Adekunle Ajayi
email: adekunle.ajayi@univ-grenoble-alpes.fr

Julien Le Sommer

Eric P Chassignet

Jean-Marc Molines

Xiaobiao Xu

Aurelie Albert

William Dewar

Diagnosing cross-scale kinetic energy exchanges from two submesoscale permitting ocean models

We used two submesoscale permitting ocean models of the North Atlantic Ocean to investigate kinetic energy exchanges at fine-scales.

• KE fluxes at fine-scales are strongly impacted by submesoscale turbulence with 10 a stronger forward cascade in winter within the mixed-layer.

Introduction

The ocean is a turbulent fluid with a broad range of energetic scales, ranging from large ∼ O(1000 km) to centimeter scales. The ocean kinetic energy is mostly concentrated in the quasi-geostrophic mesoscale eddy field with scales ∼ O(100 km) [START_REF] Stammer | Mesoscale Variability in the Atlantic Ocean from Geosat Altimetry and WOCE High-Resolution Numerical Modeling[END_REF].

Due to non-linear interactions among different length scales, energy can be transferred both from large to small (forward, or direct cascade) and from small to large scale (inverse cascade). Understanding the distribution of kinetic energy (KE) and variance across scales in oceanic flows is, therefore, key to our knowledge of ocean circulation [START_REF] Ferrari | Ocean Circulation Kinetic Energy: Reservoirs, Sources, and Sinks[END_REF].

To estimate the variance and energy associated with eddy motions at different scales, velocity wavenumber power spectral density has proven to be very efficient [START_REF] Le Traon | Spatial scales of mesoscale variability in the North Atlantic as deduced from Geosat data[END_REF][START_REF] Thomas | Submesoscale processes and dynamics[END_REF][START_REF] Fu | Eddy Dynamics From Satellite Altimetry[END_REF][START_REF] Dufau | Mesoscale resolution capability of altimetry: Present and future[END_REF][START_REF] Uchida | Seasonality of eddy kinetic energy in an eddy permitting global climate model[END_REF]. However, spectral density does not indicate the direction of kinetic energy exchanges between the different scales. A better knowledge of cross-scale energy exchanges is gained by looking at the KE cascade due to nonlinearity. This important feature in turbulence study dates back to the work of [START_REF] Charney | Geostrophic turbulence[END_REF] and [START_REF] Salmon | Baroclinic instability and geostrophic turbulence[END_REF] on geostrophic turbulence. For stratified rotating quasi-two-dimensional fluid motion, classical geostrophic turbulence theory predicts a direct cascade of energy if the flow is depth-dependent (baroclinic) but an inverse cascade of energy if the flow is depth-independent (barotropic). In particular, for the ocean with a surface intensified stratification, energy from higher baroclinic modes concentrates in the first mode and then converges toward the scale of the Rossby radius of deformation (R d ) [START_REF] Smith | The Scales and Equilibration of Mid Ocean Eddies: Forced Dissipative Flow[END_REF]. At R d , baroclinic energy is converted to barotropic mode via barotropization.

At this point, most of the energy near the deformation scale cascade towards larger scales while a small fraction undergoes direct cascades to dissipation (see Figure 1). This prediction of geostrophic turbulence theory has been observed both in numerical simulations and the real ocean but with a little discrepancy. Based on altimeter data, Scott and Wang (2005) showed that an inverse cascade of energy dominates the (Pacific) ocean at scales larger than R d . So, if one agrees that the altimeter data is reflecting the first baroclinic mode [START_REF] Smith | The Scales and Equilibration of Mid Ocean Eddies: Forced Dissipative Flow[END_REF], then this is in contrast with geostrophic turbulence theory which predicts a forward cascade for a baroclinic flow. Scott and Wang (2005) argued that there might be an inverse cascade associated with the first baroclinic mode and that this would only partially reduce the forward flux of total baroclinic energy. This total energy forward flux is the source of the kinetic energy that arrives near the deformation scale from the large-scale mean flow via baroclinic instability. From this discrepancy, two questions arise. (i) is the inverse cascade seen at the surface due to the barotropic mode? or (ii) is it possible that the baroclinic modes experience an inverse cascade? Scott and

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manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) Arbic ( 2007) using a 2-layer model simulation showed that the inverse cascade at the ocean surface is mostly baroclinic with a small contribution from the barotropic mode. The results from [START_REF] Scott | Spectral Energy Fluxes in Geostrophic Turbulence: Implications for Ocean Energetics[END_REF] are consistent with the proposed modification to geostrophic turbulence by Scott and Wang (2005). More recent literature [START_REF] Schlösser | Diagnosing the energy cascade in a model of the North Atlantic[END_REF][START_REF] Sasaki | Regionality and seasonality of submesoscale and mesoscale turbulence in the North Pacific Ocean[END_REF][START_REF] Tulloch | Scales, Growth Rates, and Spectral Fluxes of Baroclinic Instability in the Ocean[END_REF][START_REF] Aluie | Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach[END_REF][START_REF] Brüggemann | Routes to Dissipation under Different Dynamical Conditions[END_REF][START_REF] Kjellsson | The Impact of Horizontal Resolution on Energy Transfers in Global Ocean Models[END_REF][START_REF] Khatri | Surface Ocean Enstrophy, Kinetic Energy Fluxes and Spectra from Satellite Altimetry[END_REF] have also shown that an inverse cascade of energy mostly dominates the surface ocean at scales larger than R d .

In contrast, little is known regarding energy cascade at scales < R d , where oceanic motion is dominated by submesoscale motions (< 20 -50 km). Results from numerical simulation and observation have shown an injection of energy in winter at submesoscale [START_REF] Sasaki | Regionality and seasonality of submesoscale and mesoscale turbulence in the North Pacific Ocean[END_REF]. This energy injection is partly responsible for both meso and submesoscale seasonality [START_REF] Uchida | Seasonality of eddy kinetic energy in an eddy permitting global climate model[END_REF][START_REF] Capet | Submesoscale activity over the Argentinian shelf[END_REF][START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF] and has been argued to be associated with mixed layer instability (Callies, Ferrari, et al., 2015;[START_REF] Qiu | Seasonal Mesoscale and Submesoscale Eddy Variability along the North Pacific Subtropical Countercurrent[END_REF][START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF][START_REF] Brannigan | The seasonal cycle of submesoscale flows[END_REF][START_REF] Rocha | Seasonality of submesoscale dynamics in the Kuroshio Extension[END_REF]. This seasonality is responsible for the shallowing of KE spectral slope from -3 in summer to -2 in winter and is usually interpreted as a shift from turbulence dominated by interior gradients (Philips regime) to a regime dominated by surface driven turbulence (Charney regime) (Sasaki et al., 2014). Apart from the work of [START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF][START_REF] Sasaki | Regionality and seasonality of submesoscale and mesoscale turbulence in the North Pacific Ocean[END_REF]; [START_REF] Schubert | The Submesoscale Kinetic Energy Cascade: Mesoscale Absorption of Submesoscale Mixed-Layer Eddies and Frontal Downscale Fluxes[END_REF], we are unaware of any investigation on the implication of submesoscale seasonality on cross-scale energy exchanges at the basin scale and one of the objective of this study is to investigate how submesoscales modify cross-scale kinetic energy exchanges at fine-scales.

Submesoscale resolving ocean models have been developed in anticipation of the Surface

Water and Ocean Topography (SWOT) satellite mission [START_REF] Fu | Eddy Dynamics From Satellite Altimetry[END_REF]. On a global scale, satellite altimeters remain the primary source of information on the distribution of energy across scales. However, at the moment, the resolution capability of our existing oceanobserving satellite altimeters stands at roughly 70 km [START_REF] Dufau | Mesoscale resolution capability of altimetry: Present and future[END_REF]. This limitation undermines our ability to investigate energy exchanges at scales < 100 km. To solve this challenge, SWOT is implemented to provide ten times higher resolution than conventional altimeters, and numerical ocean models have been designed to prepare for SWOT. These state-of-the-art numerical experiments with high-resolution capability, thereby provide an opportunity to study cross-scale energy exchanges down to kilometric scales.

In this study, we aim to investigate the distribution and transfer of energy across different scales by using outputs of two submesoscale permitting ocean models of the North Atlantic. In particular, we focus on the seasonality and depth penetration of cross-scale KE variance and transfer with an emphasis on scales < 100 km. This paper is organized as follows; section 2 presents a description of the two numerical simulations. In section 3,

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This article is protected by copyright. All rights reserved. we examine the kinetic energy wavenumber spectral density and slope. The KE cascade, its seasonality, and the role of high frequency and ageostrophic motions on the cascade are discussed in section 4. Finally, in section 5, we summarize the findings and discuss the relevance of this work in anticipation for SWOT mission.

Numerical simulations of the North Atlantic Ocean

In this study, we use numerical outputs from two submesoscale eddy-permitting simulations of the North Atlantic: a NEMO-based simulation with a horizontal resolution of 1/60 • (NATL60) and an HYCOM-based (HYbrid Coordinate Ocean Model) simulation with a horizontal resolution of 1/50 • (HYCOM50).

The NEMO-based NATL60 has a horizontal grid spacing ranging from 1.6 km at 26 • N to 0.9 km at 65 • N. The initial and open boundary conditions are based on the GLORYS2v3 ocean reanalysis with a relaxation zone at the northern boundary for sea-ice concentration and thickness. The model has 300 vertical levels with a resolution of 1 m at the top-most layers. The grid and bathymetry follow [START_REF] Ducousso | Impact of the symmetric instability of the computational kind at mesoscale-and submesoscalepermitting resolutions[END_REF], while the atmospheric forcing is based on DFS5.2 [START_REF] Dussin | The making of the DRAKKAR forcing set DFS5[END_REF]. DFS5.2 forcing is based on ERA-interim reanalysis.

The spatial resolution of the atmospheric fields is 0.75 degrees. All variables used to compute turbulent fluxes (air temperature and humidity at 2m, wind velocity components at 10m) are 3-hourly. In order to implicitly adapt lateral viscosity and diffusivity to flow properties, a third-order upwind advection scheme is used for both momentum and tracers in the model simulation. The model was spun-up for six months, and a one-year simulation output from October 2012 to September 2013 is used in this study. The simulation output used in this study is the same as the one used in [START_REF] Amores | Up to What Extent Can We Characterize Ocean Eddies Using Present-Day Gridded Altimetric Products[END_REF], [START_REF] Buckingham | The contribution of surface and submesoscale processes to turbulence in the open ocean surface boundary layer[END_REF] and [START_REF] Ajayi | Spatial and Temporal Variability of the North Atlantic Eddy Field From Two KilometricResolution Ocean Models[END_REF]. An earlier version of this simulation set-up was used in [START_REF] Ducousso | Impact of the symmetric instability of the computational kind at mesoscale-and submesoscalepermitting resolutions[END_REF] and [START_REF] Fresnay | Reconstruction of the 3-D Dynamics From Surface Variables ina High-Resolution Simulation of North Atlantic[END_REF].

NATL60 ocean simulation has been evaluated, using in situ observations in terms of the kinetic energy levels at different wavelengths (see Figure 1 of supporting information document (SI)). In terms of the dynamics of the resolved fine-scales in the upper ocean, results from [START_REF] Buckingham | The contribution of surface and submesoscale processes to turbulence in the open ocean surface boundary layer[END_REF] show that the statistics of horizontal velocity tensor predicted by NATL60 agree reasonably well with observation (OSMOSIS datasets). However, their results also show that there is a likelihood of extreme divergent motions in OSMOSIS that is not captured by NATL60. That NATL60 underestimates divergent motions compared to observation isn't that surprising because NATL60 model simulation is without tidal forcing, one of the major sources of wave energy. The model, however, reproduces fairly well other forms of internal gravity waves (see Figure 2 of SI).

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This article is protected by copyright. All rights reserved. The HYCOM-based HYCOM50 extends from 28 • S to 80 • N and has a horizontal grid spacing ranging from 2.25 km at the equator, ∼ 1.5 km in the Gulf Stream region, and 1 km in the subpolar gyre. As for NATL60, the effective resolution is about 10-15 km. The vertical coordinate is hybrid and consists of 32 layers. The simulation is initialized using potential temperature and salinity from the GDEM climatology and spun up from rest for 20 years using climatological atmospheric forcing from ERA-40 [START_REF] Uppala | The ERA-40 re-analysis[END_REF] The model configuration and a detailed evaluation of the model results in the Gulf Stream region with observations are documented in [START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF].

In this study, we use the output from October 2012 to September 2013 for NATL60 and year 20 (last year of the simulation) for HYCOM50. Winter and summer correspond to January-February-March (JFM) and July-August-September (JAS), respectively. The summer analysis presented for NATL60 corresponds to that of the year 2013. Since NATL60 covers a smaller domain than HYCOM50, we consider the HYCOM50 outputs for the same region covered by NATL60 to have comparable results. To capture regional variability in the distribution of energy across scales, we perform spectral analysis in sub-domains of 14 10 • × 10 • boxes across the North Atlantic. We focus specifically on quantifying kinetic energy wavenumber spectral density (Eq. 1) and flux (Eq. 2) using horizontal velocity fields. In equation (1) and equation ( 2), ˆrefers to Fourier transform, * represents the complex conjugate, Re refers to the real part of a complex number and k = k 2

x + k 2 y .

Before performing spectral analysis, the 2D velocity field from each subdomain (box) is detrended in both directions, and a 50% cosine taper window (Tukey windowing) is applied for tapering. An FFT is applied to the tapered data, and a 1D isotropic spectrum is obtained by averaging in the azimuthal direction. Our spectral method is consistent with procedures previously used in [START_REF] Stammer | Mesoscale Variability in the Atlantic Ocean from Geosat Altimetry and WOCE High-Resolution Numerical Modeling[END_REF]; [START_REF] Sasaki | SSH Wavenumber Spectra in the North Pacific from a High-Resolution Realistic Simulation[END_REF][START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF].

E(k) = k+δk k u * • u (k)dk (1) Π(k) = ks k -Re u * • u • ∇ H u (k)dk (2)
Both NATL60 and HYCOM50 resolve the first Rossby radius of deformation everywhere within the model domain, and these simulations reproduce realistic eddy statistics with levels

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of kinetic energy in the range of altimetric observations [START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF], see also Figure 2). A summary of the model parameters is tabulated in Table 1. Both simulations are submesoscale permitting ocean models and a discussion on the ability of these models to resolve the dynamics of submesoscales in terms of eddy length scale, submesoscale energy and their associated seasonality can be found in [START_REF] Ajayi | Spatial and Temporal Variability of the North Atlantic Eddy Field From Two KilometricResolution Ocean Models[END_REF].

We present in Figure 3, the root-mean-square of sea surface height computed from one year daily outputs of NATL60, HYCOM50, compared with AVISO. The AVISO SSH field is derived from observations obtained by altimeter missions and then interpolated onto a 0.25 • mercator grid. In this comparison, we have used AVISO mean dynamical topography dataset from October 2012 to September 2013. The SSH fields in Figure 3 from NATL60 and HYCOM50 have been resampled onto a 0.25 • grid to have comparable results. The SSH rms of the models and AVISO data appears to be consistent in terms of the geographical pattern of energetic oceanic motions except for the differences along the Gulf Stream. The Gulf Stream seems to be more energetic in HYCOM50 compared to NATL60 and AVISO. HYCOM50 has a spin-up of 20 years while NATL60 has a spin-up of 6 months. We hypothesize that HYCOM50 long spin-up allows for the full development of the Gulf Stream energetics and this difference in terms of spin-up could be contributing to differences in the overall energetics of the two simulations. The implication of the short spin-up for NATL60 is more obvious in the time evolution of the domain-averaged kinetic energy (see Figure 3 of SI). The kinetic energy is still increasing with time and is yet to attain equilibrium. A similar curve for HYCOM50 is available in Figure 2 of [START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF]. The comparison of the KE spectral in summer of the year 2012 vs the year 2013 1 (see Figure 4 of SI) further highlights the increase in energy (for NATL60) that is characterized by higher variance and larger eddies at low wavenumbers in year 2013.

The two simulations are similar but are not without differences. HYCOM50 appears to be more energetics compared to NATL60. The disparity between the two models' energy level is not the main focus of this paper, but we shall propose a few reasons why the two models could differ in terms of energetic. Firstly, we hypothesize that the eddy structures in NATL60 are not fully developed due to the short spin-up (6 months for NATL60 versus 20 years for HYCOM50). The first two years of the HYCOM50 simulation show an increase of total kinetic energy level; see Figure 2 in [START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF]. Furthermore, the typical scale of eddies are smaller in NATL60 compared to HYCOM50 [START_REF] Ajayi | Spatial and Temporal Variability of the North Atlantic Eddy Field From Two KilometricResolution Ocean Models[END_REF], and this could be a direct consequence of the shorter duration of the model spin-up.

Secondly, the question did arise as to whether the coarser vertical resolution in HYCOM50

1 The summer analysis presented in the article corresponds to that of year 2013 -7-

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(32 hybrid vertical layers versus 300 z-levels in NATL60) could lead to a stronger inverse cascade and hence a higher energy level because of an under-resolved stratification and the depth dependence of flows. A comparison of the vorticity spectral coherence as a function of depth shows that the two simulations are essentially identical in terms of the depth penetration of energetic eddy structures [START_REF] Ajayi | Spatial and Temporal Variability of the North Atlantic Eddy Field From Two KilometricResolution Ocean Models[END_REF]. Furthermore, in section 4, a comparison of the KE spectral flux at depths for the two simulations will show that the HYCOM50 upscale energy flux is not surface intensified and that having only 32 isopycnal vertical levels is not detrimental to the representation of the dynamics in the ocean interior.

Thirdly, the choice of sub-grid parameterization is different between the two simulations and could have a substantial effect on how energy is dissipated in each model.

Up until recently, most basin-scale numerical models like those used in this study usually store simulation outputs in the form of daily averages due to limitations in storage and computational resources. This limitation comes with a caveat. Daily averaging the model outputs suppresses high-frequency motions (> f , where f is the Coriolis frequency).

These motions are mostly dominated by ageostrophic motions that include unbalanced submesoscales and fast propagating internal gravity waves. There are new shreds of evidence, based on idealized simulations that suggest that high-frequency motions (particularly wave motions) can provide a route to kinetic energy dissipation [START_REF] Barkan | Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves[END_REF][START_REF] Rocha | Stimulated generation: Extraction of energy from balanced flow by near-inertial waves[END_REF]. It would be interesting to investigate these new results in realistic simulations like NATL60 and HYCOM50. Unfortunately, NATL60 and HYCOM50 have most of their outputs stored in daily averages except for the last month of simulation for HYCOM50 and surface quantities for NATL60. To that end, the results presented in this study are based on daily averages of velocity fields from the two simulations. We have only used analysis based on hourly output where necessary to illustrate the impacts of high-frequency motions on the kinetic energy distribution and exchanges.

Distribution of Kinetic Energy

In this section, we discuss the variance at different scales of motions by analyzing the kinetic energy wavenumber power spectral density. In general, horizontal wavenumber spectral density exhibits power-law behavior, where the exponent is interpreted in terms of the dynamical processes governing the eddy energy transfer. Existing theoretical frameworks (for horizontal velocity at scale > Rd) predict a spectral slope of -3 and -5/3 for QG and SQG (surface quasi-geostrophic) turbulence respectively. A slope of -2 is also well known for a front dominated flow [START_REF] Shcherbina | Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field[END_REF][START_REF] Callies | Interpreting Energy and Tracer Spectra of Upper-Ocean Turbulence in the Submesoscale Range (1200 km)[END_REF]. Over the years, many research works have tried to establish the accuracy of these predictions by using outputs of realistic ocean models [START_REF] Sasaki | SSH Wavenumber Spectra in the North Pacific from a High-Resolution Realistic Simulation[END_REF][START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF][START_REF] Uchida | Seasonality of eddy kinetic energy in an eddy permitting global climate model[END_REF]

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al., 2017) and also recently within the context of the real ocean by using altimeter dataset [START_REF] Le Traon | Spatial scales of mesoscale variability in the North Atlantic as deduced from Geosat data[END_REF][START_REF] Dufau | Mesoscale resolution capability of altimetry: Present and future[END_REF]. Their results have argued for the non-existence of a universal wavenumber spectrum [START_REF] Le Traon | Do altimeter data agree with interior or surface quasi-geostrophic theory[END_REF]) following observed regional variability. We shall discuss in section 3.1, the distribution of kinetic energy as predicted by NATL60 & HYCOM50 and in section 3.2 we discuss the variability associated with this distribution and their associated estimated slope.

Spectral Density

In Figure 4, we present the kinetic energy spectral density as a function of depth for the two simulations. For simplicity, we show this comparison only for Box 8, a box located at the center of the North Atlantic basin. In most of the regions, the peak of the spectral density is around the mesoscale motions (100-500 km). As expected, the energy associated with large-scale motion is relatively higher than that of fine-scales. The peak of the spectral density is preserved with depth, while the variance at all scales decreases with depth. The comparison between the two simulations is illustrated better in Figure 5a where we present the depth-averages of annual KE spectral density for the two simulations in the same region (Box 8). The spectral densities from the two models agree well with an approximate slope of -3, a value that is characteristic for Quasi-Geostrophic (QG) prediction. In this QG regime, submesoscale structures are expected to be weakly energetic while energy is concentrated at the mesoscales. The depth-averages of the winter and summer KE spectral density are presented in Figure 5b. There is a seasonality in the spectral density that is mostly associated with an increase in the variance at submesoscales in winter. The spectral shape in both winter and summer are somewhat QG. We find this surprising given that previous studies [START_REF] Callies | Interpreting Energy and Tracer Spectra of Upper-Ocean Turbulence in the Submesoscale Range (1200 km)[END_REF][START_REF] Shcherbina | Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field[END_REF][START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF] have shown that in the presence of intense submesoscales in winter, KE spectral density is likely to have k -2 or k -5/3 spectral shape.

As previously highlighted, daily averaging the velocity fields before spectral estimation could suppress the signature of high-frequency motions (unbalanced submesoscales, ageostrophic wave motions) and this could affect the distribution of energy implied from this sort of spectral analysis. To ascertain this, we compared NATL60 surface KE spectral density for hourly averages versus daily averages in Figure 6a. This comparison is only possible for NATL60 because HYCOM50 dataset is stored in daily averages except for the last month of the simulation. In this comparison for NATL60 (Figure 6a), submesoscale motions are more energetic than presented in the daily spectral density. There is a tendency for the distribution (annual average) of energy at submesoscales in the hourly spectral to follow a k -2 spectra shape, a characteristics of a regime associated with fronts.

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The winter versus summer spectral density computed from NATL60 hourly averages of the velocity field (Figure 6b), clearly show how high-frequency motions and energetic submesoscales drive the seasonality of kinetic energy distribution at fine-scales. There is a shift in the spectral slope from -3 in summer to -2 in winter. This shift can be interpreted as a change in dynamics from the interior QG Philips-like regime to a surface intensified Charney-like regime [START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF]. In this Charney-like regime, submesoscales are associated with large vertical velocity and, in turn, large submesoscale buoyancy fluxes that are suggested to feed mesoscales through an inverse kinetic energy cascade. This result is consistent with the findings of [START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF]; [START_REF] Callies | Interpreting Energy and Tracer Spectra of Upper-Ocean Turbulence in the Submesoscale Range (1200 km)[END_REF], and it further evaluates the ability of NATL60 to resolve physical processes at fine-scales. In section (4), we shall also discuss how this regime change from summer to winter affects the redistribution of kinetic energy.

Spectral Slope

As we have shown in the previous section, a quick way to estimate the wavenumber spectral power law is to compute the 1D wavenumber spectral density then estimate a slope from this spectral by fitting a line to the spectral density curve within a selected wavenumber range. This method is fast and easy to implement and provides a way to investigate regional variability of ocean energetics both at the basin and global scale. For studies on mesoscale energetics using satellite datasets and model outputs, this wavenumber range is mostly within the error limits of the altimeter instrument (∼ 70 km) and the horizontal scale of meso/large scale motion (250-300 km). One drawback of this approach is that it does not account for the changes in the scale of average energetic eddy structures with latitude. Scales of motions that are mesoscales in the polar regions could be classified as submesoscales in the tropics.

To characterize the spectral signature correctly, several recent studies have tried to propose different approaches to estimate the wavenumber spectral power law. For mesoscale resolving altimetry datasets, [START_REF] Vergara | Revised Global Wave Number Spectra From Recent Altimeter Observations[END_REF] estimated spectral slope between the peak of the spectral and the minimum of the Rossby radius and the Rhines scale following [START_REF] Eden | Eddy length scales in the North Atlantic Ocean[END_REF]. A similar approach was presented in [START_REF] Sasaki | SSH Wavenumber Spectra in the North Pacific from a High-Resolution Realistic Simulation[END_REF], where the authors estimated spectral slope between a fixed wavelength of 30 km (at the lower bound), and a scale that corresponds to the peak of the KE wavenumber spectral.

In order to show how sensitive the estimated slopes are to the selected wavelength range, we present in Figure 7a To avoid the sensitivity of the estimated spectral slope to an a-priori selected wavelength range, we introduce an approach that takes into account the dynamics of the regions and the resolving capability of the model by estimating the spectral slope (Figure 7b) between the energy-containing scale [START_REF] Kjellsson | The Impact of Horizontal Resolution on Energy Transfers in Global Ocean Models[END_REF] and the effective resolution of the model [START_REF] Soufflet | On effective resolution in ocean models[END_REF]. The energy-containing scale (which represents the scale of the most energetic eddy structure) is estimated from the kinetic energy wavenumber spectral using equation ( 3) while the effective resolution (a function of the model grid-size) is taken as 5 × the model grid size, which is roughly equal to 10 km for both models. This approach takes into account the scale of the energetic eddy structures within the flow region and also takes into account the geographical variability of this scale, and therefore provides a way to infer dynamical properties of oceanic motions in different regions.

λ e = E(k x , k y )dk x dk y k 2 x + k 2 y E(k x , k y )dk x dk y (3)
We apply this technique to the output of both simulations (KE spectral density from daily averages), and we present the estimated spectral slope and the energy-containing scale (integral scale) for all the boxes in the North Atlantic (Figure 9). The estimated integral scale from the wavenumber spectral density represents the averaged scale of energetic structures in the selected region. On one hand, this scale varies regionally and fairly follows the variability of the Rossby radius of deformation with latitude, with high values in the south and relatively low values in the north. On the other hand, the estimated slope across the basin is almost uniform and follows the prediction of QG with a slope value ∼ k -3 . This consistency with the QG prediction is observed in both model outputs and also holds in the well known high energetic Gulf stream (box 1) and the low energetic OSMOSIS (box 10) regions. This result form daily fields comes with the caveat of suppressing the impact of high-frequency motions on the estimated slope values.

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In order to investigate whether accounting for high-frequency motions would affect our estimation of spectral slopes, we estimate the spectral slope (from KE spectral density computed using hourly averages of velocity fields). We do this only for NATL60 because HYCOM50 surface hourly output is available only for one month. The NATL60 spectral slope from hourly spectral density in all the regions (Figure 10) has smaller values than that of daily averages. As previously highlighted in section 3.1, this implies that the actual spectral are shallower in hourly fields (as a result of stronger variance at the fine-scales) compared to daily fields. The impact of intense submesoscale and ageostrophic flows is better illustrated in the winter/summer map of the spectral slope (Figure 11). The slopes in winter have values that are closer to k -2 throughout the domain. This indicates that high-frequency motions are quite significant in the North Atlantic ocean basin. In the next section, we shall discuss the impact of different dynamics on the redistribution of kinetic energy.

Kinetic Energy Cascade

In this section, we present and discuss the exchange of energy due to non-linearity across different scales of motion. This exchange is estimated from the horizontal velocity fields using equation [START_REF] Thomas | Submesoscale processes and dynamics[END_REF]. A positive flux represents a direct cascade of energy, while a negative value represents an inverse cascade of energy.

Annual Averages of Kinetic Energy Cascade

We show in Figure 12 the KE spectral flux computed using one year's daily outputs of surface velocity fields. For simplicity, we show plots for boxes 3, 8, and 11 representing latitudes of 35 • N, 45 • N, and 55 • N, respectively. In all the boxes and both models, the spectral flux is dominated by an inverse cascade of energy at large scales (between 25-50 km and 500 km) and a forward cascade of energy below 25-50 km. As observed earlier, the spectral slope from daily averaged fields has a value that is ∼ -3, a characteristic of QG turbulence. The energy exchanges computed using the same data show that the flux is mostly upscale with a little forward flux at fine-scales. While the inverse cascade is a well known phenomenon in geostrophic turbulence, the dynamics responsible for the forward cascade at fine-scales is, however, still a subject for discussion. One would expect a forward flux at fine-scales to be accompanied by a (k -2 or k -5/3 ) spectral slope. This sort of relationship between spectral density and flux is not observed for estimates coming from the daily fields. This finding is, however not new and agrees with the results of [START_REF] Brüggemann | Routes to Dissipation under Different Dynamical Conditions[END_REF]. The authors show that as soon as ageostrophic dynamics become important in a quasi-QG flow, the flow is no longer restricted to an inverse cascade of energy. Instead, for the flow to be in a regime that supports a forward cascade of energy.

It is interesting to note that the scale at which the inverse cascade is most intense coincides with the energy-containing scale (dashed line in Figure 12 estimated from the kinetic energy spectral density). This signifies that the inverse cascade is maximum at the scale of the most energetic eddies. Just like the energy-containing scale, the scale of the most intense inverse cascade varies with latitude with relatively smaller values in the sub-polar regions (Figure 13). Also, depending on the region, part of the submesoscale range (0 to 25-50 km) falls to the left of the zero-crossing (where the flux changes sign). This implies that submesoscales motions are involved in fluxing energy to large-scale via an inverse cascade of energy. This scale of zero-crossing varies across the basin with higher values in high EKE regions and relatively smaller values in low EKE regions (Figure 13). This regional variability in the value of the zero-crossing shows that at fine-scales, the spatial scale at which energy is injected into the flow is greater in eddy-rich regions, compared to eddy-poor regions.

Figure 14 presents the KE spectral flux for Box 8 as a function of depth. The overall shape of the flux is preserved, and the scale at which the inverse cascade is maximum is also consistent with depth. The strength of the inverse cascade decreases with depth, and the direct cascade at high wavenumbers is confined mostly to the surface. In section 3.1, the question was raised as to whether HYCOM50's higher KE, when compared to NATL60, is a consequence of HYCOM50's coarser vertical resolution, which could lead to a surface intensified inverse cascade and hence more energetic surface eddies. However, in Figure 14, we can see that both at the surface and all depth levels, the estimated inverse and direct cascade is stronger in HYCOM50 than in NATL60. This indicates that HYCOM50 upscale energy flux is not surfaced intensified and we can conclude that the disparity between the two models in terms of energy levels is most likely due to differences in the length of the spin-up as well as the choice of sub-grid scale parametrization, and that having only 32 isopycnal vertical levels is not detrimental to the representation of the dynamics in the ocean interior.

Seasonality of Energy Cascade

In this section, we present the seasonality of the kinetic energy spectral flux by comparing winter (JFM) and summer (JAS) averages. Figure 15 shows the winter cascade (in blue)

and the summer cascade (in red). There are two notable differences between the seasons.

First, there is a shift in the zero crossings to higher wavenumbers in winter. Second, there

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manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) kinetic energy dissipation is illustrated in these results. The dynamics responsible for this increase in forward cascade are likely due to an energy loss to the generation of gravity waves and unbalanced submesoscales. It is interesting to note that the scale of the most intense inverse cascade remains the same while there is a slight shift in the zero-crossing towards higher wavenumber. This result suggests that the impact of high-frequency motion on energy exchanges is mostly concentrated at fine-scales. As seen in the daily averages, the winter flux is equally stronger in hourly fields (Figure 16a). We believe that this increase is attributed to resolved internal gravity waves and intense (un)balanced submesoscales.

However in summer time both daily and hourly flux are identical.

4.4 Diagnosing Spectral Flux from SWOT NATL60 and HYCOM50 are submesoscale permitting model simulations that have been created to simulate the scales of motions that we expect SWOT to see from space. SWOT will provide measurements of sea surface heights from which velocities (based on geostrophic approximations) will be inferred. Geostrophically balanced motions dominate the ocean at meso/large-scale, and the inferred geostrophic velocities at this scale mostly reflect the absolute velocity of these large scales motions. However, geostrophy is less accurate for fine-scale motions, particularly at the submesoscales and this remains a challenge due to the projection of ageostrophic motions on SSH field. Recent studies have shown that some classes of non-wave ageostrophic motions could impact the forward cascade of kinetic energy at fine-scales [START_REF] Capet | Mesoscale to Submesoscale Transition in the California Current System. Part III: Energy Balance and Flux[END_REF]. We have equally shown in the previous sections that high-frequency motions in the form of ageostrophic waves and unbalanced submesoscales can contribute significantly to a forward cascade of energy at fine-scales.

In light of this, we are not sure if SWOT data can accurately estimate the redistribution of kinetic energy at fine-scales, given that SWOT will provide information down to ∼ 15 km. We are curious to see if the geostrophically inferred surface velocity would capture the accurate energetics at scales < 50 km where geostrophy is likely to fail.

To investigate this, we present in Figure 17 the spectral flux from total velocity and geostrophic velocity for three regions (same as for the previous sections). The geostrophic velocity is estimated from the sea surface height (SSH) using the geostrophic approximation.

The strength of the energy cascade differs between the flux computed from the total velocity and that of the geostrophic velocity. This difference is consistent in all three boxes and in the two models. In particular, at the very high wavenumbers, the forward cascade is underestimated in the flux computed from the geostrophic velocity. A possible reason for this mismatch at smaller scales could be explained by the findings of [START_REF] Brüggemann | Routes to Dissipation under Different Dynamical Conditions[END_REF] that showed that ageostrophic flows at fine scales are an excellent catalyst for energy

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manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) cascade towards dissipation. Despite the differences in terms of flux magnitude, the overall shape of the flux is consistent for the two forms of spectral flux. The scale at which the inverse cascade is maximum is the same irrespective of the type of velocity fields.

Discussion and Summary

In this study, we presented the analysis of kinetic energy wavenumber spectral density, slope, and flux by using datasets from daily and hourly outputs of two submesoscale permitting ocean models of the North Atlantic. The analysis presented has shown that in summer, the North Atlantic ocean follows the QG framework (with ∼ k -3 spectral shape) and in winter, the basin mostly reflects a k -2 spectral shape, a characteristic of a front dominated regime. The estimated kinetic energy spectral flux revealed an overall net inverse cascade of energy with a significant direct cascade of energy at high wavenumbers. The spectral flux undergoes a seasonality that is associated with a stronger forward cascade at high wavenumbers in winter. This increased forward cascade in winter is further amplified in the presence of high-frequency motions. The spectral flux as a function of depth reveals that the forward cascade at high wavenumbers is confined to the mixed layer while the inverse cascade dominates the water column down to 700m. We showed that the maximum inverse cascade occurs at a scale that coincides with the energy-containing scale.

Until recently, most basin/global scale simulations had their outputs stored in the form of daily averages. Our results show that high-frequency motions (that are only resolved in hourly outputs) affect the distribution and exchanges of kinetic energy. We observed that the difference between the daily and hourly results is mostly in the form of an increased variance and (forward) cascade at fine-scales in favor of hourly fields. High-frequency motions are dominated mainly by ageostrophic motions that include unbalanced submesoscales and fast propagating internal gravity waves. These two classes of motions are out of phase seasonally with stronger submesoscales in winter and stronger internal gravity waves in summer. It is puzzling that while the exchanges of energy at fine-scale are unaffected by high-frequency motions in summertime, the distribution of energy shows the contrary. We observed higher variance at fine-scales in power spectral density estimated from hourly fields. The reason for this disparity between the impact of high-frequency on spectral density and flux in summertime is not apparent but would be an interesting subject to investigate further.

The kilometric simulations used in this study have similar horizontal grid spacing but different numerics, sub-grid parameterization, and vertical resolution. Despite these differences, the two simulations agree well on the overall dynamics of the North Atlantic.

However, HYCOM50 is more energetic compared to NATL60 both at the surface and in the interior. We found the estimated cascade in HYCOM50 to be of higher magnitude

  manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES)

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  , with 3-hourly wind anomalies from the Fleet Numerical Meteorology and Oceanography Center 3-hourly Navy Operational Global Atmospheric Prediction System (NOGAPS) for the year 2003. The horizontal viscosity operator is a combination of Laplacian and Biharmonic. The bathymetry is based on the Naval Research Laboratory (NRL) digital bathymetry database.

  the average KE wavenumber spectral density and slope for box 3 in March for three different selected wavenumber ranges. The dashed lines with colors red, blue, and black represent the 10-100 km, 10-250 km, and 70-250 km, wavelength, respectively. The estimated slopes for these three different wavelength ranges have different values, therefore raising the question as to which slope is most representative of the dynamics of this region. We repeat this analysis for all the boxes and present the map in Figure8. The mismatch is particularly pronounced in the sub-polar region, where the scales of the eddy structures are relatively smaller. The 70-250 km wavelength range is a typical wavelength for estimating spectral slope for satellite datasets because 70 km roughly corresponds to the wavelength where the satellite data becomes noisy. The spectral slope in this range is consistent with the already published work of[START_REF] Dufau | Mesoscale resolution capability of altimetry: Present and future[END_REF] and[START_REF] Chassignet | Impact of Horizontal Resolution (1/12 • to 1/50 • ) on Gulf Stream Separation, Penetration, and Variability[END_REF].

  ftp://ftp.hycom.org/pub/xbxu/ATLb0.02/ and http://meom-group.github.io/swot-natl60/access-

568

data.html, respectively. 569

Acknowledgments

We thank three anonymous reviewers for providing helpful and stimulating comments that have greatly improved the manuscript. Adekunle Ajayi is partly funded by the University Grenoble Alpes AGIR research grant. Aurlie Albert is funded by the CMEMS Global High-Resolution MFC 22-GLO-HR project. Julien Le Sommer contributions are funded by CNES through their participation in the SWOT Science Team. Eric Chassignet and Xiaobiao Xu are supported by the Office of Naval Research (Grant N00014-15-1-2594) and the NSF Physical Oceanography Program (Award 1537136). William Dewar is supported by the French "Make Our Planet Great Again" program managed by the Agence Nationale de la Recherche under the Programme dInvestissement dAvenir, with the reference ANR-18-MPGA-0002 and by NSF grants OCE-1829856 and OCE-1941963. We

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-24-

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manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) is a stronger forward cascade within the submesoscale range in winter. As highlighted in the preceding section, a zero-crossing at the high wavenumbers partly indicates how much submesoscale motions are involved in feeding large-scale motions via an inverse cascade of energy. So, a shift to higher wavenumbers in wintertime signifies that smaller-scale structures are involved in fluxing energy to larger scales. It is noteworthy that the integral scale and scale of the maximum inverse cascade also undergo seasonality. There is a shift in the scale to high wavenumber from winter to summer. This can be interpreted as a reduction in the average size of energetic eddies structures in winter. This sort of seasonality in eddy length-scale is documented in [START_REF] Ajayi | Spatial and Temporal Variability of the North Atlantic Eddy Field From Two KilometricResolution Ocean Models[END_REF].

It is interesting to understand the contribution of the different dynamics on the seasonality of the energy cascade. Recent studies have shown that submesoscales are energetic in wintertime [START_REF] Mensa | Seasonality of the submesoscale dynamics in the Gulf Stream region[END_REF][START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF][START_REF] Callies | The role of mixed-layer instabilities in submesoscale turbulence[END_REF][START_REF] Rocha | Seasonality of submesoscale dynamics in the Kuroshio Extension[END_REF], and their emergence is forced by mechanisms such as frontogenesis, wind-induced frontal instabilities, mixed layer instability among many others [START_REF] Thomas | Submesoscale processes and dynamics[END_REF][START_REF] Mcwilliams | Submesoscale currents in the ocean[END_REF]. [START_REF] Sasaki | Impact of oceanic scale-interactions on the seasonal modulation of ocean dynamics by the atmosphere[END_REF] argued that submesoscales generated via mixed layer instability could feed large scale motion via an inverse cascade of energy, hence a shift in the zerocrossing towards high wavenumbers. More recently, [START_REF] Schubert | The Submesoscale Kinetic Energy Cascade: Mesoscale Absorption of Submesoscale Mixed-Layer Eddies and Frontal Downscale Fluxes[END_REF] used both the coarse-graining approach [START_REF] Aluie | Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach[END_REF] and spectral analysis to investigate the role of mixed layer baroclinic instabilities on kinetic energy exchanges. Their results show that mesoscale oceanic eddies are strengthened by the absorption of submesoscale mixed layer eddies and that the forward cascade of energy at very fine-scales occur mostly in frontogentic regions. Following these aforementioned findings, we hypothesize that the increased forward cascade presented in this study, could be associated with frontogenesis and submesoscale frontal instabilities. This seasonality highlights how submesoscale motions modulate the redistribution of energy between scales of motions; hence, the need for climate (ocean) models with submesoscale resolving capability.

Impact of High-Frequency Motions on Energy Cascade

In section 3.1, we observed that in the presence of high-frequency motions, the spectral densities (computed from hourly fields) are shallower with an increased variance at finescales compared to daily averaged fields. In this section, we are going to discuss the impact of this increased variance on energy exchanges.

The contribution of high-frequency motions to kinetic energy spectral flux is highlighted in Figure 16a where we show the comparison of the spectral flux computed from daily versus hourly fields. The magnitude of the forward cascade at submesoscales is significantly stronger in hourly spectral flux. That high-frequency motions can provide a pathway to

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manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) compared to NATL60 for both direct and inverse cascade. The difference in energy levels between the two models could be due to the difference in length of spin-up or/and the choice of subgrid-scale parameterization. Initially, we thought that HYCOM50 having just 32 hybrid layers in the vertical, could lead to a more surface intensified energy cascade in HYCOM50 than in NATL60. Nevertheless, this is not the case, because across all scales and at depth, HYCOM50 seems to show stronger energetic compared to NATL60. NATL60 and HYCOM50 are designed mainly to serve as an observational dataset for the anticipated SWOT mission. SWOT will provide sea surface height, and by using geostrophic approximation, we would obtain the geostrophic velocity, a requisite for computing crossscale energy transfer. At fine-scale, geostrophic approximation is however less accurate.

Thus, accurately diagnosing surface velocity from sea surface height at fine-scales remains a challenge, and this has an impact on the estimate of kinetic energy cascade. Our results show that at fine-scales, not accounting for the ageostrophic motions could affect at all scales, the true magnitude of the estimated cascade of kinetic energy.

The results presented in this study are based on the output of ocean numerical simulations that are forced with realistic atmospheric winds. Recent literature suggests that air-sea coupling at fine-scales could affect the evolution and energetics of oceanic eddies. [START_REF] Renault | Modulation of wind work by oceanic current interaction with the atmosphere[END_REF] using a coupled/uncoupled model of the California Upwelling System argued that the ocean-atmosphere interactions have feedback that acts as an oceanic eddy killer. This feedback deflects energy from the geostrophic current into the atmosphere and dampens geostrophic kinetic energy. A possible future study would be to recompute the (kinetic energy transfer) diagnostics in this study using datasets from an ocean-atmosphere coupled simulation. This sort of analysis would take into account the direct impact of air-sea interaction on the ocean's kinetic energy exchanges.

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This article is protected by copyright. All rights reserved. (b) A schematic to illustrate the proposed dynamical approach to estimate spectral slope. λe is the energy-containing scale (which represents the scale of the most energetic eddy structure) and it is estimated from the kinetic energy wavenumber spectral density by using equation (3) while Er is the effective resolution (a function of the model grid-size) and is taken as 5 × the model grid size.

Er is roughly equally to 10 km for both NATL60 and HYCOM50.

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Namory Méité

Koffi Léon

Monique Tohoué Konan
email: cmonique.tognonvi@upgc.edu.ci

Tognonvi

Irié Bi

Goure Hervé
email: dgoure_herve2610@yahoo.fr

Moussa Doubi

Samuel Gomina

Oyetola

Namory M Éit

Koffi Konan

Monique Tohou

Bi Tognonvi

Iri É Herv

Goure Doubi

Moussa Gomina
email: emoussa.gomina@ensicaen.fr

Samuel Oyetola
email: foyetolasamuel@yahoo.fr

Konan

; Monique

Tohoué Tognonvi

; Bi

Irié Hervé

Properties of hydric and biodegradability of cassava starch-based bioplastics reinforced with thermally modified kaolin

Keywords: Carbohydrate Polymers Cassava starch-based bioplastic, Kaolin, Metakaolin, Hydric properties, Biodegradability

Introduction

The ever-growing utilization of plastic materials from petrochemical sources is necessarily accompanied by environmental repercussions. The vast majority of these plastic wastes are non-biodegradable. They can remain in the environment for very long periods (100 to 1000 years). In addition, the incineration of such wastes is very polluting. It releases significant amounts of carbon dioxide and other toxic gases harmful to the environment and human health [START_REF] Belyamani | Développement d'un matériau thermoplastique biodégradable et hydrosoluble à base d'une protéine du lait[END_REF].

Addressing plastic pollution, therefore, requires the development of biodegradable biopolymers, as an alternative to synthetic polymers. Thermoplastic packaging has considerably expanded in recent years. They possess the advantage of being inexpensive (raw materials), lighter, impact resistant and easy to implement. In addition, they are biodegradable, which prevents them from piling up in landfills. Biodegradation is a catalyzed degradation (in the soil or on the soil surface) by micro-organisms [START_REF] Siracusa | Microbial degradation of synthetic biopolymers waste[END_REF]. Then, the material structure is simplified to finally convert into H2O, CO2, CH4, and/or into a new biomass and eventually to a non-toxic residue for humans and the environment.

J o u r n a l P r e -p r o o f

Starch is a natural polymer that can be easily plasticized by means of glycerol [START_REF] Tyagi | Properties of cassava starch based bioplastic reinforced by nanoclay[END_REF]. However, starch-based bioplastics are generally characterized by weak mechanical properties and a high water sensitivity [START_REF] Kaewtatip | Structure and properties of pregelatinized cassava starch/kaolin composites[END_REF][START_REF] Souza | Cassava starch biodegradable films: Influence of glycerol and clay nanoparticles content on tensile and barrier properties and glass transition temperature[END_REF]. Their functional properties can be improved by using reinforcements such as vegetable fibers, celluloses and clays. The growing interest in clays is justified by their abundance in nature, their nanometric size, and their biocompatibility. The montmorillonite type lamellar structure clays are increasingly used as reinforcements in polymer matrices because of their ability to easily exfoliate [START_REF] Islam | Effects of plasticizers and clays on the physical, chemical, mechanical, thermal, and morphological properties of potato starch-based nanocomposite films[END_REF]. By dispersing them at the nanometric level, these minerals considerably increase the mechanical properties and the impermeability level with a low charge rate.

On the other hand, kaolinitic clays, although abundantly available in Côte d'Ivoire, remain hardly used [START_REF] Sei | Role of iron oxid the phosphate adsorption properties of kaolinites from the Ivory Coast[END_REF][START_REF] Konan | Caracterization of Azaguie-Blida site clay materials (Anyama, Côte d'Ivoire) and J o u r n a l P r e -p r o o f determination of ceramic products mechanical properties[END_REF]. In fact, the interlayer hydrogen bonding and the low permanent charge of the sheets give them a non-expandable character which makes their dispersion in the polymer matrix difficult. Obtaining less cohesive kaolinite has often been achieved through a chemical treatment with dimethyl sulfoxide (DMSO). [START_REF] Meite | Structural and thermomechanical study of plastic films made from cassava-starch reinforced with kaolin and metakaolin[END_REF] have showed that the thermal treatment of the kaolin (labelled KF) at 700 °C for 1 hour improves the physico-chemical properties of the bioplastics. The utilization of heattreated kaolin as reinforcement in bioplastics is likely to avoid environmental toxicity issues contrary to chemical additives. In this study, hydric and biodegradability properties of cassava starch-based bioplastics reinforced with crude kaolin or heat treated kaolinitic clay at 700 °C called metakaolin with respect to the interaction between cassava starch and kaolin, in two different crystalline forms were studied. After discussing the notable structural differences between kaolin and metakaolin, evidenced by different techniques, the water adsorption and the mass loss of the samples as a function of the exposure time on the soil surface and the burial time in the ground were evaluated.

J o u r n a l P r e -p r o o f

Materials and methods

Materials

The starch used is obtained from a variety of cassava called Bocou 2 (Manihot Esculenta crantz). The tubers were harvested in the region of Yamoussoukro, on the site of 06°53'785'' N and 05°14'441''W geographic coordinates. Glycerol (50% volume) provided by a local company was used as a plasticizer to manufacture the starch-based bioplastics. A 0.1 mol/L hydrochloric acid solution prepared from a commercial solution (HCl, Sigma-Aldrich) was used to promote starch chains destructuring. A sodium hydroxide of 0.1 mol/L (NaOH, Sigma-Aldrich) was also used for the pH stabilization. The kaolin clay (labelled KB) was collected from Yaou, a village located in South-Est of Côte d'Ivoire. The geographic coordinates of the sampling site are 05 ° 15'013''N and 03 ° 37'485''W. The metakaolin (denoted MKB) was obtained after calcining the crude kaolin at 700 °C for 1 h by means of a programmable Nabertherm type furnace with a heating rate of 5 °C/min.

Bioplastic preparation

Non-reinforced bioplastics (BP) and bioplastics containing 5 wt% of crude kaolin (BPKB) or metakaolin (BPMKB) were prepared according to the procedure described in previous work through the casting/evaporation method [START_REF] Meite | Structural and thermomechanical study of plastic films made from cassava-starch reinforced with kaolin and metakaolin[END_REF]. A mixture of 2.5 g of the starch, 4 mL of glycerol (50% Vol.), and 3 mL of HCl (0.1 mol/L) was poured into 25 mL of distilled water under magnetic stirring (250 tr/min) for 30 min. Thereafter, 5 wt% KB or MKB was added followed by 30 min of magnetic stirring at room temperature (range of 20-25°C). The obtained homogeneous mixture was then heated by means of an electronic hot plate up to 100 ± 1°C under constant stirring. After 10 min of stirring, 2 mL of NaOH (0.1 mol/L) was added in order to decrease the mixture viscosity and acidity, still under thermal agitation for another 5 min. Finally, this hot gel-like suspension was cast in Petri dishes and allowed to dry at room temperature for 72 h before demoulding. The tests were repeated three times in each case.

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Methods

Chemical compositions

The chemical analysis of the clay used in this study was determined by means of Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES) method using a Thermo Jarrell Ash Corporation IRIS spectrometer. Before analysis, clay sample was dried (110 C for 24 h) and then about 20 mg were dissolved in an acidic solution (fluorhydric and nitric acids) by means of a microwave digestion technique. The obtained diluted solutions were then submitted to ICP-AES analysis. The latter was based on exciting the metal atoms/ions using a plasma and analyzing the emission wavelength of the electromagnetic radiation, which was typical of that particular metal [START_REF] Arvis | Inductively coupled plasma-atomic emission spectrometry in exploration geochemistry[END_REF].

Specific surface area measurement

The specific surface area of kaolin and metakaolin was performed on a Micromeritics Tristar II type device using the BET method (Brunauer, Emmett and Teller). Before the measurements, the samples were degassed under vacuum at 200 °C for 16 h.

Amylose and amylopectin contents

For the starch, the amylose and amylopectin contents were determined in accordance with the method developed by [START_REF] Freitas | Amylose contents, rheological properties and gelatinization kinetics of yam (Dioscorea alata) and cassava (Manihot utilissima) starches[END_REF]. This method was based on a calibration curve obtained from a mixture in water of pure amylose and amylopectine in mass proportions ranging from 0 to 100%. A lipid free starch was prepared according to Soxhlet method for 6 h and dried at 80 °C for 3 h. 0.5 g of the obtained product was dissolved in 100 mL of distilled water. Adding 0.1 mL of Lugol (I2 /KI) (Sigma-Aldrich) to 5 mL of the 5 times diluted solution enabled to measure the absorbance or optical density (OD) and therefore to determine the amylose content using the calibration curve. The amylopectin content was then deducted from the relation (1):

J o u r n a l P r e -p r o o f 𝐴𝑚𝑦𝑙𝑜𝑝𝑒𝑐𝑡𝑖𝑛 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 (𝑤𝑡%) = 100 -𝐴𝑚𝑦𝑙𝑜𝑠𝑒 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 (𝑤𝑡%)

(1)

Ash content

Ash content of the starch (Ta) was evaluated through a calcination process at 550 °C using Nabertherm-type furnace for 3 h. Ta has been calculated according to the relation ( 2):

𝑇𝑎 = 𝑀𝑎 𝑀𝑖 × 100 (2)
With Ma, mass of starch ash and Mi, the initial mass.

pH measurements

pH measurements were carried out on the starch supernatant by means of inoLab pH/ION/Cond 750 type pH-Meter. The supernatant was obtained after centrifugation at 3000 rpm for 10 min from the slurries prepared with 2.5 g of starch and 5% of KB or MKB in 25 mL of distilled water.

X-ray diffraction

The X-ray diffraction experiments were performed using a Siemens d5000 diffractometer.

This apparatus was equipped with a copper anticathode (λ = 1.54 Å). The analyses were carried out on powdered material (KB and MKB) with particle size below 100 µm. Patterns were collected over the 2θ range of 5-60˚ with a step size of 0.02˚ and a counting time of 10.1 seconds per step.

Scanning electron microscopy

The microstructure observation of the samples was carried out using a MEB FEG Supra 40 VP Zeiss scanning electron microscope (SEM). For calibration, we chose a diameter of 30 mm and a probe's energy of 20.1 KeV. The working distance was set at WD = 8.4 mm. The bioplastic samples were mounted on platinum stubs for viewing. The acquisition of SEM images was performed in at least three different areas.

Hydric property measurements

J o u r n a l P r e -p r o o f

The water solubility of the bioplastics produced was assessed by measuring the weight loss during an immersion time of 24 h in pure water.

Adsorption isotherms were obtained by maintaining the plastic films of 15 x 30 x 1.4 mm 3 in dimensions in a controlled chamber at a constant temperature of 25 °C and a given relative humidity (RH varying from 0 to 97.8 %) [START_REF] Greenspan | Humidity fixed points of binary saturated aqueous solutions[END_REF]. Samples were weighed using a precision balance at regular interval time of 4 h until a constant mass. These measurements enabled to obtain the wet mass (Me) of the product. The dry weight (Ms) was determined after drying at 105 °C for 48 h. Knowing those two weights (Me and Ms) allowed to infer the bioplastic water (or moisture) content (Xi) at the equilibrium according to the relation (3):

𝑋 𝑖 = 𝑀 𝑒 -𝑀 𝑠 𝑀 𝑠 (3)
Isotherms were obtained by plotting the water content (Xi) as a function of the water activity (aw varying from 0 to 1).

The coefficients of the diffusion and permeability of water were measured by the gravimetric method on the previously dried samples (105 °C for 48 h). The point cloud was obtained by drawing the mass of the absorbed water as a function of time according to the relation (4):

𝑴 𝒕 -𝑴 𝟎 𝑴 ∞ = 𝟒 𝒆 √ 𝑫 𝝅 𝒕 𝟏/𝟐 (4)
where M0 (g) was the initial mass, Mt, the mass at a given time t, 𝑀 ∞ the mass at the equilibrium, t, the time in second and D, the diffusion coefficient (m².s -1 ).

The slope of the correlation line enabled to determine the diffusion coefficient (D) in accordance with the relations (5):

𝑫 = 𝝅 × ( 𝜶𝒆 𝟒 ) 𝟐 (5)
with α the slope of the correlation line (kg.s -1 ) and e the thickness of the bioplastics film (m) [START_REF] Greenspan | Humidity fixed points of binary saturated aqueous solutions[END_REF].

The coefficient of water permeability (P) was assessed following the relation (6):

J o u r n a l P r e -p r o o f

𝑷 = 𝜶𝒆 𝑨×𝑴(𝒑 𝟏 -𝒑 𝟐 ) (6)
where A is the area of the exposed film (m 2 ), M, the molecular mass of water (kg.mol -1 ), and p1 -p2 the difference of the vapor pressure on the film (Pa) (Chivrac et al., 2010).

Biodegradability

The biodegradability was assessed by in situ tests. The bioplastics film of (15 x 30 x 1.4 mm 3 ) in dimension were either completely buried 3 cm deep in the ground or deposited on the surface of 100 g of soil, placed in containers (climatic chamber at T = 25 °C, P = 1 bar). Then, they were watered each three days to ensure a fairly high humidity. After a determined exposure time, the mass changes were recorded for each sample. To identify microorganisms, a medium composed of 1 g of meat peptone (emulsifier), 5 g of NaCl, 2 g of KH2PO4, 20 g of plastic film and 20 g of agar agar (E406 gelling agent) was prepared. The whole was placed in 1000 mL of distilled water and sterilized at 121 °C for 15 min. Then, the inoculum was prepared by homogenizing 10 g of soil in 90 mL of physiological water (NaCl 9/1000 mL of distilled water). The petri dishes were poured by flooding (1 mL of inoculum). These tests were repeated three times for each formulation.

Results and discussion

Physico-chemical characterization of the cassava starch and the kaolin

The amylose and amylopectin contents were 21.2 and 78.8 %, respectively. These values were consistent with those generally observed for cassava starches [START_REF] Sidibé | Comportement hydrothermique des amidons de 4 variétés de manioc (Manihot esculenta Crantz) cultivées en Côte d'Ivoire[END_REF]. The water content was Te =10.22 ±0.01%. This value was lower than the one obtained by [START_REF] Belibi | Elaboration et caractérisation des biofilms à base d'amidon de manioc renforcés par des charges minérales bi et tri-dimensionnelles[END_REF] for the cassava starch shrub (12.9%) and by [START_REF] Yéboué | Valeur nutritive et propriétés organoleptiques de l'attiéké, de l'attoukpou et du placali, trois mets à base de manioc, couramment consommés en Côte d'Ivoire[END_REF] for cassava starch IAC (15.15%). This difference could be explained by several internal factors, namely: the starch physicochemical composition, the botanical origin, the variety of cassava but also by the humidity of the storage atmosphere (T= 25°C; RH= 50%). The pH of the supernatant from cassava starch slurries was 4.7. This acid character which could be attributed to the nature of J o u r n a l P r e -p r o o f the soil and/or to the method of starch extraction has also been reported by other authors [START_REF] Mbey | Films composites amidon de manioc-kaolinite : influence de la dispersion de l'argile et des interactions argile-amidon sur les propriétés des films[END_REF][START_REF] Yéboué | Valeur nutritive et propriétés organoleptiques de l'attiéké, de l'attoukpou et du placali, trois mets à base de manioc, couramment consommés en Côte d'Ivoire[END_REF].

Chemical and mineralogical composition of kaolin (KB) along with its physical parameters are documented in Table 1. The chemical analysis showed that KB was mainly composed of silica and alumina. Iron, titanium, potassium and sodium were also present but in very small quantities. Combining the chemical composition results with the ideal chemical formula of the mineralogical phases detected by X-ray diffraction (Figure 1), and using the law of mixtures, allowed to determine the kaolin mineralogical proportions as follows: 75% of kaolinite, 11%

of illite and 14 % of quartz. The specific surface area estimated at 43.5 m 2 /g was relatively high for a kaolinitic clay. This could result from the presence of iron oxide highlighted by the chemical analysis. However, peaks corresponding to the ferric phases were not detected by XRD analysis (Figure 1), probably because of their low content. The density value obtained corresponded to that generally observed for a kaolinitic type clay [START_REF] Amon | Physico-chemical and structural properties of clay-based ceramic filters from Côte d'Ivoire[END_REF].

Effect of the thermal treatment on the kaolin

J o u r n a l P r e -p r o o f The diffractogram of MKB presented only the peaks of quartz. The disappearance of the characteristic peaks of kaolinite and illite was linked to the transformation of kaolin into metakaolin during the heat treatment. The metakaolin, product of the heat treatment above 500 °C of the kaolin, was characterized by an absence of a long-range order in the arrangement of the atoms of the main clay phases [START_REF] Konan | Etude comparative de la déshydroxylation/amorphisation dans deux kaolins de cristallinité différente[END_REF][START_REF] Meite | Structural and thermomechanical study of plastic films made from cassava-starch reinforced with kaolin and metakaolin[END_REF].

Kaolinite transformation into metakaolinite can be described by the following reaction (7):

kaolinite (𝐴𝑙 2 𝑂 3 . 2𝑆𝑖𝑂 2 . 2𝐻 2 𝑂) 400-700°𝐶
→ metakaolinite (𝐴𝑙 2 𝑂 3 . 2𝑆𝑖𝑂 2 ) + 2𝐻 2 𝑂 (7).

The departure of hydroxyl groups in the form of water contained in the mineral led to significant structural modifications within the metakaolinite. The structural change is characterized by a loss of crystallinity, weight loss and a concomitant change in aluminium coordination from octahedral to tetrahedral [START_REF] Sperinck | Dehydroxylation of kaolinite to metakaolin-a molecular dynamics study[END_REF].

Visual aspect of the bioplastics

The bioplastics BP, BPKB and BPMKB obtained are shown in

Solubility

The solubility value for BP was 35.6 %. This value decreased to 29.6 % and 22.1 % for BPKB and BPMKB respectively. The reduction in the solubility on addition of clay minerals suggests an improvement of the water resistance of the materials. This increase in the water resistance of bioplastics when they are reinforced with kaolin could be explained by the [START_REF] Tyagi | Properties of cassava starch based bioplastic reinforced by nanoclay[END_REF]. The drop in the solubility could also be explained by the hydrophobic character of both kaolin and metakaolin. Owing to their nanometric sizes, clay particles could fill the bioplastics pores, increasing their compactness and improving their resistance to water. This water resistance of bioplastics was more pronounced when metakaolin was used as a reinforcement.

Water adsorption

Figure 3 shows the change in the water content at equilibrium as a function of water activity for the bioplastics BP, BPKB and BPMKB. The obtained isotherms had a similar appearance to those generally observed for hydrophilic materials. They showed two phases: a first phase (from 0 to 0.7) where the adsorption was low and a second one where the adsorption increased rapidly (aw higher than 0.7). For the moisture content lower than 0.7, all bioplastics had almost identical behavior. For activities (aw) ranged from 0.7 to 0.9, the adsorbed water content decreased when the bioplastic was reinforced with clay. This decrease was more marked when the reinforcement was metakaolin. This could be explained by the compact arrangement of the macromolecular chains in BPMKB since the free volume (pores) existing between the macromolecules were reduced due to the interactions between the starch molecules and the metakaolin platelets.

These results were in line with the ones observed with extruded wheat starch-based bioplastics reinforced with nanoclay (Wahyuningtiyas & Suryanto, 2018 ). Water permeability and diffusion dropped when bioplastics were reinforced with kaolin and metakaolin. The decrease was more pronounced when the mineral load was metakaolin. This decrease in water permeability and diffusion could be explained by the reduction in the free volumes (pores) existing between the starch macromolecules. Incorporating the thermally treated clay further decreased the water sensibility and diffusion of bioplastics. The molecular interactions between metakaolin platelets and functional groups of starch macromolecules would lead to the production of a more compact material. These results were in accordance with those obtained by Chivrac et al. (2010), who observed a reduction in the diffusion coefficient of bioplastics based on cassava starch reinforced with montmorillonite. Also, these variations were in line with those obtained for the solubility of bioplastics when heat treated kaolin was used as reinforcement instead of crude kaolin.

Diffusion and permeability coefficients of bioplastics

Microstructure of bioplastics

J o u r n a l P r e -p r o o f porous and irregular surface. This may be due to a weak cohesion between the starch and the kaolin. In the case of BPMKB, despite the presence of some surface defects, the microstructure appeared denser suggesting a better interaction between the starch and the metakaolin. It has been shown that incorporating clay in the bioplastic decreases the material solubility. During the film formation process, starch may react with the clay allowing clay fine particle dispersion within the gelatinized starch. Since, the process was performed around 100 C, the water that was present on the film layer had evaporated [START_REF] Cruz-Tirado | Bioactive Andean sweet potato starch-based foam incorporated with oregano or thyme essential oil[END_REF]. However, the water vapor that was trapped inside the clay platelet would cause deformation and cracks in the case of BPKB related to the poor dispersion of the kaolin. In the case of BPMKB, due to the thermal treatment, there was no water in the structure. This may allow a stronger interaction between the metakaolin and the starch. The evaporation of the water present on the film surface would cause deformation, but no cracks, as shown in the SEM images.

J o u r n a l P r e -p r o o f

Interaction mechanism

The decrease in the solubility, diffusion and permeability of water of the thermally modified kaolin-reinforced bioplastics could be attributed to the improvement of their microstructure.

The good dispersion of the fine particles of metakaolin platelets in BPMKB allowed to strongly reduce the starch macromolecule pore size inducing a more compact arrangement of those macromolecular chains. Through the electron doublets available on the oxygen atoms, the basal surfaces interacted with the functional groups of the starch macromolecules according to the mechanism proposed in Figure 6. Due to its amorphous character which increased its reactivity, metakaolin could strongly interact with starch macromolecules [START_REF] Angellier | Nanocristaux d'amidon de maïs cireux pour applications composites[END_REF][START_REF] Tyagi | Properties of cassava starch based bioplastic reinforced by nanoclay[END_REF]. These interactions led to the creation of strong hydrogen bonds thus promoting the improvement of the microstructure of the final material [START_REF] Monteiro | Incorporation of bentonite clay in cassava starch films for the reduction of water vapor permeability[END_REF].

Biodegradability of bioplastics

The biodegradability of the bioplastics produced was assessed by determining the mass loss of the samples as a function of the exposure time on the soil surface and the burial time in the ground (Figure 7). The obtained values of mass loss were almost zero during the first two weeks for all studied bioplastics and regardless of the environmental medium. It was the period of adaptation of microorganisms to their new environment before growing. Between two and three weeks, a rapid increase in weight loss was observed for all the bioplastics due to strong growth and significant microbial activity. Beyond three weeks, biodegradation increased slowly for all bioplastics in the considered environments due to a reduction in the nutrients essential for the microorganism proliferation. After twenty weeks of burial in the ground, the degradation rate was 77%, 86% and 94%, respectively for BP, BPKB and BPMKB against 72%, 78%, 80% when exposing on the ground surface.

J o u r n a l P r e -p r o o f The significant degradation observed for all bioplastics when they were buried in the ground could be explained by a larger contact surface with microorganisms. In addition, the temperature and humidity conditions would be favorable for greater microbial activity in the soil. [START_REF] Harding | Biodegradable" plastics: A myth of marketing?[END_REF] showed that the climatic conditions, the pH of the medium, the environment and the dimensions of bioplastics had an impact on the rate of biodegradation.

To identify the microorganisms responsible for the biodegradation of the various bioplastics produced, microbiological tests by seeding on a petri dish were carried out (Figure 8). Observing the petri dishes containing BP revealed the presence of branched white filaments oriented in all directions. Whereas those containing BPKB and BPMKB showed the presence of numerous colored spots. The number of these spots was higher in the case of BPMKB. The presence of branched filaments in BP revealed the development of fungi. The growth of fungi generally resulted in an apical extension. The apical compartment had a very thin cell wall at the end which enabled it to extend in length by means of internal cytoplasmic turgor pressure.

On the other hand, the presence of colored spots in BPKB and BPMKB reflected the proliferation of bacteria. This bacterial growth was induced by an increase in the number of cells resulting from cell division. In general, bacterial growth, qualified as exponential due to the duplication process through binary fission, was faster than that of fungi [START_REF] Madigan | Brock, biologie des micro-organismes[END_REF][START_REF] Edhirej | Preparation and characterization of cassava starch/peel composite film[END_REF]. For the BPMKB plastic film, a significant presence of colored spots could explain the more pronounced degradation resulting in higher mass loss observed in Figure 7.

Authors contributions

-Namory Méité : Performed wet lab analysis using optimized protocols and editing of the manuscript.

-Léon Koffi Konan : Guided and monitored the experiment in reviewing and editing of the manuscript.

-Monique Tohoué Tognonvi : Helped in writing and clays data analysis -Bi Irié Hervé Gouré Doubi : Helped in writing and drafting of the manuscript -Moussa Gomina : Helped in writing and drafting of the manuscript.

-Samuel Oyetola : Helped in reviewing and editing of the manuscript.

J o u r n a l P r e -p r o o f 4 Conclusion

The thermal treatment of kaolin at 700 °C for 1 hour enabled to obtain metakaolin with an amorphous and dehydroxylated structure. Bioplastics made from cassava starch reinforced with 5 % by mass of metakaolin presented lower water sensitivity and more compact microstructure than non-reinforced BP and those reinforced with crude kaolin. Moreover, the biodegradability of these bioplastics was slightly improved due to bacterial activity regardless of the exposure environment. The improvement in the hydric properties and the biodegradable nature indicated that heat treatment could help to open up more prospects for the use of kaolinitic clays in the dissemination of starch-based bioplastics. The permeability of cassava starch-based bioplastics reinforced with calcined clay platelets to certain gases such as dioxygen (O2), ethylene (C2H4) and carbon dioxide (CO2) will be investigated in future works.

Figure 1

 1 Figure1shows the x-ray diffraction patterns of both the crude kaolin and the metakaolin.

Figure 1 :

 1 Figure 1: X-ray diffraction patterns of kaolin (KB) and metakaolin (MKB).

Figure 2 .

 2 The visual observation of the bioplastics appearance revealed a better dispersion of metakaolin in the J o u r n a l P r e -p r o o f matrix, resulting in a more homogeneous and more transparent material than bioplastic incorporating crude kaolin. In general, adding mineral clays into the bioplastic resulted in a loss of transparency due to the red color provided by the Kaolin. The transparency of BPMKB against BPKB could be explained by the decomposition of the coloring oxides present in kaolin such as iron oxyhydroxides under the heat influence. Often, this reduction in the transparency is beneficial for the preservation of certain products because the light accelerates their oxidation.

Figure 2 :

 2 Figure 2: Photographs of the produced bioplastics. BP, Non-reinforced bioplastics; BPKB,

  r n a l P r e -p r o o f fineness of the clay particles and the interactions between the macromolecules of starch and the clay (Wahyuningtiyas

Figure 3 :

 3 Figure 3: Adsorption isotherms of bioplastics. BP, Non-reinforced bioplastics; BPKB,

  r n a l P r e -p r o o f

Figure 4

 4 Figure 4 depicts the variation of the weight of absorbed water as a function of time for the

Figure 4 :

 4 Figure 4: Change in the mass of the absorbed water as a function of time.

Figure 5

 5 Figure 5 depicts the microstructure of the studied bioplastics. SEM images of BP showed a

Figure 5 :

 5 Figure 5: Scanning Electron Microscopy images of bioplastics. BP, Non-reinforced bioplastics; BPKB, Reinforced bioplastics with crude kaolin; BPMKB, Reinforced bioplastics with metakaolin

Figure 6 :

 6 Figure 6: Schematic representation of the interactions between starch macromolecules

Figure 7 :

 7 Figure 7: Degradation of elaborated bioplastics exposed to different environment over time.

Figure 8 :

 8 Figure 8: Images of bioplastics colonised by microorganisms.

  r n a l P r e -p r o o f

Table 1 :

 1 Physico-chemical and mineralogical parameters of the studied kaolin (KB)

	Oxide	SiO2 Al2O3	Fe2O3 K2O TiO2 Na2O CaO MgO
	Chemical composition (wt%)	64.4 29.6	3.3	1.3	0.8	0.8	-	-
	Mineralogical composition (%)	Kaolinite = 75 ;	Illite = 11;		Quartz = 14
	Specific surface area (m 2 /g)			43.5
	Density				2.6

Table 2 :

 2 Coefficients of diffusion and permeability of bioplastics. BP, Non-reinforced bioplastics; BPKB, Reinforced bioplastics with crude kaolin; BPMKB, Reinforced bioplastics with metakaolin

	Bioplastics	Permeability (10 -11 mol.m -1 s -1 Pa -1 )	Diffusion (10 -12 m 2 s -1 )
	BP	3.78 ±0.03	3.58 ± 0.04
	BPKB	3.58 ±0.05	3.18 ± 0.01
	BPMKB	2.76 ±0.04	2.83 ± 0.02

J o u r n a l P r e -p r o o f