembly, Spongy Architecture, Liquid Crystalline Behaviour and Phase Diagram of Laponite Nanoplatelets in Alcohol-Water Binary Solvents[END_REF] . At low ionic strength (< 10 -3 mol. L -1 ), isotropic liquid and gel phases are found at low clay concentration (< 2.0 wt%) while these dispersions form repulsive glass when the concentration of Laponite increases. For the range of concentrations, we used in this study, the samples of pure Laponite or CNC do not exhibit any liquid crystalline behavior and hance do not show birefringence. On this basis, it is therefore not surprising to find that the CNC/L mixtures prepared with the lowest concentrations of Laponite (< 0.5 wt%) remain isotropic.

However, all samples prepared above 1 wt% concentration of Laponite form arrested phases and exhibit optical birefringence with a clear evolution after ten months. This indicates the particles are locally ordered but they do not reach thermodynamic equilibrium, both rotational and translational motion of CNC and Laponite being hindered in the arrested phase. S4). The position and extent of these domains, delimited by topological defects, are highlighted when a retardation filter (here a λ-plate at 530 nm) is inserted at 45° with respect to the polarizers (Figure 1h-l). If so, blue (red) colors correspond to an orientation of particles in the nematic domains with their normal parallel (perpendicular) to the slow axis of the λ-plate. These nematic domains are randomly oriented throughout the samples whatever the concentration of CNC and Laponite.

Interestingly, we also evidenced the formation of small tactoids with increasing the concentration of CNC (Figure S3). These tactoids seem to be more frequent when the concentration of Laponite increases (Figure S3d) and the use of a retardation filter help us to distinguish them from the birefringent background (Figure S3h and Figure S4). Although clear tactoids were never identify in pure Laponite samples, we can assume that they are related to a nematic phase of CNC nanorods, trapped in the arrested phase of clay nanosheets. The incorporation of Laponite probably induces depletion interactions as observed in other clayinorganic nanoparticle mixed dispersions [START_REF] Kleshchanok | Effects of Added Silica Nanoparticles on Hectorite Gels[END_REF][START_REF] Landman | Effects of Added Silica Nanoparticles on the Nematic Liquid Crystal Phase Formation in Beidellite Suspensions[END_REF][START_REF] Bailey | Smectite Clay-Inorganic Nanoparticle Mixed Suspensions: Phase Behaviour and Rheology[END_REF] .

Small-Angle X-ray scattering experiments

We investigated the structural organization of the different binary mixtures by performing laboratory Small-Angle X-ray Scattering experiments. SAXS profiles for CNC/L binary mixtures prepared at 2.0 wt% and 3.0 wt% of CNC are displayed in Figure 2. All curves present similar shape with a monotonous decrease of the scattered intensity I with increasing the scattering vector modulus as I(Q) ~ Q -2.1 in the Q-range 0.02-0.12 Å -1 . The exponent of the power law is characteristic of bidimensional objects, even if the slightly higher value of 2 seems to indicate that some more complex interplays occur between particles in these arrested phases as shown from POM observations (Figures 1 andS3). In the low Q-region, SAXS profiles are flattened due to the form factor coming from CNC nanorods. We also noticed a slight effect on the slope for CNC/L mixtures prepared at 3.0 wt% of CNC, probably due to the formation of droplets as evidenced from POM images (Figure S4). Although it is hard to extract any correlation peaks from the SAXS profiles, these results suggest that incorporation of CNCs in Laponite dispersions do not strongly modify the microstructural properties of the binary mixtures for distances between ~75 and 5 nm.

Rheological study and gelation behavior

Optical observations reveal that CNC/L samples prepared with Laponite concentration higher than 0.5 wt% sustained inverted vial test, indicating gel-like formation. To characterize the gelation behavior, we performed a detailed rheological analysis of the binary mixtures. The evolution of the flow curves (viscosity η versus shear stress σ) at varying concentrations of Laponite are shown in Figure 3 and Figures S5-S6. For all mixtures, we observed a decrease in the viscosity with increasing shear stress, indicating that the CNC/L composites exhibit a shear thinning behavior related to the alignment of the solid particles along the shear field. Whatever the CNC concentration, the flow curves still exhibit a finite viscosity at rest (η 0 ) when the Laponite concentration is lower than 0.5 wt% denoting the fluidity of the phase. By contrast, higher Laponite addition always led to the appearance of a yield stress (σ y ) in the flow curves with a significant shear thinning behavior. Flow curves of complex anisotropic clay dispersions can be modeled using a viscosity-shear model [START_REF] Paineau | Aqueous Suspensions of Natural Swelling Clay Minerals. 2. Rheological Characterization[END_REF][START_REF] Landman | Effects of Added Silica Nanoparticles on the Nematic Liquid Crystal Phase Formation in Beidellite Suspensions[END_REF][START_REF] Baravian | Rheological Determination of Interaction Potential Energy for Aqueous Clay Suspensions[END_REF] inspired from the Quemada hard-sphere model [START_REF] Quemada | Energy of Interaction in Colloids and Its Implications in Rheological Modeling[END_REF] . This model is based on the definition of an effective hydrodynamic volume fraction. It allows deriving a relevant physical interpretation of the flow curves. The viscosity is defined as:

In this equation, corresponds to the infinite shear viscosity, represents a critical shear stress that is related to the average potential energy of the system and is an adimensional term whose value reflects the state of the suspension: is equal to 1 for Newtonian fluids. If only shear-thinning behavior occurs, is positive and is equal to:

This parameter becomes negative for solid-like dispersion and the yield stress can be determined: The flow curves were fitted with eq. 2 by adjusting the set of three parameters , and using the least-squares method (Figure 3a, b and Figure S6). In most cases, good agreement is obtained between experimental and calculated flow curves, except for the highest concentration of Laponite for which the flow curves display a second inflexion close to the yield stress. This feature can be related to shear banding attributed to the breaking of large structures in the geometry gap of the rheometer [START_REF] Paineau | Aqueous Suspensions of Natural Swelling Clay Minerals. 2. Rheological Characterization[END_REF][START_REF] Fogang | Understanding Viscosity Reduction of a Long-Tail Sulfobetaine Viscoelastic Surfactant by Organic Compounds †[END_REF] . For this case, the flow curves were adjusted only on the high shear stress range. The evolution of the value of parameter is represented in Figure 3c. The sol-gel transition defined as the sign inversion of occurs around a Laponite concentration of ~0.4 wt%, in accordance with optical observations (Figures 1 andS3). The sol-gel transition seems however slightly shifted to lower clay concentration when the amount of CNC in the binary mixture is increased. The yield stress values obtained from the viscosity-shear model shows a linear dependence against the concentration of Laponite (Figure 3d) similar to the observations reported for pure clay dispersions [START_REF] Paineau | Aqueous Suspensions of Natural Swelling Clay Minerals. 2. Rheological Characterization[END_REF][START_REF] Michot | Sol-Gel and Isotropic/Nematic Transitions in Aqueous Suspensions of Natural Nontronite Clay. Influence of Particle Anisotropy. 2. Gel Structure and Mechanical Properties[END_REF] . Remarkably, we note that the increase of CNC concentration drastically modifies the mechanical properties of the binary mixtures since the yield stress values are always higher for samples prepared with 3.0 wt% of CNC. Variation of the critical oscillation stress  0 with the yield stress  y for CNC/L aqueous suspension shows a linear behavior (Figure S7).

To complete this investigation, we performed dynamical rheological experiments on our different CNC/L binary mixtures (Figure 4). Oscillation amplitude sweeps were first carried out depending on the concentration of both CNC and Laponite. The evolution of elastic (G') and viscous (G") moduli as a function of shear strain are shown in Figure 4c and Figure S8. The G'

and G'' values increase linearly with the concentration of Laponite in CNC suspension. At low shear strain, G' and G'' values are constant corresponding to the so-called linear viscoelastic region (LVR) before they cross over each other. The strain at which G' and G'' intersect is called as yielding strain. The value of shear stress at the limit of the LVR plateau is referred as the critical oscillation stress (σ 0 ) and is obtained using tangent analysis method. The critical oscillation stress values are plotted against the concentration of Laponite (Figure 4d). As for flow curves, σ 0 increases with Laponite concentration and can be related to the strengthening of the gel phase. Interestingly, a linear relationship is observed between yield stress values obtained from flow curves and the critical oscillation stress from dynamic rheological measurements (Figure S6). This feature confirms the consistency of the results obtained by both methods in defining the yield stress.

Storage modulus (G') and Loss modulus (G'') are plotted against angular frequency for different CNC/L mixtures (Figure 4a and S9). Based on amplitude sweep, we defined a common value of strain for frequency sweep experiments. Regardless of the concentration of Laponite and CNC, G' is always one order of magnitude higher than G'' and almost independent with frequency, for gel samples. This limited dependence of G' values indicates that the arrested phases observed from POM images display an elastic behavior. It is observed that the average values of both G' and G'' increase with the concentration of Laponite in the mixture. To illustrate this point, G' taken arbitrarily at an angular frequency (ω) of 10 rad/s, plotted as a function of the concentration of Laponite (Figure 4b). The storage modulus increases linearly with the concentration of Laponite while the effect of CNC concentration is a

Phase diagram

The physico-chemical properties, the surface properties, dimensions of CNC particles and the ionic strength of the system has a tremendous role in the rheological properties and the phase transitions happening within the system [START_REF] Shafeiei-Sabet | Influence of Degree of Sulfation on the Rheology of Cellulose Nanocrystal Suspensions[END_REF] . The anisotropic shape of Laponite particles along with its inhomogeneous charge distribution and also the large aspect ratio and easily orienting properties of CNC particles with its self-assembly behaviour makes CNC/L composite system exhibit complex interactions in aqueous systems. The relationship between structure and property as well as the processability of these composite systems can be understood by the rheological and optical studies. At lower concentrations of Laponite, we observed isotropic phases in single component system. However, when we prepared the CNC/L composite system, birefringence is observed even at low concentrations of Laponite (Figure 1). As the concentration of Laponite in CNC suspension increases, the formation of tactoids in the form of anisotropic microdroplets takes place and remain trapped in the arrested phase as evidenced from POM investigations (Figures 1 andS3). In order to form a tactoid, it needs both an attractive and a repulsive energy to gather the mesogens together in the form of a microdroplet and to arrange it in a liquid crystalline order respectively [START_REF] Maclachlan | Liquid Crystalline Tactoids: Ordered Structure, Defective Coalescence and Evolution in Confined Geometries[END_REF] . We observed that there exists a complex interplay between repulsive and attractive forces as well as the loss of rotational and translational motion in the gel phase which limit the phase separation.

The mechanical properties of CNC/L composite system have also been investigated through rheological studies. The steady state flow curves of CNC/L system shown in Figure 3 depicts the shear thinning behaviour of this system. Due to the alignment of the molecules along the shear field, the system exhibits a shear thinning behaviour as the shear rate increases. The shear thinning behaviour at low shear rates is not significant due to the weak association of the particles in the system [START_REF] Xu | Rheology and Microstructure of Aqueous Suspensions of Nanocrystalline Cellulose Rods[END_REF] . On increasing the shear rate, there is a tremendous increase in shear thinning behaviour and can be ascribed to the restriction in the motion of particles due to the formation of network structure by CNC and Laponite particles within the system. The formation of lyotropic liquid crystalline phase due to the alignment of particles along the shear field can also be a reason for this power-law having non-linear behaviour at high shear rates. The pristine CNC aqueous suspensions exhibit Newtonian behaviour and are isotropic till 3.0 wt% concentration [START_REF] Xu | Rheology and Microstructure of Aqueous Suspensions of Nanocrystalline Cellulose Rods[END_REF] .

Up on the addition of Laponite to CNC, this behaviour gets disturbed and at low concentrations of CNC itself, abundant variations in shear stress can be seen. This behaviour is attributed to the gelation taking place in CNC/L systems which inhibits the particle motion. This is due to the electrostatic interactions taking place between CNC surfaces and Laponite edges, which are having negative and positive charges respectively. Another reason for this is the formation of hydrogen bond between the hydroxyl groups which induces the formation of a 3D network structure. At higher concentrations of Laponite, inflection points can be seen in viscosity versus shear stress graphs (Figure 3) and is due to the process of shear banding in the system. The Here, the viscoelastic nature of the system arises mainly due to the presence of CNC and Laponite particles, since water as a solvent has zero G' values at all frequency ranges, a typical property of Newtonian fluid [START_REF] Buffa | Cellulose Nanocrystals in Aqueous Suspensions: Rheology of Lyotropic Chiral Liquid Crystals[END_REF] . In total, the self-assembly of CNC and Laponite particles within the CNC/L composite systems are responsible for the enhancement of optical properties as well as the rheological properties like elastic modulus, yield stress and viscosity. The hydrogen bond which is a reversible non-covalent interaction arising between CNC and Laponite particles, and the depletion interactions between them are mainly responsible for this physical cross-linking and self-assembly of particles leading to the complex structure formation. The incorporation of Laponite probably induces depletion interactions. At low concentration of CNC and high L, it forms cooperative gels (co-gels), where we did not observe any birefringence from the gels. At high concentrations of Laponite, the gel formation is unavoidable at any pH. Hence in the birefringent gel, the structure could be that the CNC particles are trapped as tactoids in the gel formed by Laponite due to the depletion interactions (Figure 5).

The pH values of 3.0 wt% CNC with varying Laponite concentration ranges from 8.26 to 10 with their conductivity values increases in a non-linear manner from 280 µS/cm to 640 µS/cm (Figure S10). There is a lot of scope to go to higher concentrations and explore the phase behavior, in particular the transition from isotropic to birefringent gel. It should involve a thorough examination of the effect of aging, salt, temperature or higher concentration of the CNC/L system that will be the scope of a future study.

Elaboration of functional nanocomposites

We first investigated the fabrication of nanocomposites thin films by the solvent evaporation method. The obtained thin films made from the binary mixtures are transparent in nature. Interestingly, the increase of Laponite concentration in the resulting films also induces a shift of the 00l Bragg reflections to higher Q-values, suggesting a decrease of the interlamellar distance between Laponite particles. To confirm this trend, we reported in Figure 7f the evolution of basal spacing determined from the position of the 001 reflection, such as d = 2/Q. The d-spacing evolves from 18 to 14 Å with increasing the concentration of Laponite from 0 to 3.0 wt%, whatever the initial concentration of CNC. The lack of CNC effect indicates that this evolution is only due to the swelling behavior of Laponite. However, we obviously did not observe any effect in the other crystallographic directions. The dye adsorption capacity of pure CNC films is very limited compared to CNC/L composite films; whose adsorption capacity increases with the concentration of Laponite. In addition, for CNC/L composite films, the adsorption capacity raises quickly within the first five hours before reaching a plateau corresponding to the maximum upload (Figure 8b). Pure Laponite films are very difficult to prepare and to handle since they start to break in the dye solution immediately after soaking.

The adsorption capacity of films is determined using two kinetic models: Pseudo first order (PFO) and Pseudo second order (PSO) kinetic models. According to PFO kinetic model,

=

where q e and q t represents equilibrium adsorption capacity and adsorption capacity at different soaking times respectively (mmolg -1 ). Here t is the time of adsorption (hours) and k 1 is the rate constant (minute -1 ) of PFO kinetics. Also, PSO kinetics is given by the equation,

= +

where k 2 is the rate constant (mmol -1 gminute) of PSO kinetics [START_REF] Hwang | Dye Adsorption Mechanisms in TiO2 Films, and Their Effects on the Photodynamic and Photovoltaic Properties in Dye-Sensitized Solar Cells[END_REF][START_REF] Ahmad | Improved Adsorption Performance of Rubber-Based Hydrogel: Optimisation through Response Surface Methodology, Isotherm, and Kinetic Studies[END_REF][START_REF] Wu | Carboxylated Cellulose Nanocrystal Microbeads for Removal of Organic Dyes from Wastewater: Effects of Kinetics and Diffusion on Binding and Release[END_REF] . The rate constant and R 2 values obtained from the linear fit of the curve using PSO equation is shown in Table S1 in supporting information. As PSO kinetic model follows a better fit with the experimental data, the adsorption data can be well represented by this model suggesting the mechanism of adsorption to be chemisorption involved between adsorbate and the adsorbent. The rate constant and R 2 values obtained from the linear fit of the curve using PFO equation is shown in Table S2 (Supporting information). As PFO kinetic model follows a better fit with the experimental data, the adsorption data can be well represented by this model. Tables S1 andS2 in Supporting information give the rate constant and

Flame test on aerogels

The CNC/L aerogel samples were prepared via freeze drying method, which has been found to be of light weight possessing a lot of small pores. The method of freeze drying has been used to preserve the gel structure from collapsing due to the effects of drying forces. As shown in figure 9c, the petals of a flower can hold the as prepared aerogel sample indicating that they are too light in weight. The porosity of pure CNC aerogel samples was calculated using the equation, porosity = (1-) x 100%, where is 1.6 g/cm [START_REF] Andrienko | Introduction to Liquid Crystals[END_REF] and is the density of the prepared aerogel. Density of the prepared aerogel was measured by cutting the aerogel sample into cylindrical pieces having height and diameter 0.7 and 1 cm, respectively, and thereby calculating its volume, and the mass of the aerogel in grams is determined by Mettler Toledo weighing balance. The calculated porosity of pure CNC aerogel samples is found to be 96.4%. Similarly, porosity of CNC/L composite aerogel samples are determined using cylindrical shaped aerogel sample of 3.0 wt% CNC and 2.0 wt% Laponite. The height and diameter of the aerogel sample are measured to be 0.7 and 1 cm and the porosity was found to be 98.5 %. CNC/L composite aerogel samples exhibited an enhancement in the porosity as compared to pure CNC aerogels.

We performed flame retardant tests on the as prepared aerogels. Pure CNC samples and the CNC/L composite samples were undergone flame tests and the CNC/L composite samples were found to be flame retardant whereas the pure CNC aerogel does not sustain flame test as shown in Figure 9 (d-f). Aerogels made of pure 3.0 wt% CNC, with the given size, got burnt completely in 18 s, whereas 3.0 wt% CNC with 0.5, 1.0 and 2.0 wt% Laponite, aerogel samples became fire retardant and the images of burnt aerogels at 100s are as shown in figure 9 (g-i). With increase in the concentration of Laponite in the aerogels, they became more and more flame retardant, which is apparent from figure 9 (g-i). An in-depth analysis is needed to understand the internal structure of the aerogels. Thus, the composite aerogels can act as efficient flame-retardant materials, though more thorough tests such varying oxygen, horizontal and vertical flame tests, which may find some new applications as heat insulators in domestic and industrial appliances.

CONCLUSION

The rheological, optical and structural properties of CNC/L composite system have been carefully investigated here in this paper. We expect that as the concentration of CNC increased, the interparticle distance decreased exhibiting excellent birefringent properties which were confirmed by imaging the samples placed between cross polarizers. Most of the investigated concentrations of CNC/L, the suspensions exhibited elastic behavior since, G'>G" in all the frequency sweep graphs and the viscosity profile confirmed the shear thinning behavior exhibited by the CNC/L composite systems. SAXS experiments reveal limited modifications of the microstructural properties of both Laponite and CNC. It appears that the arrested phase is mainly governed by the Laponite concentration, although the presence of CNC shifts the sol/gel transition to lower Laponite concentration. We proposed a phase diagram for the CNC/L binary system which consists of isotropic fluid, co-gels and birefringent gels. We have shown that the films made of the binary mixtures act as efficient dye removal agents. The films are able to remove cationic dyes such as Rhodamine B and Nile blue. Aerogels made of binary mixtures act as efficient flame blockers. From a fundamental point of view, in the field of colloidal binary mixtures, our system serves as a model binary system with complex interactions, and from an applied point of view, we demonstrated that the transparent composite films act as efficient dye removal agents from the solution. They may be further used in photonic applications and thin films for food packaging applications.

Figure 1 .

 1 Figure 1. Naked-eye (top) and microscopic (bottom) optical observations between crossed

Figure 2 .

 2 Figure 2. SAXS profiles for CNC/L binary mixtures prepared with a) 2.0 wt% and b) 3.0 wt%

Figure 3 .

 3 Figure 3. Viscosity versus shear stress plots of a) 2.0 wt% and b) 3.0 wt% CNC at varying

Figure 4 .

 4 Figure 4. a) Frequency sweep plots of 3.0 wt% CNC with varying concentrations of Laponite b)

  minimum shear stress required to disrupt the gel structure and to maintain the flow is termed to be the dynamic yield stress. Here, we determined the dynamic yield stress values of the composite system using Quemada model. They all show an increase in the yield stress values with an increase in the concentration of Laponite in CNC aqueous suspensions. This behavior was further verified by performing oscillation tests such as frequency sweep tests and amplitude sweep tests. Linear viscoelastic measurements reveal the gel nature and the complex network formation within our composite system as the G' values are higher than that of G'' and they are almost independent of the angular frequency and also the G' values increase as the concentration of CNC increases which is a clear indicative of the strengthening of the gel structure within the system.Based on the observations, we propose a phase diagram for the binary mixture system as shown in Figure5. Phase diagram of CNC/L system shows that it can exhibit two phases, the isotropic 22 suspension and the birefringent gel. At varying concentration of CNC in aqueous suspension without Laponite, behaves as an isotropic suspension. As we add Laponite to the aqueous suspension of CNC, birefringent gel formation takes place. From 0.5 wt% added Laponite onwards, the CNC suspensions even at very low concentrations exhibit birefringent gel behaviour.

Figure 5 .

 5 Figure 5. Phase Diagram of CNC/L Composite system. It consists of colloidal fluid ( ),

Figure 6 (

 6 a-d) displays characteristics images of transparent composite films of 3.0 wt% CNC with varying concentrations of Laponite. The transmittance curves for both 2.0 and 3.0 wt% CNC films with varying concentrations of Laponite are reported in Figure S11. The results indicate that the films are transparent over the whole range of wavelength investigated. The

Figure 6 .

 6 Figure 6. Transparent films of 3.0 wt% CNC with a) 0 wt% b) 0.3 wt% c) 0.7 wt% and d) 1.0

Figure 7 .

 7 Figure 7. 2D WAXS patterns of thin-films prepared from a 3.0 wt% CNC with a) 0 wt%; b) 0.5

Figure 8 :Figure 8

 88 Figure 8: a) Absorbance spectra at varying soaking times. b) C t /C 0 vs soaking time, d) q t versus

  R 2 values of PSO and PFO of 3.0 wt% CNC with varying concentrations of Laponite soaked in Rhodamine B and Nile blue dye respectively. Figures S12, S13, S14 and S15 in Supporting information shows respectively the UV-Vis absorbance spectra as well as the PFO and PSO kinetics of 3.0 wt% CNC with varying concentrations of Laponite films soaked in Rhodamine B and Nile blue dye respectively. Next, we focused our studies on the composite aerogels to study their structure and flame-retardant behavior.

Figure 9 :

 9 Figure 9: Flame test on pure CNC and CNC/L composite aerogels. Freeze drying process in

Table 1 .

 1 Characteristic properties of CNC and Laponite used in this work.

		Cellulose Nanocrystals
	Materials	(CNCs)	Laponite (L)
	Properties
	Molecular formula	[(C 6 O 5 H 10 ) 22-28 SO 3 Na] 4-6	Na 0.38 Si 8 (Mg 5.72 Li 0.18 ) O 20 (OH) 4
	Specific Density	1600 kg/m 3	2700 kg/m 3
	Size	Length: 100-300 nm	Diameter: 25 nm
		Diameter: 2-20 nm	Thickness: 0.92 nm
	Zeta potential	-31.6 mV	-36 mV
	pH (in water)	7.0 -8.5	8.0 -10.0
	Optical observations
	The composite samples of CNC/L were transferred to 10 ml glass vials and were allowed to rest
	for at least 2 days at room temperature. Polarized optical observations were first carried out by
	naked-eye inspections on vial samples placed between crossed-polarizers in a home-made setup
	equipped with a Panasonic DMC-FZ18 camera. Microscopic observations were performed on a
	polarizing microscope (BX51-P, Olympus) coupled with an Olympus XZ-1 F1.8 camera. In this

ACKNOWLEDGMENT

Catherine Tom acknowledges the support from Department of Science and Technology, Govt. of India for INSPIRE fellowship. Erwan Paineau thanks Stéphan Rouzière and Marianne Impéror for their support in SAXS experiments and the implementation of analysis tools and Antoine Boury for SEM acquisition. Ravi Kumar Pujala acknowledges the Department of Science and Technology for INSPIRE Faculty Award Grant [DST/INSPIRE/04/2016/002370] and a Core Research Grant [CRG/2020/006281] from SERB, Government of India.

ASSOCIATED CONTENT

Supporting Information.

The Supporting Information is available free of charge via the Internet at http://pubs.acs.org. S1) and Nile blue (Table S1)

Wide

AUTHOR INFORMATION

Corresponding Author

Ravi Kumar Pujala *pujalaravikumar@iisertirupati.ac.in Erwan Paineau *erwan-nicolas.paineau@universite-paris-saclay.fr

Author Contributions


Pierre Le Métayer
email: pierre.lemetayer@supergrid-institute.com

Juan Paez

Sellé Touré

Cyril Buttay

Drazen Dujic

Eric Lamard

Piotr Dworakowski

Break-even distance for MVDC electricity networks according to power loss criteria

Keywords: », «Efficiency», «Power transmission», «Photovoltaic»

The medium voltage direct current (MVDC) technology is emerging in electricity networks including point-to-point transmission, distribution networks and collection networks for renewable energy sources. In this article the MVDC break-even distance (with respect to AC distribution) is calculated according to the overall energy efficiency criteria. The break-even distance is found to vary from less than 10 km to several tens of kilometres depending on power and voltage ratings and network topology.

Introduction

In recent years, the electrical power system has started to evolve from a centralized architecture, with large power plants, to a more distributed architecture integrating many smaller power sources, mainly wind and photovoltaic (PV). The power transmission and distribution systems have to face this evolution and adapt accordingly. The high voltage direct current (HVDC) technology is expanding in the transmission grids. It offers an economically viable solution for long-distance transmission of bulk power, especially when underground or underwater cables are used. Similar reasons that have made the HVDC technology gain momentum in power transmission networks are now causing the medium voltage direct current (MVDC) technology to emerge for power distribution. Recently, Siemens has proposed a product for MVDC links, offering among other advantages lower overall losses and power flow controllability [START_REF] Siemens | siemens.com Global Website[END_REF]. ABB makes a similar analysis in [START_REF] Abb | MVDC and Grid Interties: enabling new features in distribution, sub-transmission and industrial networks[END_REF]. The "Angle DC" project in United Kingdom is an example of converting two existing MVAC circuits to operate as MVDC circuits [START_REF] Yu | Initial designs for the ANGLE DC project; converting existing AC cable and overhead line into DC operation[END_REF], with, as a result, an expected 23% increase in transmitted power capacity. Moreover, the converter stations supplied by General Electric will provide reactive power control capability on both AC networks, which will improve the power quality in the local region and hence reduce the operating losses in the networks. CIGRÉ has provided some foundations for the MVDC grid development in [START_REF]Medium voltage direct current (MVDC) grid feasibility study', e-cigre[END_REF] and the efforts continue in the ongoing working group C6/B4.37. In large offshore wind farms the distance between the wind turbines and the HVDC converter station may exceed tens of kilometres. Since underwater cables are used, then MVDC may be considered [START_REF] Prada Gil | Feasibility analysis of offshore wind power plants with DC collection grid[END_REF], [START_REF] Métayer | Unidirectional thyristor-based DC-DC converter for HVDC connection of offshore wind farms[END_REF]. Large solar power plants, some of which spread over kilometres may also benefit from MVDC, especially because PV modules are inherently producing DC power [START_REF] Cabrera-Tobar | Topologies for large scale photovoltaic power plants[END_REF], [START_REF] Siddique | DC collector grid configurations for large photovoltaic parks[END_REF]. The electrified railway infrastructure may see a new standard of MVDC power supply at 9 kV [START_REF] Verdicchio | New Medium-Voltage DC Railway Electrification System[END_REF]. Ships are also getting more electric and the standards include the MVDC power distribution networks up to 35 kV [START_REF]IEEE Recommended Practice for 1 kV to 35 kV Medium-Voltage DC Power Systems on Ships[END_REF]. All the above clearly shows that MVDC technology have advantages for some specific applications. The criteria for an application to switch to DC will depend strongly on the result of a cost-benefit analysis. One of the important performance indicators is the energy efficiency which is a component of the operational expenditure (OPEX). Power losses in DC cables are lower than in AC cables, as there is no circulation of reactive current in DC and therefore no corresponding Joule losses in the conductors. However, considering that the DC system has to be connected at some point to an existing AC system, a DC-AC converter station is required. This station comes at a given cost and adds power losses. For high voltage links, it has been demonstrated that a break-even-distance exists, where HVDC becomes advantageous over HVAC. The HVDC/HVAC break-even-distance is approximately 50 km in case of submarine cables [START_REF] Schavemaker | Electrical Power System Essentials[END_REF]. In this paper, an MVDC/MVAC break-even distance is calculated according to the overall energy efficiency criteria. The power losses in underground cables and DC-AC converter stations are considered, assuming some hypotheses, in particular regarding the equivalent voltage and power between AC and DC. This study strictly focuses on the efficiency criteria, as accurate cost estimations are not within the scope of the authors' work. Three case studies are presented. The first one is a point-to-point transmission, the elementary block of electricity networks. The second one is a distribution network, a common type of network in today's grid. Third one is a collection network for a large PV installation, to give an example of a network with a particular production profile. The novel aspects of this work are as follows:

-The calculation of break-even distances for MVDC, with clear underlying hypotheses, -The study of the effect on the break-even distance of the power repartition in a multi-terminal network, -The study of the effect of the production profile on the break-even distance.

Methodology

The DC electricity networks are expected to develop together with AC networks following similar principles. The elementary electricity interconnection unit is the point-to-point (P2P) transmission line and it can be realised in AC or DC as presented in Fig. 1a. In the current AC grid, a distribution network is commonly realised as a ring where the individual loads are supplied from a ring main unit (RMU) [START_REF] Leeuwerke | Developments in ring main unit design for improved MV network performance[END_REF]. A normally open point (NOP) separates the system into two radial networks as presented in Fig. 1b. The same ring network architecture can be considered for the collection network of renewable energy sources such as PV or wind. A symmetric monopole line configuration with high impedance grounding is selected for the MVDC line. It offers a good robustness to fault events while reducing isolation constraints. Considering voltage source converter (VSC) AC-DC stations with sinusoidal pulse width modulation, the MVDC voltage is defined as:

> 2 2 3 ≈ 1.6 (1)
where UDC is the DC line-line voltage and UAC is the 3-phase AC line-line RMS voltage. Then, for the comparative analysis of AC and DC, the transmission voltages equivalence between both options can be assumed to be described by [START_REF] Siemens | siemens.com Global Website[END_REF]. A complementary approach to define the equivalence on voltages is to consider the DC voltage that a cable insulation can withstand compared to its AC ratings. In [START_REF] Buchner | Review of CIGRE TB 496 regarding Prequalification Test on Extruded MVDC Cables[END_REF] a 12/20 kV MVAC cable was reported to pass a 55 kV DC test. The conclusion of [START_REF]Medium voltage direct current (MVDC) grid feasibility study', e-cigre[END_REF] is that a MVAC cable rated for X kV AC nominal voltage is recommended for ±X kV DC. The authors follow this recommendation for the choice of the voltage levels.

The comparative analysis of power losses takes into account the cable and AC-DC stations. Other elements of the network are not considered in this analysis. In particular, the transformers (Fig. 1) are assumed to have the same efficiency in both AC and DC systems. The same cables are considered for the DC and AC lines assuming that the MVDC market demand will not allow the development of specific technologies in the short term. One should note that three conductors are used in AC systems while only two are used in DC. This fact should be taken into account when analysing the cost. The cable parameters are presented in Table I, according to [START_REF] Nexans | Underground Power Cables Catalogue 03-2010[END_REF]. For both AC and DC, it is considered the use of single-core, unarmoured copper cables. For the AC case the resistance is calculated taking into account the skin effect [START_REF] Riba | Analysis of formulas to calculate the AC resistance of different conductors' configurations[END_REF]. The cable temperature is assumed to be 70°C. Cable losses calculations are performed based on load flow analysis [START_REF] Macqueen | Time based load-flow analysis and loss costing in electrical distribution systems[END_REF]. The nominal power of the network for each voltage level is calculated according to the maximum cable current. In this analysis a value of Imax = 1 kA is retained. The value of 1 A/mm 2 is a typical current density according to [START_REF] Nexans | Underground Power Cables Catalogue 03-2010[END_REF]. Therefore, the nominal power is calculated as the minimal power between DC and AC transmission that gives the maximal current per cable as expressed in [START_REF] Abb | MVDC and Grid Interties: enabling new features in distribution, sub-transmission and industrial networks[END_REF]. Table II presents the nominal power obtained for each voltage level. The AC-DC converter stations are only required in the MVDC systems. The efficiency of each AC-DC station is assumed to be that presented in [START_REF] Nagel | A 24 MVA inverter using IGCT series connection for medium voltage applications[END_REF]. The reported efficiency of the studied 24 MW 3-level neutral point clamped (NPC) inverter based on IGCTs is approximately 99.1% at low fractions of the nominal power. In this article, the conservative value of efficiency at 99% is considered in the entire power range of the AC-DC converter station.

= √3 , (2)
In the distribution or collection network, if the load or the energy source requires a power conversion equipment then it is assumed that this equipment has the same efficiency in both AC and DC. For example, considering a PV source, the PV inverter and transformer required for the MVAC network is assumed to have the same efficiency as the step-up DC-DC converter needed for the MVDC network.

Point-to-point transmission

In this section the break-even distance for a point-to-point transmission is studied. In order to calculate it, the power losses in the cables are calculated for the different voltage levels defined in Table II.

The power losses are calculated for different distances using the nominal power defined for each voltage level (Table II) and cable parameters (Table I). The results are presented in Fig. 2. The figure shows the losses obtained in the cable for the AC and DC interconnection, as well as the total losses for the DC case if the AC-DC station losses are included. In this case, two AC-DC stations are considered, one at each side of the interconnection, which increases losses by 2 percentage points. It is observed that for all the distances, the losses in the cable are lower in DC. However, because the added losses of the AC-DC stations, the overall losses in the DC installation are higher for distances shorter than the break-even distance (crossing point of red and green curves in the figure). Above this point, DC presents lower losses compared to AC. It is observed how the break-even distance changes with the voltage level. As the voltage increases, the break-even distance shifts to longer distances.

The dashed black line in the figure represents 5% of losses related to the nominal power in each case. This line is shown as reference and gives an idea of the maximum allowed distance for each configuration in terms of losses. Selecting a higher voltage level could be interesting to decrease the losses to an acceptable value. The limit of 5% is given as reference but another limit could be taken from a technical and economic analysis.

The results of Fig. 2 were obtained at the nominal power level of the line. However, according to the application, it could be expected that the line does not operate at nominal power all the time. This is the case when interconnecting renewable sources for example. Then, it is worth analysing the losses for a fixed distance in function of power. Fig. 3 shows the results of this analysis for a given case. It is observed that, for low power loads, AC offers lower losses than DC. However, above a break-even power point the losses in the DC installation are lower than in AC. Therefore, the load profile of the application influences as well the interest of DC transmission over AC. It is observed that the breakeven power changes according to the length of the line. Fig. 4 shows the break-even distance and break-even power for each voltage level. The curves represent the distances and powers for which the losses of the point-to-point transmission are the same for AC and DC. The area above each break-even curve (dashed zone) represents the zone where DC transmission gives lower losses. The area below each curve (coloured zone) represents the zone where AC transmission gives lower losses. The dashed lines for each case represent the limits of the transmission scheme. The maximal power is given for the maximal current allowed in the cable (1 kA is considered), and the maximal distances are given by a limit of 5% of losses. Above these limits the transmission should be done at a higher voltage level.

It can be observed that as the power decreases, the transmission distance becomes longer and the breakeven distance increases. However, at low power the trend for the break-even curve is inversed. This is due to the predominant influence of the capacitive current in the cable (see Table I). In AC transmission at low power and long distance, the capacitive current can be of the same order of magnitude as the active current, causing the corresponding Joule power loss in the conductors to degrade efficiency noticeably.

Distribution network at constant load

The ring or radial distribution network differs from the previous case of point-to-point transmission by the fact that the total power of the installation does not transit through the total length of the cable. Indeed, for a radial network, the power in the cable decreases at each RMU to reach its minimum in the last segment of cable. This means that the losses in the cables of a radial network, of total power P, running along a distance d, will be lower than its point-to-point counterpart. Contrary to the point-topoint configuration the distribution of loads along the line matters in the resulting power losses.

In this section only the 10 kV 17.3 MW configuration is studied according to Table II. The power of a load PRMU is fixed to 250 kW giving in total 69 power loads. A constant-in-time power load is considered. In order to have representative values, a stochastic approach is taken. The power losses in the cables are calculated based on load flow analysis [START_REF] Macqueen | Time based load-flow analysis and loss costing in electrical distribution systems[END_REF] for different total network length. For each total network length, 1000 random RMU repartitions are evaluated. Random distributions are generated while keeping a condition of minimum distance of 60 m between two RMUs. Fig. 5 -Power losses in the 10 kV distribution network over increasing distance: solid line -average power losses, dashed line -min and max power losses according to the random distribution of loads.

It can be observed that, compared with the same voltage/power than in the point-to-point case, the average break-even distance is farther away for the distribution network. This can be explained by the fact that the full power doesn't transit through the whole line. As shown in the previous section, in the case of the point-to-point transmission, the break-even distance gets farther away when the transmitted power decreases. It should be noted that the DC radial distribution network only requires one AC-DC station where two are required in the point-to-point transmission.

The dotted lines in Fig. 5 correspond to the extreme distribution cases giving the minimum and maximum losses. The extreme losses in AC and DC come from the same distribution cases respectively. Thus the break-even distance range calculated for the 1000 random distribution cases in Fig. 5 is between 7.5 km and 13 km. It can be observed that, for the extreme cases, the deviation from the mean is larger in AC than in DC. Fig. 6 illustrates this point. The efficiency of the cable transmission for AC and DC is represented for the 1000 random distribution cases, for a total network length of 30 km. The significant deviation is more noticeable with the increase of distance. The AC transmission efficiency ranges from 91.6% to 96.1% where the DC transmission efficiency ranges from 97.4% to 98.6%. It is observed again from Fig. 5 that for higher losses (low efficiency cases) the break-even distance is shorter. Fig. 7 shows the repartition of RMUs along one total network length (30 km), sorted by increasing efficiency. The density of black dots is higher at long distance and low efficiency, and at short distance and high efficiency. Indeed, when most of the RMUs are located at the other end of the distribution network, the network tends to behave more like a P2P network (with the total power transmitted through the complete distance), with higher losses and shorter break-even distance.

PV collection network with varying power production

Just as in the P2P case, the power transmitted through a distribution network is not necessarily constant over time. As seen in the point-to-point transmission section, the variation in efficiency of the cable transmission with transmitted power should be taken into account in the comparison between AC and DC networks. The previous section presented the distribution network transmitting power to loads but the same ring or radial network can be used for the collection of power from sources. The example of PV collection is taken here to illustrate a network with varying transmitted power. The nature of PV energy production is that the power varies in a wide range according to the irradiation. In order to observe the effect of the variable irradiation, the same random repartition cases of RMUs as in the previous section are considered and the losses are evaluated for different power levels delivered by the sources. All sources are considered to produce the same power.

The statistical study of irradiance rates gave different weighted average efficiencies that can be used to evaluate the performance of a PV system depending on its geolocation [START_REF] Salam | Efficiency for photovoltaic inverter: A technological review[END_REF]. The "European efficiency" [START_REF] Salam | Efficiency for photovoltaic inverter: A technological review[END_REF] is used here. By applying its coefficients to the losses calculations, the "European efficiency-based" break-even distance can be found. The knowledge of the production profile enables to find a break-even distance directly accounting for variable transmitted power, contrary to the general case presented in the previous section where break-even powers had to be calculated. = 0.03 * "% + 0.06 * %&% + 0.13 * '&% + 0.1 * (&% + 0.48 * "&% + 0.2 * %&&% (3) Fig. 8 -European efficiency-based efficiency of the 10 kV PV collection network over increasing distances: solid line -average power losses, dashed line -min and max power losses according to the random distribution of sources It can be observed that taking into account the power variation of the sources results in a break-even distance farther away than in the constant power case. One should note that this procedure can be done in a similar manner for a wind energy installation by using wind speed distributions [START_REF] Lagier | Potential of silicon carbide MOSFETs in the DC/DC converters for future HVDC offshore wind farms[END_REF].

The results of this study can be used as a guideline for the design of the DC-DC converter used in the RMU of the DC architecture. The base hypothesis of the presented break-even distances is the equivalence of the RMU efficiency in both DC and AC architecture. Thus, by taking into account the efficiency of a state of the art AC RMU (in the PV example: string inverter and 50Hz transformer), one can estimate the target efficiency for the DC RMU corresponding to a target break-even distance.

Conclusion

The break-even distance for HVDC has been studied extensively in literature. This paper proposed an efficiency-based break-even distance for MVDC considering different case studies. The point-to-point case showed that the MVDC break-even distance is typically shorter than its HVDC counterpart and depends on voltage and power levels. Compared to HVDC, multi-terminal MVDC are much more commonplace. The case study of the distribution network showed that the low utilization factor of the line pushes the break-even distance farther away than in the point-to-point case. Finally it was observed that light load conditions of renewable energy applications such as PV drives away the break-even distance even more. These consideration can be used to define target efficiencies of future DC-DC converters interfacing MVDC network sources and loads. If the MVDC network was considered without any connection to AC network then the benefits of DC would be significant and the break-even distance would be much shorter. The economic study still needs to be addressed in order to have an equivalent to the existing HVDC break-even distance.

Fig. 1 -

 1 Fig. 1 -Studied architectures in MVAC and MVDC: a) point-to-point transmission; b) distribution/collection ring network (two radial networks)

Fig. 2 -

 2 Fig. 2 -Power losses in function of the distance for the point-to-point transmission at 3 different voltages. The dashed black line represents 5% of losses related to the nominal power.

Fig. 3 -

 3 Fig. 3 -Power losses in function of the power for the point-to-point transmission at fixed distances for the voltage level of 10 kVac / ±10 kVdc.

Fig. 4 -

 4 Fig.4-Break-even distance and power of point to point transmission in terms of losses for different voltage levels. Dashed area represents the power and distance range where DC transmission results in lower losses. The dashed line represents the limits of the transmission scheme (maximal current or maximal losses).

Fig. 6 -

 6 Fig. 6 -Cable transmission efficiency of the 10 kV, 30 km distribution network in function of repartition of RMUs: AC (red) and DC (blue)

Fig. 7 -

 7 Fig. 7 -Random repartition cases of RMUs along a total network length of 30 km. Each black dot represents an RMU. The 1000 configurations are stacked along the vertical axis, ranked from lower (bottom) to higher (top) efficiency.

Table I : Cable parameters

 I

	Network nominal voltage	Cable rating	Section [mm²]	DC resistance @ 20°C [Ω/km]	DC resistance @ 70°C [Ω/km]	AC resistance @ 70°C [Ω/km]	Inductance [mH/km]	Capacitance [µF/km]	Capacitive current [A/km]
	10 kVac / ±10 kVdc	12 kV 1000	0.0176	0.0211	0.0273	0.268	0.904	1.80
	20 kVac / ±20 kVdc	22 kV 1000	0.0176	0.0211	0.0273	0.283	0.584	2.33
	33 kVac / ±33 kVdc	36 kV 1000	0.0176	0.0211	0.0273	0.290	0.380	2.52

Table II : Nominal power at different voltages

 II

	10 kV	±10 kV	17.3 MW
	20 kV	±20 kV	34.6 MW
	33 kV	±33 kV	57.2 MW

Acknowledgements

This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" Program (ANE-ITE-002-01)