Jacek Jagiello
email: jacek.jagiello@micromeritics.com

Jimena Castro-Gutiérrez

Rafael Luan

Sehn Canevesi

Alain Celzard

Vanessa Fierro
email: vanessa.fierro@univ-lorraine.fr

A comprehensive analysis of hierarchical porous carbons using a dualshape 2D-NLDFT model with adjustable slit-cylinder pore shape boundary

Keywords: NLDFT model, pore shape, slit-cylinder boundary, hierarchical porous carbons, pore size distribution

A thorough characterization of the textural properties of hierarchical porous carbons (HPCs) is of utmost importance as it provides information that aids in the selection of a suitable material for a given application and in understanding the phenomena observed once the material becomes part of a system. Gas adsorption-desorption isotherms coupled with the application of density functional theory (DFT) models to these isotherms are common tools for the textural characterization of HPCs, for which pore shape is an essential factor for the determination of pore size distributions (PSDs). By analyzing the experimental adsorption data of a series of CO 2 -activated HPCs with a progressive development of porosity, it is shown that artifacts are found in the derived PSDs when a slit-cylinder pore shape boundary is fixed at 2 nm, which is the case for the original dual-shape non-local DFT (2D-NLDFT-HS) and the hybrid quenched solid DFT (QSDFT) models. This study presents a new dual-shape 2D-NLDFT-HS (DS-HS) model that, combined with the 2D-NLDFT-HS model for CO 2 , provides the possibility of analyzing simultaneously N 2 and CO 2 adsorption-desorption isotherms and adjusting at the same time the limits for the assumed slit and cylindrical pore shapes. Using the DS-HS approach and adjusting the slit-cylinder boundary at 3 nm allowed eliminating PSDs artifacts. The interactive adjustment of the slit-cylindrical pore shape boundary of the DS-HS model represents a major advantage of this approach allowing for a comprehensive analysis of the adsorption data and a more accurate description of the textural properties of HPC materials.

Introduction

Hierarchical porous carbons (HPCs), i.e., materials with pores of different widths (w) that can be classified as micro-, meso-and macropores (w < 2 nm, 2 < w < 50 nm, and 50 nm < w, respectively), [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF] have attracted the interest of the chemistry and engineering scientific community due to their versatility. Carbon precursors are abundant in nature and, depending on their origin and processing, the obtained HPCs can exhibit an interesting combination of characteristics that make them suitable for a wide range of applications like gas adsorption and separation, [START_REF] Singh | Biomass Derived Porous Carbon for CO2 Capture[END_REF][START_REF] Saufi | Fabrication of Carbon Membranes for Gas Separation--a Review[END_REF] wastewater treatment, [START_REF] Ben Mosbah | Current State of Porous Carbon for Wastewater Treatment[END_REF] drug delivery and bioimaging, [START_REF] Zhang | Recent Advances in the Synthesis of Spherical and NanoMOF-Derived Multifunctional Porous Carbon for Nanomedicine Applications[END_REF] catalysis, [START_REF] De | Biomass-Derived Porous Carbon Materials: Synthesis and Catalytic Applications[END_REF][START_REF] Quílez-Bermejo | Metal-Free Heteroatom-Doped Carbon-Based Catalysts for ORR: A Critical Assessment about the Role of Heteroatoms[END_REF] energy storage in batteries and supercapacitors, [START_REF] Roberts | Porous Carbon Spheres and Monoliths: Morphology Control, Pore Size Tuning and Their Applications as Li-Ion Battery Anode Materials[END_REF][START_REF] Castro-Gutiérrez | Energy Storage in Supercapacitors: Focus on Tannin-Derived Carbon Electrodes[END_REF][START_REF] Pérez-Rodríguez | Chapter 10 -Emerging Carbon Nanostructures in Electrochemical Processes[END_REF] hydrogen storage, [START_REF] Yang | Recent Advances in Hydrogen Storage Technologies Based on Nanoporous Carbon Materials[END_REF] among others. [START_REF] Benzigar | Recent Advances in Functionalized Micro and Mesoporous Carbon Materials: Synthesis and Applications[END_REF][START_REF]Green Carbon Materials: Advances and Applications[END_REF] For instance, it has been shown that a hierarchical porous carbon (HPC) with ordered mesopores connected through narrow micropores can be used as molecular sieve for the separation of linear and branched alkanes. [START_REF] Castro-Gutiérrez | Molecular Sieving of Linear and Branched C6 Alkanes by Tannin-Derived Carbons[END_REF] Moreover, HPCs with ordered or disordered structures had also been tested as electrodes for supercapacitors or batteries, showing that the well-connected hierarchical micro-mesopore structure provides short diffusion paths for ions and electrons, resulting in high-rate capabilities of the assembled energy storage devices. [START_REF] Castro-Gutiérrez | High-Rate Capability of Supercapacitors Based on Tannin-Derived Ordered Mesoporous Carbons[END_REF][START_REF] Díez | A Simple and General Approach for in Situ Synthesis of Sulfur-Porous Carbon Composites for Lithium-Sulfur Batteries[END_REF] HPCs are normally synthesized by either hard-or soft-template methods. In the former, an inorganic material is used as a template around which the carbon precursor is polymerized, then this composite is carbonized, and the template needs to be removed in a subsequent step.

In soft-template methods, a surfactant is used as a template that, along with the carbon precursor, forms a mesophase; upon carbonization, the surfactant is eliminated, creating mesopores. [START_REF] Inagaki | Templated Mesoporous Carbons: Synthesis and Applications[END_REF] Although carbon precursors of petrochemical origin such as resorcinol or phenolic resins have been extensively employed to produce HPCs, the use of biomass-derived precursors such as cellulose, glucose, lignin and condensed tannins, among others, has increased over the last decades in the search for "greener" technologies and processes. [START_REF] White | Porous Carbon Materials from Sustainable Precursors[END_REF] In this sense, different research groups have successfully produced high added-value materials from condensed tannins, particularly, HPCs by a microwave-assisted method, [START_REF] Ramasahayam | Novel Tannin-Based Si, P Co-Doped Carbon for Supercapacitor Applications[END_REF][START_REF] Bairi | Electrocatalytic and Supercapacitor Performance of Phosphorous and Nitrogen Co-Doped Porous Carbons Synthesized from Aminated Tannins[END_REF] using either silica hard templates [START_REF] Sanchez-Sanchez | Excellent Electrochemical Performances of Nanocast Ordered Mesoporous Carbons Based on Tannin-Related Polyphenols as Supercapacitor Electrodes[END_REF] or soft-template methods such as evaporation-induced self-assembly (EISA), [START_REF] Schlienger | Direct Synthesis of Ordered Mesoporous Polymer and Carbon Materials by a Biosourced Precursor[END_REF] phase separation [START_REF] Braghiroli | Easy and Eco-Friendly Synthesis of Ordered Mesoporous Carbons by Self-Assembly of Tannin with a Block Copolymer[END_REF][START_REF] Sanchez-Sanchez | Ordered Mesoporous Carbons Obtained by Soft-Templating of Tannin in Mild Conditions[END_REF] and mechano-synthesis. [START_REF] Castro-Gutiérrez | Synthesis of Perfectly Ordered Mesoporous Carbons by Water-Assisted Mechanochemical Self-Assembly of Tannin[END_REF][START_REF] Zhang | Solid-State Synthesis of Ordered Mesoporous Carbon Catalysts via a Mechanochemical Assembly through Coordination Cross-Linking[END_REF] The final properties of the synthesized HPCs, such as porosity, surface chemistry, stability and conductivity, depend largely on the chosen precursor/template pair. In order to understand the observed phenomena related to the use of HPCs in different applications, a thorough characterization of their physicochemical properties is of utmost importance, especially that of their porosity. For this purpose, the acquisition of gas (N 2 , Ar, CO 2 or H 2 ) adsorption-desorption isotherms coupled with Grand Canonical Monte Carlo simulations [START_REF] Barrera | Pore Size Distribution of Ordered Nanostructured Carbon CMK-3 by Means of Experimental Techniques and Monte Carlo Simulations[END_REF][START_REF] Soares Maia | Characterization of Activated Carbons from Peach Stones through the Mixed Geometry Model[END_REF][START_REF] Cimino | Experimental and Theoretical Studies of Scanning Adsorption-Desorption Isotherms[END_REF] or the application of different density functional theory (DFT) models to these isotherms allows obtaining the pore size distribution (PSD). DFT approaches are among the most widely used tools for the textural characterization of HPCs, [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF][START_REF] Jagiello | Comparison of DFT Characterization Methods Based on N2, Ar, CO2, and H2 Adsorption Applied to Carbons with Various Pore Size Distributions[END_REF][START_REF] Landers | Density Functional Theory Methods for Characterization of Porous Materials[END_REF] must likely due to their commercial availability as software.

However, the obtained PSD and the derived values, e.g., average pore widths or surface area, depend on the assumptions of the applied model. [START_REF] Ania | Engaging Nanoporous Carbons in "beyond Adsorption" Applications: Characterization, Challenges and Performance[END_REF] Pore shape is an essential factor in calculating the gas adsorption models used to analyze PSDs. In the case of templated micro-mesoporous HPCs, the most common pore shapes assumed in gas adsorption modeling are slits for micropores created during carbonization and cylinders for mesopores resulting from the templating process. [START_REF] Gor | Quenched Solid Density Functional Theory Method for Characterization of Mesoporous Carbons by Nitrogen Adsorption[END_REF][START_REF] Jagiello | A Dual Shape Pore Model to Analyze the Gas Adsorption Data of Hierarchical Micro-Mesoporous Carbons[END_REF] The gas adsorption potential is stronger in cylindrical pores than in slits of the same width, therefore the theoretical adsorption isotherm calculated for a cylindrical pore of a given width is shifted to a lower pressure than that for a slit pore. Consequently, the PSD calculated from a given isotherm using the cylindrical model will be shifted to larger pore sizes than that of the slit pore model; hence, the results are affected by an inherent ambiguity related to the pore shape assumption. In an effort to overcome this uncertainty, this work aims to present a comprehensive approach where the desorption branch of N 2 isotherms is considered an equilibrium branch [START_REF] Landers | Density Functional Theory Methods for Characterization of Porous Materials[END_REF] and is analyzed using a dual-shape 2D non-local DFT model for heterogeneous surface (2D-NLDFT-HS). [START_REF] Jagiello | A Dual Shape Pore Model to Analyze the Gas Adsorption Data of Hierarchical Micro-Mesoporous Carbons[END_REF] For simplicity, herein, the new dual-shape 2D-NLDFT-HS model is referred to as the DS-HS model. In this model, the slit-shape kernel is applied to pore widths w < w s and the cylinder-shape kernel to w > w c , where the parameters w s and w c are the upper and lower bounds of the slit and cylinder kernels, respectively. These limits are not known a priori, but in our approach they can be adjusted interactively based on the analysis results. In this way, the model allows defining overlapping ranges of pore shapes to account for cases of mixed pore shape, i.e., w s > w c , similarly to the previously studied case of combined slit and channel finite pores across the whole range of pore sizes. [START_REF] Jagiello | Using a New Finite Slit Pore Model for NLDFT Analysis of Carbon Pore Structure[END_REF] In this work, the dual-gas analysis method is applied, [START_REF] Jagiello | Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2[END_REF] in which the DS-HS model and the 2D-NLDFT-HS model for CO 2 36 are fitted simultaneously to the N 2 and CO 2 isotherms to obtain a single PSD. Both adsorption isotherms were measured on a series of activated ordered mesoporous carbons (OMCs) reported earlier. [START_REF] Castro-Gutiérrez | High-Rate Capability of Supercapacitors Based on Tannin-Derived Ordered Mesoporous Carbons[END_REF] The PSD results obtained using the new approach are then compared to those calculated using the hybrid quenched solid DFT (QSDFT) model. [START_REF] Gor | Quenched Solid Density Functional Theory Method for Characterization of Mesoporous Carbons by Nitrogen Adsorption[END_REF][START_REF] Neimark | Quenched Solid Density Functional Theory and Pore Size Analysis of Micro-Mesoporous Carbons[END_REF] 2. Experimental

Raw materials

Mimosa tannin kindly provided by the company SilvaChimica (St Michele Mondovi, Italy), and commercialized as Fintan OP, was used as carbon precursor, and Pluronic® F127 (Sigma-Aldrich) was used as pore-directing agent. The materials were used as received.

Synthesis of activated micro-mesoporous OMCs

Activated micro-mesoporous OMCs were synthesized by a surfactant-water-assisted mechanochemical meso-structuration (SWAMM) method and physically activated as detailed elsewhere. [START_REF] Castro-Gutiérrez | Synthesis of Perfectly Ordered Mesoporous Carbons by Water-Assisted Mechanochemical Self-Assembly of Tannin[END_REF] Briefly, tannin (T), surfactant (Pluronic: P) and water (W) were mixed in a planetary ball mill (PM100, Retsch) in a T:P:W mass ratio of 2:0.75:1.75 g. After 60 min of milling, a mesophase was recovered and was directly subjected to carbonization at 900 °C under N 2 flow. The resulting OMC was ground to reduce the particle size and placed in an oven for activation. The temperature was raised to 900 °C under N 2 atmosphere, then the gas flow was changed to CO 2 and the temperature was held for times ranging from 15 to 105 min.

Finally, the material was left to cool naturally under N 2 flow. Herein, the activated OMCs are referred to as A-t, where t stands for the activation time in minutes.

Characterization of materials

As specified in our previous study, 15 N 2 and CO 2 adsorption isotherms were acquired with ASAP 2020 and ASAP 2420 devices (Micromeritics) at 77 and 273 K, respectively. Prior to data acquisition, the samples were degassed at 110 °C under secondary vacuum for at least 48 h.

Transmission electron microscopy (TEM) images were obtained using a JEM-ARM 200F

Cold FEG TEM/STEM (Jeol). For observation, powdered samples were dispersed in ethanol by low-power sonication, and then a drop of suspension was deposited on a TEM grid (carbon-coated copper, 200 mesh). From these TEM images, histograms of pore widths in the mesoporous range were obtained using the Fiji image processing software (ImageJ, version 1.52i) and its "analyze particles" tool. A detailed explanation of the methodology employed is provided in the Supporting information (SI).

Dual-shape 2D-NLDFT-HS (DS-HS) model

As mentioned in the introduction, the DS-HS model uses two 2D-NLDFT-HS kernels to fit the desorption branch of the experimental N 2 isotherm: the previously developed slit-shape kernel 2D-HS-SLIT (K slit ) [START_REF] Jagiello | 2D-NLDFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation[END_REF] and the recently developed cylinder-shape kernel 2D-HS-CYL (K cyl ). [START_REF] Jagiello | A Dual Shape Pore Model to Analyze the Gas Adsorption Data of Hierarchical Micro-Mesoporous Carbons[END_REF] These kernels were calculated as equilibrium ones considering the heterogeneous rough surface of the pore walls. Their theoretical isotherms do not show layering transitions, thus eliminating the artifacts associated with such transitions observed in the PSD results calculated from standard NLDFT kernels. [START_REF] Neimark | Quenched Solid Density Functional Theory and Pore Size Analysis of Micro-Mesoporous Carbons[END_REF][START_REF] Jagiello | 2D-NLDFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation[END_REF] It is important to note that the experimental desorption data was only recorded down to a relative pressure of ~10 -3 , so in order to have a "complete" branch, the experimental adsorption branch was used to append the desorption data to the lowest measured relative pressures. This merging of the adsorption and desorption branches is carried out considering that the process of gas adsorption is reversible in the lowpressure region, associated with micropores.

It is assumed that the effective PSD function is a sum of functions representing the slit and cylindrical pores:

(1 ) so the total N 2 isotherm (Q N2 ) is given by the sum of the following integrals:

(

) 2
where x is the relative pressure and the lower limit of 0.36 nm for the first term corresponds to the minimum detectable pore size determined and which is related to the kinetic diameter of the N 2 molecule.

In the initial version of the DS-HS model, [START_REF] Jagiello | A Dual Shape Pore Model to Analyze the Gas Adsorption Data of Hierarchical Micro-Mesoporous Carbons[END_REF] both shape limits w s and w c were equal to 2 nm;

in the present version, these limits are adjustable and are set based on the analysis results.

Additionally, the CO 2 isotherm at 273 K might be fitted simultaneously with the N 2 isotherm, using the 2D-HS kernel for CO 2 (K CO2 ). [START_REF] Jagiello | Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2[END_REF] Because CO 2 adsorption at 273 K below 1 atm is highly sensitive to the size of ultramicropores (w < 0.7 nm) and it has very low sensitivity in the mesopore range, [START_REF] Jagiello | Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2[END_REF][START_REF] Ravikovitch | Unified Approach to Pore Size Characterization of Microporous Carbonaceous Materials from N 2 , Ar, and CO 2 Adsorption Isotherms[END_REF] this isotherm is fitted only in the range of slit pores where the following integral gives the theoretical adsorption isotherm:

(3 )

Results and discussion

The adsorption data recently reported on a series of CO 2 -activated OMCs [START_REF] Castro-Gutiérrez | High-Rate Capability of Supercapacitors Based on Tannin-Derived Ordered Mesoporous Carbons[END_REF] In the first step of data analysis, the theoretical isotherms given by Equations ( 2) and (3) were simultaneously fitted to the corresponding experimental N 2 and CO 2 isotherms. As mentioned above, the desorption branch of the N 2 isotherm is considered an equilibrium branch. The fitting is performed using the SAIEUS program, as detailed in earlier works. [START_REF] Jagiello | A Dual Shape Pore Model to Analyze the Gas Adsorption Data of Hierarchical Micro-Mesoporous Carbons[END_REF][START_REF] Jagiello | Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2[END_REF][START_REF] Jagiello | Stable Numerical Solution of the Adsorption Integral Equation Using Splines[END_REF] In this first step of data analysis, it is assumed, as it was done before, that the slit and cylinder model limits are equal to 2 nm: w s = w c = 2 nm. Selected fitting results for the least activated, moderately activated, and most activated samples (A-15, A-60, and A105) are shown in Figure 1, and the results for the remaining samples are shown in Figure S1. The calculated isotherms accurately fit the experimental points for all samples and the PSDs resulting from the fits are shown for all samples in Figure 2. The fact that textural properties of the carbon samples change systematically upon gradual activation allows for a logical interpretation of their PSD evolution. Clearly, the micropore peak broadens to larger pores with increasing activation time. In contrast, the mesopore peak resulting from the templating process remains symmetric in the same position, showing an increase in the volume of these pores. These textural changes can be explained by the burn-off of the carbon material on the pore walls, which causes the micropores to widen and the mesopore surface to become coarser. The increase in coarseness and irregularity of the mesopore surface is reflected by the widening of the mesopore peak in the calculated PSD associated with the less steep transition step on the desorption isotherms, as seen for example in Figure1.

Tabular data describing the textural parameters obtained from the PSDs calculated with the slit-cylinder boundary at w s = w c = 2 nm are included in Table 1 and discussed in Section 4.2. the carbon kernels described earlier by Gor et al. [START_REF] Gor | Quenched Solid Density Functional Theory Method for Characterization of Mesoporous Carbons by Nitrogen Adsorption[END_REF] For the analysis of the A-t series, the hybrid QSDFT kernel was applied here, consisting of equilibrium isotherms calculated for both slit and cylindrical pore models, where the range of slit-cylinder boundary is fixed at 2 nm, i.e., w s = w c = 2 nm. This kernel is applied for the analysis of the desorption branch of the N 2 isotherm like our model. The results from the hybrid QSDFT model are presented in Figure 2 (solid blue lines) along with those obtained from the DS-HS model.

Even though the two methods are based on different assumptions and the QSDFT is a onedimensional model, the results show qualitatively reasonable agreement between the PSDs calculated by these methods. A more detailed view of the results shows that the DS-HS model gives smooth and continuous PSDs while the PSD plots calculated using the hybrid QSDFT model show sharp peaks and discontinuities. Furthermore, the DS-HS distributions calculated by the SAIEUS program [START_REF] Jagiello | A Dual Shape Pore Model to Analyze the Gas Adsorption Data of Hierarchical Micro-Mesoporous Carbons[END_REF][START_REF] Jagiello | Dual Gas Analysis of Microporous Carbons Using 2D-NLDFT Heterogeneous Surface Model and Combined Adsorption Data of N2 and CO2[END_REF][START_REF] Jagiello | Stable Numerical Solution of the Adsorption Integral Equation Using Splines[END_REF] originate and terminate at zero on the y-axis. In contrast, the hybrid QSDFT distributions originate at relatively high values on that axis. Because the multiple plots in Figure 2 may be difficult to examine, Figure 3 shows the PSD results for a single sample, A-105, which more clearly illustrates the mentioned differences. Such a trend is indeed observed for non-activated and slightly activated samples. However, this trend is broken for samples activated for t ≥ 45 min, where unexpected peaks begin to appear for w > 2 nm. We suspect that this is an artifact due to the change of applied model at 2 nm from slit to cylinder. To test this hypothesis, the isotherms of the sample activated for the longest time (105 min) were analyzed using two additional pore shape limits, (i) w s = 3 nm and w c = 2 nm, and (ii) w s = w c = 3 nm. Comparison of the calculation results shows significant differences in the PSDs depending on the assumed shape limits (Figure 4a) and practically no difference in the fitted isotherms as shown in Figure 4b. The accepted shape limits cannot be verified based on the goodness of the model fit, but the fact that the additional peak appears above 2 nm when w c = 2 nm indicates the interference of the cylindrical model in this transition part of the PSD. Recalling that the origin of the slit micropores is the carbonization process followed by the activation which widens these pores, there is no reason to assume the presence of cylindrical pores near w = 2 nm. Based on these observations, we consider that, for the samples under study, the boundary between the slit and cylindrical pore models should be w s = w c = 3 nm. This logical conclusion, obtained from the elegant systematic trend in the PSD variation for our samples, is however not universal. Other carbon materials may have different properties, which may be investigated using this interactive approach.

Nevertheless, in the second step of our data analysis, the slit-cylinder boundary is assumed to be 3 nm. Figure 5 presents the PSDs calculated in this way (with w s = w c = 3 nm), now exhibiting a regular trend in their variations with increasing activation time. Again, there is practically no difference between fitting curves (not shown) of the different shape models for all samples.

The high accuracy observed in the simultaneous fit of N 2 and CO 2 isotherms (Figure 1 and Figure S1) for all activated OMC samples indicates that the N 2 isotherms are well equilibrated. In contrast, it was previously reported that deviations of the dual-gas fit of N 2 and CO 2 isotherms indicated an under-equilibrated state of the N 2 isotherm at low relative pressure due to slow diffusion into the carbon ultra-micropores. [START_REF] Jagiello | Enhanced Resolution of Ultra Micropore Size Determination of Biochars and Activated Carbons by Dual Gas Analysis Using N2 and CO2 with 2D-NLDFT Adsorption Models[END_REF] of the N 2 isotherm, see Figure 6b. Figure 6c compares the PSDs obtained from the fitting of (i) full N 2 and CO 2 , (ii) full N 2 and (iii) full CO 2 and high-pressure N 2 isotherms. From this comparison, it can be observed that the micropore peak obtained from analysis (iii) is shifted to a value about 0.1 nm lower than that calculated using the N 2 isotherm alone (ii). This shift can be seen in Figure 5 where the PSDs calculated from the single N 2 isotherm (dotted line plots) show good agreement with those calculated from both N 2 and CO 2 isotherms for all samples except the non-activated one. The analysis of this series of carbon materials shows the advantage of using the dual-gas model that allows for the detection of under-equilibrated N 2 isotherms, which in turn allows for better understanding of the data and improved PSD results. processing are significantly broader and do not follow the same trend (Figure 7a-c). Image processing indeed highly depends on the quality of the image and on the processing procedure (contrast, definition, processing algorithm, among others). For example, the criterion for choosing the value of the threshold parameter can be very subjective and can change the results considerably; in particular, Figure S3 shows that varying the threshold from 10 to 20 % can change the peak center of the histograms from 4.3 to 5.1 nm. Thus, in these cases, the results of textural characterization of the mesopores from image processing of OMC, A-75 and A-90 must be considered with caution. In addition, the image processing focuses only on a specific particle (the one captured in the image) whereas the PSDs obtained from the adsorption isotherm analysis provide an average of the information obtained from many particles. Nonetheless, Figure 7 shows that the PSDs are within the range of the corresponding histograms, which demonstrates an approximate qualitative agreement between the two descriptions. For a complete pore characterization of activated OMCs, Table 1 presents textural parameters commonly reported for porous carbon materials and the volume and surface area of slit pores (V slit and S slit , respectively) calculated with the new DS-HS model with slitcylinder boundary at w s = w c = 3 nm. Primary values in Table 1 were calculated for the model with slit-cylinder boundary at w s = w c = 3 nm; the values in brackets represent the differences between the quantities calculated with the shape boundaries at 3 and 2 nm. It is important to note that, as expected, the most significant differences between textural parameters calculated for the two boundaries appear for samples with a higher degree of activation for t ≥ 45 min, where the artifacts occurred on the PSDs calculated using the model with the 2 nm shape boundary. For both boundary values the increments in total surface areas are relatively smaller than those in total pore volumes; this difference is to be expected because the pore volume increases with the pore width, while surface area decreases with the pore width.

Table 1. Textural parameters calculated using the DS-HS model. Primary values were calculated for the model with w s = w c = 3 nm, values in brackets represent the differences between the quantities calculated with the shape boundaries at 3 and 2 nm.

Sample S total (m 2 g -1 )

V total (cm 3 g -1 )

V meso (cm 3 g -1 )

V µ (cm 3 g -1 )

S slit (m 2 g -1 )

V slit (cm 4.9

S total and V total : total surface and volume; V meso volume of pores between 2 and 50 nm; V µ volume of pores under 2 nm; S slit and V slit surface and volume of pores with slit geometry; Peak meso pore diameter where the peak of the mesopore size distribution is located.

The DS-HS model is again compared to the hybrid QSDFT model in Figure 8 where overall agreement is observed between the two models for the calculated average pore volume, surface area and pore volume in the range of pore widths up to 6 nm (w av,<6nm , S <6nm and V <6nm , respectively). However, it should be noted that w av,<6nm determined by the hybrid QSDFT model is larger than that determined by the DS-HS model for OMC, A-15 and A-30,

where the fraction of ultra-micropores is higher (Figure 8a). This is because the hybrid QSDFT only fits N 2 isotherms, while our method also fits CO 2 adsorption data. CO 2 molecules have easier access to the narrower micropores, thus allowing a better assessment of the ultra-microporosity, as previously mentioned. The differences in w av,<6nm determined by both models become smaller with activation, which reduces the percentage of ultramicroporosity and thus the number of pores only accessible to CO 2 molecules. Additionally, Figures 8d and 8e compare the contributions to pore volume and surface area in the 2 -4 nm range for samples A-75, A-90, and A-105, from which it is clear that the hybrid QSDFT model has a larger contribution related to artifact peaks resulting from the transition at the assumed slit-cylindrical shape boundary. It is worth realizing here that the small contributions to pore volume and surface area calculated from the DS-HS model in this range for samples A-90 and A-105 are due to the widening of the microporosity, which is not considered an artifact (see Figure 5).

Conclusion

In the present study, a new version of the dual-shape 2D-NLDFT-HS (DS-HS) model is used for the textural characterization of hierarchical porous carbons. The DS-HS model uses the 2D-NLDFT-HS kernels developed for slit and cylindrical pore shapes to fit the experimental N 2 adsorption data and introduces the possibility of adjusting the slit-cylindrical pore shape ranges. Based on the analysis of our series of hierarchical porous carbons with increasing degree of activation, it was found that the slit-cylinder boundary traditionally set at 2 nm appeared to cause artifacts on the PSD calculated for highly activated carbons. A logical conclusion was reached thanks to the elegant systematic trend of the PSD variation for our samples. The appropriate shape boundary for our samples should be 3 nm, eliminating these artifacts. This result is not universal, however, and other carbon materials may have different properties, which may be investigated using this interactive approach.

In addition, the dual-gas analysis method allows for the simultaneous fitting of N 2 and CO 2 kernels to the corresponding isotherm data, which has led to a more accurate description of the PSDs in the ultra-micropore range. Since the slit-cylinder boundary is not independently proven and is often arbitrarily set at 2nm, the ability to adjust and investigate its effects in the DS-HS model is a significant advantage over methods using a fixed boundary, as exemplified by the comparison with the hybrid QSDFT model performed as part of this study.

Supporting information

Document containing additional figures and an explanation of the methodology followed for processing TEM images.

  provides an excellent opportunity to analyze and describe the progression of pore structure changes upon activation of these HPCs in a detailed and systematic manner. The database of adsorption isotherms for the studied series of activated carbons consists of eight N 2 isotherms measured at 77 K and eight CO 2 isotherms measured at 273 K. The samples are denoted by A-t, where t represents the activation time in minutes, the initial non-activated carbon sample being referred to as OMC. The results of applying the DS-HS model to the isotherm database and the effect of varying the limits w s and w c are discussed below. 4.1. PSD analysis assuming a slit-cylinder boundary at w s = w c = 2 nm

10 - 8 Figure 1 .

 81 Figure 1. Selected experimental branches of N 2 desorption and CO 2 adsorption isotherms (circular and square symbols, respectively) for A-15, A-60, and A-105 samples, in logarithm and linear scales (left and right column, respectively). The lines show the results from the simultaneous fits of the DS-HS kernel and the 2D-HS kernel for CO 2 to the corresponding N 2 and CO 2 isotherms, assuming a slit-cylinder boundary at w s = w c = 2 nm.

Figure 2 .

 2 Figure 2. PSDs calculated using the DS-HS model assuming a slit pores in the width range

Figure 3 . 4 . 2 .

 342 Figure 3. Comparison of PSD results calculated using two methods: the dual-shape DS-HS

Figure 4 .

 4 Figure 4. PSD analysis of isotherms of the OMC sample activated for 105 min (A-105). (a)

  Such a deviation is observed for the non-activated OMC sample in Figure6a, again indicating a minor underequilibration of the N 2 isotherm at low relative pressures. Despite the perfect fit of the N 2 kernel to the individual N 2 isotherm shown in this figure, because of the equilibration problem at low relative pressure, we consider that the CO 2 isotherm provides better information about the ultra-micropores in the OMC sample. To provide the most accurate PSD characterization of this sample, the full CO 2 isotherm was simultaneously fitted with the higher-pressure part

Figure 5 .

 5 Figure 5. PSDs calculated using the DS-HS model assuming a slit-cylinder boundary at w s =

Figure 6 .

 6 Figure 6. PSD analysis of the non-activated OMC sample. (a) Fit of the full N 2 and CO 2

Figure 7 .

 7 Figure 7. TEM images of OMC, A-75, and A-90 samples (top). (a-c) Histograms of pore

Figure 8 .

 8 Figure 8. Textural properties calculated with DS-HS and hybrid QSDFT models: (a) average

3 g -1 )

								Peak meso
								(nm)
	OMC	797 (43)	0.35	0.20	0.15	639 (49)	0.16 (0.01)	4.8
	A-15	1151 (-5)	0.55	0.29	0.26	920 (-6)	0.26	5.0
	A-30	1407 (-3)	0.73	0.38	0.35	1112 (-3)	0.35	5.0
	A-45	163 (-4)	0.97	0.51 (-0.01)	0.46 (0.01)	1246 (17)	0.4 (0.01)	5.0
	A-60	1568 (-8)	0.89	0.47 (-0.01)	0.42 (0.01)	1212 (13)	0.42 (.01)	5.0
	A-75	1729 (-15)	1.16	0.64 (-0.04)	0.52 (0.04)	1260 (56)	0.52 (0.04)	5.0
	A-90	1697 (-49)	1.30 (-0.01)	0.76 (-0.11)	0.54 (0.011)	1180 (181)	0.59 (0.16)	4.9
	A-105	1755 (-45)	1.25	0.67 (-0.11)	0.58 (0.10)	1272 (154)	0.60 (0.12)

Acknowledgment J.J. would like to thank Dr. Jeffrey Kenvin of Micromeritics for creative discussions on the data deconvolution methods used in this work. J.C.G. gratefully acknowledges CONACYT-SENER (601021/438978) for the assigned scholarship to support her PhD studies, resulting in the work presented here. This study was partly supported by the French PIA project "Lorraine


Philippe Blanchard
email: p.blanchard@afssa.fr

Frank Schurr

Olivier Celle

Nicolas Cougoule

Patrick Drajnudel

Richard Thiéry

Jean-Paul Faucon

Magali Ribière

Blanchard Philippe

First detection of Israeli acute paralysis virus (IAPV) in France, a dicistrovirus affecting honeybees (Apis mellifera)

Keywords: Israeli acute paralysis virus (IAPV), RT-PCR detection, winter losses, Apis mellifera

Bee samples were collected in French apiaries that displayed severe losses and mortality during the winter (from November 2007 to March 2008). They were screened for the presence of Israeli acute paralysis virus (IAPV) by using RT-PCR. Five out of 35 surveyed apiaries, located in two different geographical areas, were found positive. This represents the first reported detection of IAPV in France. The specificity of the PCR products was checked by sequencing. The phylogenetic analysis showed that French isolates of IAPV were closely related to a cluster including American and Australian isolates. Nevertheless, most of American isolates previously reported to be associated to Colony Collapse Disorder (CCD) and an Israeli isolate first isolated in 2004 from dead bees were included in another cluster.

Since IAPV was detected in only 14 % of the affected apiaries, it was not possible to establish a causal link between IAPV and the severe winter losses that occurred.

Short communication

Israeli acute paralysis virus (IAPV) was first described in 2004 in Israel, where severe bee mortality has inflicted heavy losses on Israeli apiculture [START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF]. Based on homology and genomic structure, IAPV was characterized as a new member of the Dicistroviridae family [START_REF] Christian | Family Dicistroviridae[END_REF], closely related to Kashmir bee virus (KBV) and Acute bee paralysis virus (ABPV), but genetically and serologically distinct [START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF]. Recently, the presence of IAPV has been strongly correlated with a new syndrome of honey bee losses observed in the United States, called the Colony Collapse Disorder (CCD) [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF]. These authors reported that IAPV could be a statistically significant marker for CCD. However, this hypothesis still remains under discussion [START_REF] Stokstad | Genomics: Puzzling decline of U.S. bees linked to virus from Australia[END_REF][START_REF] Chen | Historical presence of Israeli acute paralysis virus in the United States[END_REF][START_REF] Anderson | The latest buzz about colony collapse disorder[END_REF][START_REF] Cox-Foster | Response to " The latest buzz about colony collapse disorder[END_REF]. IAPV has been isolated in Israel, Australia and different states of USA such as Florida, California, Maryland and Pennsylvania [START_REF] Chen | Historical presence of Israeli acute paralysis virus in the United States[END_REF][START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF][START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF]. In this paper, we report the first detection of IAPV in bee samples from France, collected in 2008.

During the last winter, honey bee colony losses and mortalities have occurred in French apiaries. In some cases, beekeepers have reported up to 90% mortality rate of the colonies.

A preliminary survey was conducted on 35 apiaries showing severe winter losses in various parts of France (16 departments) to assess the pathological context. Given that last winter losses can suggest those observed in case of CCD such as a rapid loss from a colony of its adult bee population [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF], it appeared interesting to assess the presence of IAPV. To date, IAPV has never been investigated in France. Furthermore, Acute bee paralysis virus (ABPV) and Kashmir bee virus (KBV) have been looked for, since (i) they are genetically closely related to IAPV and (ii) all positive samples for IAPV also contained KBV in a recent report on CCD [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF]. Moreover, ABPV was detected in bees from colonies infested with Varroa destructor, and presenting high winter mortality [START_REF] Bakonyi | Detection of acute bee paralysis virus by RT-PCR in honey bee and Varroa destructor field samples: rapid screening of representative Hungarian apiaries[END_REF][START_REF] Siede | A real time based survey on acute bee paralysis virus in german bee colonies[END_REF].

Thirty-five apiaries distributed on all the French territory were sampled (one hive per apiary).

Sample preparation, RNA extraction and cDNA synthesis were performed as described previously [START_REF] Blanchard | Evaluation of a real-time two-step RT-PCR assay for quantitation of Chronic bee paralysis virus (CBPV) genome in experimentally-infected bee tissues and in life stages of a symptomatic colony[END_REF][START_REF] Ribière | Molecular diagnosis of chronic bee paralysis virus infection[END_REF]. Molecular diagnosis (ABPV, IAPV and KBV) were performed using primer pairs described previously [START_REF] Bakonyi | Detection of acute bee paralysis virus by RT-PCR in honey bee and Varroa destructor field samples: rapid screening of representative Hungarian apiaries[END_REF][START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF][START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF][START_REF] Stoltz | Molecular diagnosis of Kashmir bee virus infection[END_REF] (Table 1). Unexpectedly, among the 35 apiaries, IAPV was detected in five apiaries located in two distinct regions, including three in the department of Lozère and 2 in the department of Rhône in France. PCR products (768bp) obtained from IAPV-positive samples were sequenced in both orientations by using primers IAPV_IGR_F and IAPV_IGR_R described by [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF] and compared to IAPV, ABPV and KBV sequences available on GenBank [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF][START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF][START_REF] De Miranda | Complete nucleotide sequence of Kashmir bee virus and comparison with acute bee paralysis virus[END_REF][START_REF] Govan | Analysis of the complete genome sequence of acute bee paralysis virus shows that it belongs to the novel group of insect-infecting RNA viruses[END_REF]. After exclusion of the primer sequences, the nucleotide sequences reported in Table 2 were aligned by using the CLUSTAL_X program (Thompson et al., 1997). The phylogenetic tree was constructed by using the maximum likelihood method as implemented in the PHYLOWIN program [START_REF] Galtier | SeaView and Phylo_win, two graphic tools for sequence alignment and molecular phylogeny[END_REF] and 500 bootstrap replicates. The phylogenetic tree was visualized using TreeView [START_REF] Page | TreeView: an application to display phylogenetic trees on personal computers[END_REF] (Figure 1). The IAPV sequences from French isolates described in this paper were submitted to the GenBank database under Accession Nos. EU604006, EU604007, EU604008, EU604009 and EU604010.

IAPV isolates segregated in two main lineages supported by strong bootstrap values and clearly separated from KBV and ABPV as already shown by [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF]. Lineage A contained two isolates from the United States, two from Australia and all French isolates that grouped together. Lineage B contained most of American isolates (15/17), including the isolate first described in Israel and two Australian isolates. Overall IAPV isolates tended to segregate according to their geographical origin.

During this study, 85% of apiaries were diagnosed with one or several diseases and/or pathogens, such as varroasis (50%), ABPV (40%) and nosemosis (30%) (unpublished results), in agreement with previous studies demonstrating the crucial role of diseases in winter losses [START_REF] Bakonyi | Detection of acute bee paralysis virus by RT-PCR in honey bee and Varroa destructor field samples: rapid screening of representative Hungarian apiaries[END_REF][START_REF] Faucon | Honey bee winter mortality in France in 1999 and 2000[END_REF][START_REF] Siede | A real time based survey on acute bee paralysis virus in german bee colonies[END_REF]. All IAPV-positive apiaries were also positive for varroasis, three were positive for nosemosis (N. ceranae) and three for ABPV. Furthermore, KBV was also detected, but only in the samples where IAPV was found. Therefore, although IAPV was detected in a significant number of the surveyed apiaries (14%), it was not possible to establish a causal relationship between IAPV and the severe winter losses which occurred in France, unlike the CCD-related cases described by [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF]. Future work will seek to investigate the prevalence of IAPV in France. In this purpose sensitivity of PCR test will be assessed.

Since KBV and IAPV were always concomitantly detected in the analysed samples, the relationship between these viruses was investigated further. The RT-PCR products obtained from KBV positive samples were checked by sequencing. Pair-wise comparison with IAPV sequences [START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF] and KBV sequences [START_REF] De Miranda | Complete nucleotide sequence of Kashmir bee virus and comparison with acute bee paralysis virus[END_REF] showed that the sequences obtained in our study were more closely related to IAPV (8% of divergence) than to KBV (13% of divergence). French KBV-like sequences obtained in this study were also closely related (2-3% mean distance) to a putative KBV sequence from Australia (AUSbee AF034541), previously shown to be genetically distant to other KBV isolates obtained from USA [START_REF] Hung | Nucleotide sequence variations in Kashmir bee virus isolated from Apis mellifera L. and Varroa jacobsoni Oud[END_REF]. The same primers were used to identify KBV in French bee samples [START_REF] Tentcheva | Prevalence and Seasonal Variations of Six Bee Viruses in Apis mellifera L. and Varroa destructor Mite Populations in France[END_REF]. However, KBV-like sequences reported by the same authors (AY669845 -AY669846) are more closely related to the IAPV sequence described by Maori et al. (2007) (2% divergence), than to the KBV sequence (14% divergence) described by de [START_REF] De Miranda | Complete nucleotide sequence of Kashmir bee virus and comparison with acute bee paralysis virus[END_REF] (not shown). Altogether, these observations raise the question of the specificity of the primers used [START_REF] Stoltz | Molecular diagnosis of Kashmir bee virus infection[END_REF] and suggest that they could also amplify IAPV. If so, it could be hypothesized that IAPV was already present in France in 2002, but identified as KBV by [START_REF] Tentcheva | Prevalence and Seasonal Variations of Six Bee Viruses in Apis mellifera L. and Varroa destructor Mite Populations in France[END_REF]. Further studies are necessary to ascertain this hypothesis, such as full length sequencing of various IAPV and KBV isolates, and retrospective analysis of available honey bee samples.

The exact role of IAPV in winter mortalities of the bee colonies in France and the conditions of its importation are not known at present. French isolates are clustering in sub-lineage A with two Australian isolates coming of apparently healthy bees and two isolates from USA, whereas other IAPV isolates recovered from cases associated with mortalities [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF][START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF] are included in sub-lineage B (Figure 1). This suggests that different IAPV isolates may possess different pathogenic properties, as already pointed out by [START_REF] Chen | Historical presence of Israeli acute paralysis virus in the United States[END_REF]. Alternatively, other factors such as the influence of the environment or concurrent pathologies may affect the health status of the apiaries. This survey is currently ongoing to further investigate the involvement of other pathologies such as varroasis, nosemosis, or due to other viruses in the severe winter losses that occurred in France in 2007-2008.

Table 2.

IAPV isolates used in phylogenetic analysis a,b,c,d 100 percent identity between each sequence Figure 1.

Maximum likelihood phylogenetic tree based on 727 nt sequence, including the intergenic region (IGR) of 20 IAPV isolates from Israel [START_REF] Maori | Isolation and characterization of Israeli acute paralysis virus, a dicistrovirus affecting honeybees in Israel: evidence for diversity due to intra-and inter-species recombination[END_REF], the United States, Australia [START_REF] Cox-Foster | A metagenomic survey of microbes in honey bee colony collapse disorder[END_REF] and France (this study). ABPV and KBV were used as an outgroup.

The number of each node represents the bootstrap values as the result of 500 replicates.

Bootstraps values <50% were omitted. The scale corresponds to the number of substitutions per site.

Table 1 Primer

 1

	ABPV 1 ABPV 2	Sequence (5'-3') CATATTGGCGAGCCACTATG CCACTTCCACACAACTATCG	Length (bp) 398	Amplification target Viral RNA capsid gene	Position (GenBank accession no.) 8115 -8512 (AF126050)	Reference Bakonyi et al., (2002)
	IAPV_IGR_F CGATGAACAACGGAAGGTTT IAPV_IGR_R ATCGGCTAAGGGGTTTGTTT	767	Viral RNA Intergenic Region	6128 -6894 (NC009025)	Cox-Foster et al., (2007)
	IAPV F IAPV R	AGACACCAATCACGGACCTCAC AGATTTGTCTGTCTCCCAGTGCACAT	475	Viral RNA capsid gene	8860 -9334 (NC009025)	Maori et al., (2007)
	KBV 1 KBV 2	GATGAACGTCGACCTATTGA TGTGGGTTGGCTATGAGTCA	414	Viral RNA polymerase gene	5406 -5819 (AY275710)	Stoltz et al., (1995)

Acknowledgements

The authors are grateful to the collaborators and beekeepers for having kindly provided bee samples. The help of Ms. Cristina Gastaldi in improving the English of the manuscript is gratefully acknowledged.

Captions to figures

Table 1.

 Thompson, J.D., Gibson, T.J., Plewniak, F., Jeanmougin, F., Higgins, D.G., 1997. The CLUSTAL_X windows interface: flexible strategies for multiple sequence alignment aided by quality analysis tools. Nucleic Acids Res. 25,[4876][4877][4878][4879][4880][4881][4882]