Maelenn Chevreuil
email: maelenn.chevreuil@laposte.net

Lauriane Lecoq

Shishan Wang

Laetitia Gargowitsch

Naïma Nhiri

Eric Jacquet

Thomas Zinn

Sonia Fieulaine

Stéphane Bressanelli
email: stephane.bressanelli@i2bc.paris-saclay.fr

Guillaume Tresset
email: guillaume.tresset@universite-paris-saclay.fr

Nonsymmetrical Dynamics of the HBV Capsid Assembly and Disassembly Evidenced by Their Transient Species

Keywords: Hepatitis B virus, self-assembly, disassembly, dynamics, TR-SAXS

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Viruses, described as "organisms at the edge of life", do not have their own metabolism and require a host cell to replicate. All viruses comprise at least a nucleocapsid, that is, a protein shell called capsid surrounding and protecting the genome. Their survival depends on the ability of this nucleocapsid to assemble and sometimes also to completely disassemble in the host cell. Since some viral capsids 1 can be easily disassembled and reassembled in vitro by change of pH, ionic strength or temperature, in vitro studies of these mechanisms have increased in the past twenty years. However, despite these efforts, the dynamical pathway of viral assembly and disassembly is still an ill-known process.

Worldwide, about 240 million people suffer from an hepatitis B infection caused by the hepatitis B virus (HBV). It affects the liver and can cause serious complications such as cancer or cirrhosis. HBV is a DNA virus with an icosahedral capsid composed, in 95% of cases, of 120 dimers of the capsid protein, hereafter called subunits. The wild-type capsid protein is a 183-residue polypeptide comprising an assembly domain (N-terminal domain, NTD; residues 1-149) and a nucleic acid-binding domain (C-terminal domain, CTD; residues 150-183) located inside the capsid. To facilitate the study of HBV assembly and disassembly, we used a truncated protein engineered by Nassal et al. and containing only the NTD, [START_REF] Birnbaum | Hepatitis B virus nucleocapsid assembly: primary structure requirements in the core protein[END_REF] which allows us to take only into account the interactions between proteins. We refer to the mutant capsid protein containing the first 149 residues as Cp149. Just like the wild-type capsid protein, Cp149 is able to make up icosahedral capsids mostly comprising 120 subunits arrayed with T = 4 quasi-equivalence 3 (see Fig. S1 in SI).

The stability of the Cp149 capsids is mainly based on a delicate balance between two interactions (see Fig. 1.A): (i) a shortrange attraction due to hydrophobic and/or van der Waals forces, which holds the subunits together; and (ii) a long-range electrostatic repulsion, which allows the capsid to disassemble. The last one, often described as one of the most important driving forces during the assembly and disassembly of the capsid, is crucially affected by the subunits charge distribution and magnitude. [START_REF] Zandi | On virus growth and form[END_REF] However, these data are still unclear. Some estimated values of the corresponding energies have been deduced from theoretical calculations 5 or indirectly from kinetic experiments, [START_REF] Kegel | Competing Hydrophobic and Screened-Coulomb Interactions in Hepatitis B Virus Capsid Assembly[END_REF][START_REF] Šiber | Role of electrostatic interactions in the assembly of empty spherical viral capsids[END_REF] notably by static light scattering. [START_REF] Sun | Role of Protein Charge Density on Hepatitis B Virus Capsid Formation[END_REF] In a previous publication, we examined the melting temperature T m of empty capsids derived from the cowpea chlorotic mottle virus (CCMV), a small icosahedral plant virus, the capsid of which is also made of dimeric subunits. Using a fluorescence thermal shift assay to determine T m and a mean-field theory, [START_REF] Chen | Investigating the thermal dissociation of viral capsid by lattice model[END_REF] we were able to demonstrate a close relationship between T m and the subunit interactions via the effective charge of a subunit Z, the pairwise potential separating nearest neighbors and the Debye length κ -1 . 10 This relationship is given by a linear equation,

T m = A + BZ 2 κ -1 (1)
where A and B denote constants. The disassembly was monitored experimentally through the fluorescence intensity I F of a mixture containing capsids and fluorescent markers, whose emission was enhanced when they bound on the hydrophobic sites of the subunits. [START_REF] Tresset | Two-Dimensional Phase Transition of Viral Capsid Gives Insights into Subunit Interactions[END_REF] As the temperature was increased, the capsids experienced an order-disorder phase transition and further hydrophobic sites became exposed. T m was chosen as the temperature maximizing dI F /dT .

We applied the same methodology for Cp149 capsids and Figure 1.B gives T m as a function of κ -1 , the latter being tuned by varying the salinity. By fitting the data with Eq.

(1), we arrived at = -6k B T 0 and |Z| = 1.6e, with k B the Boltzmann constant, T 0 the room temperature and e the electric charge. For comparison, still in the case of Cp149 subunits, Ceres et al. estimated the subunit-subunit energy to be -6.8k B T 0 in high salt condition, [START_REF] Ceres | Weak Protein-Protein Interactions Are Sufficient To Drive Assembly of Hepatitis B Virus Capsids[END_REF] which is close to the value we found for . By contrast, the charge estimated by Sun et al.

on free dimers in solution by electrophoretic mobility was about -14.5e per subunit at the same pH. [START_REF] Sun | Role of Protein Charge Density on Hepatitis B Virus Capsid Formation[END_REF] This discrepancy can be explained by the fact that since, in our measurements, the subunits were assembled into capsids, fewer residues were ionized because less accessible to the solvent, reducing thereby the effective charge Z.

Sun et al. experiments were carried out on free dimers in solution by electrophoretic

mobility whereas we did it on whole capsids by thermal shift assay. The difference probably comes from the charges differencies that exist between the two dimers configurations. As we said in our manuscript, the dimers organized in capsid have less ionized residues because residues are less accessible to the solvent. This ionization difference explain why the effective charge Z on the whole capsid is lower than on free dimers.

Despite substantial experimental and theoretical efforts devoted to the assembly and disassembly of HBV capsids, many questions remain unanswered. If the nucleation-growth mechanism [START_REF] Zandi | Classical nucleation theory of virus capsids[END_REF][START_REF] Hagan | Advances in Chemical Physics[END_REF] is well admitted by the community for the assembly of empty capsids, the nature of the early and late intermediates is still unclear. Early intermediates for HBV capsids have been reported to be trimers 14 or pentamers [START_REF] Holmes | Assembly Pathway of Hepatitis B Core Virus-like Particles from Genetically Fused Dimers[END_REF] detect the presence of oligomers, the size and nature of which remain yet unknown. [START_REF] Singh | Observed Hysteresis of Virus Capsid Disassembly Is Implicit in Kinetic Models of Assembly[END_REF] A major difficulty in the experimental study of the assembly and disassembly processes of icosahedral capsids is the coexistence of several transient species. Time-resolved small-angle X-ray scattering (TR-SAXS) with synchrotron source enables to track complex phenomena in soft matter with a temporal resolution of a few milliseconds and a spatial resolution of a few nanometers. [START_REF] Narayanan | Recent applications of synchrotron radiation and neutrons in the study of soft matter[END_REF] Complemented with singular value decomposition (SVD), 21,[START_REF] Williamson | Analysis of self-associating proteins by singular value decomposition of solution scattering data[END_REF] structural information and time evolution of the major long-lived species can be directly extracted with no prior assumption. A detailed description of SVD analysis is given in SI. TR-SAXS was successfully used for investigating the assembly [START_REF] Berthet-Colominas | Kinetic study of the self-assembly of brome mosaic virus capsid[END_REF][START_REF] Tuma | Detection of intermediates and kinetic control during assembly of bacteriophage P22 procapsid[END_REF][START_REF] Kler | RNA encapsidation by SV40-derived nanoparticles follows a rapid two-state mechanism[END_REF][START_REF] Tresset | Norovirus Capsid Proteins Self-Assemble through Biphasic Kinetics via Long-Lived Stave-like Intermediates[END_REF][START_REF] Law-Hine | Identification of a major intermediate along the self-assembly pathway of an icosahedral viral capsid by using an analytical model of a spherical patch[END_REF][START_REF] Burke | Nanoparticle-Templated Self-Assembly of Viral Capsids Probed by Time-Resolved Absorbance Spectroscopy and X-Ray Scattering[END_REF][START_REF] Chevreuil | Nonequilibrium self-assembly 23 dynamics of icosahedral viral capsids packaging genome or polyelectrolyte[END_REF] and disassembly [START_REF] Law-Hine | Reconstruction of the Disassembly Pathway of an Icosahedral Viral Capsid and Shape Determination of Two Successive Intermediates[END_REF][START_REF] Asor | pH stability and disassembly mechanism of wild-type simian virus 40[END_REF] of a number of icosahedral capsids either empty or containing a cargo such as genomic nucleic acids, polymers or inorganic nanoparticles. Of particular interest here, Law-Hine et al. unveiled some of the transient species along the assembly and disassembly pathways of CCMV empty capsids, [START_REF] Law-Hine | Identification of a major intermediate along the self-assembly pathway of an icosahedral viral capsid by using an analytical model of a spherical patch[END_REF][START_REF] Law-Hine | Reconstruction of the Disassembly Pathway of an Icosahedral Viral Capsid and Shape Determination of Two Successive Intermediates[END_REF] which are made of 90 subunits (T = 3). In both pathways, even though the timescales were different, one common large intermediate species comprising about 35 subunits was found. In conditions of capsid assembly, CCMV subunits have an interaction energy of -4.6k B T 0 , 10 that is, weaker than that of Cp149 subunits. A question then arises:

Can one still find common transient species or similar steps along the assembly and disassembly pathways of Cp149 capsids, and what would it entail in the biological context of the HBV life cycle?

Here, by combining TR-SAXS and SVD analysis, we report first on the influence of subunit concentration and salinity on the assembly pathways, and we describe several distinct phases. The disassembly pathway is then investigated and we unveil an unexpected transient species. We finish by a discussion relating our findings to the known steps of the HBV life cycle.

Methods

Sample preparations

Buffer solutions

Expression of Cp149 capsids

The expression of Cp149 capsids was adapted from a protocol developed previously. [START_REF] Heger-Stevic | Methods in Molecular Biology[END_REF] Briefly, the pRSF-T7-HBc149opt plasmid was incorporated into E.coli BL21 * CodonPlus cells and grown at 37 • C overnight on a LB-agar plate containing 50 µg.mL -1 kanamycine and 34 µg.mL -1 chloramphenicol. Then, a single colony was inoculated into 2×10 mL LB medium and grown at 37 • C overnight. It was then transferred into 2×500 mL of LB medium containing 50 µg.mL -1 kanamycine and 34 µg.mL -1 chloramphenicol and incubated for 5 to 6 h at 37 • C. When OD 600 reached 0.8, the bacterial cells were grown at 25 • C overnight after induction with 1 mM IPTG.

Purification of Cp149 capsids

The purification of Cp149 capsids was adapted from a protocol developed previously. [START_REF] Heger-Stevic | Methods in Molecular Biology[END_REF] Bacterial cells containing Cp149 capsids were pelleted by centrifugation (6,000×g, 20 min) and re-suspended in 15 mL of lysis buffer. 15 mg of chicken lysozyme, 300 µL of protease inhibitor cocktail solution 50× and 750 µL of 10% Triton-X-100 were added to the cell suspension and incubated on ice for 45 min. Then, benzonase nuclease was added to the suspension and mixed for 30 min at room temperature. The cells were lysed by sonication and then centrifuged at 8,000×g for 1 h to remove cell debris. The supernatant was loaded onto a step gradient from 10 to 60% (w/v) sucrose buffer and centrifuged with a SW-32Ti

Beckman Coulter rotor at 28,800×g for 3 h at 4 • C. The gradient fractions containing Cp149 capsids were identified by 15% SDS-PAGE and precipitated by slow addition of AmSO 4 to 20% saturation. After incubation on ice for 1 h and centrifugation at 25,000×g for 1 h, pellets were resuspended in purification buffer. The protein solution was centrifuged again for 15 min to remove insoluble pellets and the supernatant containing soluble capsids was dialyzed overnight in purification buffer at 4 • C. For disassembly experiments, the capsid solution was dialysed against capsid buffer. The capsid stock concentration, with 29450 M -1 .cm -1 as molar attenuation coefficient, was 2.4 mg.mL -1 and the absorbance ratio A 260 /A 280 was around 0.61.

Purification of Cp149 subunits

All Cp149 subunits used for assembly assays were dissociated from previously purified Cp149 capsids into dimeric subunits as described elsewhere. [START_REF] Porterfield | Full-Length Hepatitis B Virus Core Protein Packages Viral and Heterologous RNA with Similarly High Levels of Cooperativity[END_REF] Briefly, Cp149 capsids expressed and purified from E.coli were disassembled by dialysis at 4 • C into disassembly buffer. Following dialysis, the solution was centrifuged at 20,000×g for 15 min at 4 • C in order to remove all the elements that could aggregate and then obstruct the separation column. Cp149 subunits were then purified by size exclusion chromatography (SEC) using a Superdex S200 increase GL previously equilibrated in disassembly buffer. Fractions containing subunits were identified with absorbance at 280 nm and dialysed against subunit buffer. The subunit stock concentration was 1.17 mg.mL -1 and the absorbance ratio A 260 /A 280 was around 0.57.

Small-angle X-ray scattering

Assembly experiments

Time-resolved small-angle X-ray scattering (TR-SAXS) assembly experiments were carried out with the ID02 beamline at the European Synchrotron Radiation Facility (Grenoble, France). [START_REF] Narayanan | A multipurpose instrument for time-resolved ultrasmall-angle and coherent X-ray scattering[END_REF] SAXS patterns were recorded using a high speed and ultra-low noise area CCD detector (Rayonix MX-170HS). The sample-to-detector distance was set to 1.3 m or 3 m.

With scattering wavenumbers q = 4π/λ sin (θ/2), where θ is the scattering angle and λ = 0.995 Å the X-ray wavelength (at a photon energy of 12.46 keV), these distances provided qvalues ranging from 6.4×10 -2 to 5.7 nm -1 or from 2.7×10 -2 to 2.4 nm -1 . The experimental setup included a stopped-flow device (Biologic SFM-400) used to mix the subunits with the assembly triggering buffer. The mixed solutions were then injected through a quartz capillary of diameter 1.4 mm and the flow was stabilized with a hard stop valve. The total delay time for the solution to reach the capillary including the mixing time was less than 10 ms in all experiments. Beam exposure time was set to 20 ms. The scattering intensities were converted into absolute units after subtracting the contribution of the buffer solution.

Experimental uncertainties were calculated after circular averaging using the SAXSutilities software package.

Disassembly experiments

TR-SAXS disassembly experiments were carried out with the SWING beamline at the Synchrotron SOLEIL (Gif-sur-Yvette, France). Two-dimensional scattering images were recorded with an AVIEX large-area CCD detector. The sample-to-detector distances was set to 1.5 m which provided scattering wavenumbers q ranging from about 5×10 -2 to 2.5 nm -1 . The Cp149 capsids were manually mixed with the disassembly triggering buffer. The mixed solution was then injected via an injection robot through a capillary. The total delay time including mixing, safety checks and injection was a few minutes, which explains why we did not capture the early stage of the kinetics. Beam exposure time was set to 250 ms. The scattering intensities were also converted into absolute units after subtracting the contribution of the buffer solution. The experimental uncertainties were calculated after circular averaging using the FOXTROT package.

Results

Assembly experiments

In vitro HBV assembly experiments were performed by quickly mixing a solution of subunits with a high salt solution, both at pH 9 (See detailed description of sample measurements in Methods.). The temperature was maintained at T=20 • C and the final concentrations in subunits and salt are reported in the table 2. A total of six different conditions were assayed. The assembly kinetics were performed and collected over different time intervals, ranging from 6 minutes for the shortest to 19 minutes for the longest.

Table 2:

The asterisks indicate conditions with several replicates.

Summary table of the experimental conditions

Cp149 subunit concentration (g.L -1 ) 0.3 0.6 0.9 NaCl concentration (M) 0.5 * 1 * 1.5 * 0.5 1 * 0.5

SAXS curves from a typical assembly kinetics are presented on Fig. 2.A. In the early time steps, the scattering intensities exhibited a monotonic decrease with the wavenumber q indicating that subunits were the only species in solution. A few seconds after triggering the assembly, the scattering intensities displayed oscillations with a first minimum at q = 0.23 In order to get a better insight into the assembly pathways, we extracted the radius of gyration R g as well as the mean aggregation number N w at each time step and for each kinetic experiment by using the code DATRG. [START_REF] Petoukhov | ATSAS 2.1 -towards automated and web-supported small-angle scattering data analysis[END_REF] We subsequently computed the corresponding timescales, i.e., τ Rg and τ N w , by fitting the latter quantities with single exponential decay functions (see Table S1 in SI). An example of the extracted time evolutions for N w and R g as well as their respective fits are presented in Fig. 3.A. The extracted timescales τ N w and τ Rg revealed two early phases during the assembly process. As shown on Fig. 3.A, there was a first phase, ascribed to a nucleation, where both the size and the mass of the species increased but at different rates, R g plateauing earlier than N w . This nucleation phase was followed by a growth phase, where N w continued to increase while R g no longer evolved significantly. After a few seconds, R g and N w both reached their equilibrium values. However, if N w and R g remained stable as early as a few seconds after the onset of assembly, we still noticed form factors arches more pronounced over time (Fig. 3.B), which reflects self-organization process dynamics. This is highlighted on Fig. 3.C that depicts the time evolution of the first minimum of the form factors P (q), and which allowed us to extract a third timescale τ P . For the kinetics presented on Fig. 3.C, τ P was around 400±70 s, which is two orders of magnitude larger than the two other timescales.

For the other kinetics, τ P was between 303 ± 65 s and 588 ± 70 s. This evolution can be ascribed to a third phase, namely, the relaxation of capsid-like objects into fully assembled capsids.

By comparing τ N w and τ P across the various kinetics (Fig. 3.D), we identified a different assembly dynamics depending upon the experimental conditions. The kinetics carried out at 0.3 g.L -1 in subunits and 1.5 M in salt exhibited values for τ N w and τ P with the same order of magnitude, unlike all the other kinetics. Additionally, the ratio τ N w /τ Rg was five to ten fold higher than the ratios calculated in the other experimental conditions (see Fig. S7 in SI). These observations indicate that the relaxation phase did not occur under high salt and low subunit concentration.

To summarize on the assembly pathways, our findings suggest that, during the nucleation phase, several subunits quickly agglomerated to form disordered objects of the size of a capsid but with a lower mass. During the growth phase, the objects self-organized while capturing free subunits in solution until reaching a mass close to that of a capsid. At this point, these capsid-like objects continued to self-organize and relaxed structurally towards icosahedral capsids. However, in harsh conditions, i.e., with high salt and low subunit concentration, the latter phase was inhibited. We believe that the electrostatic repulsion between subunits was screened by the highly concentrated salt, which subsequently enhanced the effective subunitsubunit attraction. As a result, the capsid-like objects could not rearrange themselves and ended up kinetically trapped with many defects.

Disassembly experiments

In vitro disassembly of Cp149 capsids was carried out by mixing manually a solution of capsids with a 6 M urea solution, both at pH 9 and 10 • C (See detailed description of sample measurements in Methods.). The sample was dialyzed in capsid buffer overnight two days before the measurements. In order to estimate the number of contributing species during the early phase, we performed a SVD analysis on the time-resolved scattering patterns. Solely two species were contributing significantly and the comparison of the scattering patterns extracted from the SVD analysis with the experimental patterns of capsids and subunits showed a good agree-ment (data not shown). As far as the whole kinetics is concerned, SVD analysis indicated three significant contributions (see Fig. S5 in SI), namely, free subunits, capsids and an unknown transient species, and Fig. 5.A shows their extracted scattering patterns. Notice that the Guinier region on the pattern of the transient species (in magenta) was not visible in our range of q-values, which confirmed that the species was much larger than a capsid. We then tried to understand the nature of the clusters. We first repeated the disassembly experiment by SAXS and static light scattering (SLS) in various conditions, and each time, we observed a strong but transient increase of the scattering intensity (see Fig. S9 in SI).

Consequently, we could rule out the possibility of radiation damage or of an experimental mistake. Then, we noticed the almost perfect overlap between the scattering patterns of subunits and that of the clusters at high q-values, which suggested that the latter were made of subunits. Using the small and medium q-values of the scattering curve, we looked for information about their long-range organization. Indeed, this region of the curve reflects the fractal nature of the clusters (see Fig. S10 in SI). As shown on Fig. 5.B, by dividing the form factor of subunits, we computed the structure factor S(q) of the clusters. We thus obtained a fractal dimension of 1.8, indicating that inside the clusters, more or less attractive and repulsive interactions counterbalance each other, which is reminiscent to the self-avoiding walk model in polymers. As a consequence, one can hypothesize that the oligomers observed by Singh et al., [START_REF] Singh | Observed Hysteresis of Virus Capsid Disassembly Is Implicit in Kinetic Models of Assembly[END_REF] whose size and nature remained unknown, were clusters of subunits organized into a branching fractal structure. Figure 5.C gives the estimated mass fraction of each species via a least-squares minimization. It should be noted that there was a significant amount of subunits (approximately 60%) from the beginning of the kinetics, which can be explained by the fact that the first data point was collected seven minutes after the mixing due to technical constraints, and also because the capsids were stored at pH 9, which may have contributed to start the dissociation process.

Discussion & Conclusions

In the literature, for HBV and many other viruses, the assembly dynamics of empty capsids is often described by the nucleation-growth mechanism. If our observations do not question this model, they introduce a third slow phase of relaxation. It is not yet clear whether the relaxation phase reflects the self-organization of capsid-like objects into icosahedral capsids made of 120 subunits rather than the capture of the last missing subunits. It seems quite plausible that both events occur simultaneously, in particular because they are not mutually exclusive. Indeed, even if N w seems unchanged during the relaxation phase, given the large uncertainties shown on Fig. 3.A, it is possible that we were not able to detect the capture of a few missing subunits. This assumption of a slow relaxation following the growth phase is supported by theoretical studies, [START_REF] Hagan | Advances in Chemical Physics[END_REF] which demonstrated that the insertion of the final subunit is energetically costly but ensures the metastability of capsids against a change of the environment. It is also supported by previous studies on Cp149 capsids [START_REF] Pierson | Detection of Late Intermediates in Virus Capsid Assembly by Charge Detection Mass Spectrometry[END_REF][START_REF] Kondylis | Evolution of Intermediates during Capsid Assembly of Hepatitis B Virus with Phenylpropenamide-Based Antivirals[END_REF] reporting the presence of long-lived species made of 104, 111 or 117 subunits in the late stage of assembly kinetics. Besides, one can imagine that such incomplete capsids may also display a number of defects in their icosahedral order. In a recent article, Panahandeh et al. showed through Monte Carlo simulations that a disorder-order transition can take place during the assembly of icosahedral capsids. [START_REF] Panahandeh | How a Virus Circumvents Energy Barriers to Form Symmetric Shells[END_REF] The transition allow the objects to correct the defects in the icosahedral order, such as rearrangement of pentamers or hexamers of dimers positioned in a "wrong" location, that inevitably occur during the growth phase. Depending upon the elastic and subunit-subunit interaction energies, the authors observed the formation of transient disordered capsid-like objects that can evolve either with icosahedral order or into misassembled shells. We think therefore that the relaxation phase is closely related to the disorder-order transition, with capsid-like objects correcting their structural defects while capturing the last missing subunits. High salt conditions most likely induce high elastic and interaction energies impairing the correction of misplaced subunits, and lead to the kinetically trapped, disordered capsid-like objects seen in our experiments.

As exposed earlier, we did not find, in our assembly conditions, one of the late intermediates comprising more than 100 subunits previously proposed in the literature. [START_REF] Pierson | Detection of Late Intermediates in Virus Capsid Assembly by Charge Detection Mass Spectrometry[END_REF][START_REF] Kondylis | Evolution of Intermediates during Capsid Assembly of Hepatitis B Virus with Phenylpropenamide-Based Antivirals[END_REF] It should be noted that TR-SAXS cannot distinguish reliably objects with similar form factors. [START_REF] Williamson | Analysis of self-associating proteins by singular value decomposition of solution scattering data[END_REF] In particular, the late intermediates postulated in nucleation-growth-closure models have form factors too close to that of a complete capsid (see Fig. S8 in SI) to be separated by SVD.

Perhaps for similar reasons, we could not distinguish clearly T = 3 capsids from T = 4.

Sun et al. [START_REF] Sun | A dimorphism shift of hepatitis B virus capsids in response to ionic conditions[END_REF] found a significant change in the proportions of T = 3 and T = 4 capsids upon an increase of salt concentration. This result is also reported in numerous publications of Zlotnick, Jacobson and coworkers (e.g. [START_REF] Harms | Monitoring Assembly of Virus Capsids with Nanofluidic Devices[END_REF] ) using resistive-pulse sensing, a single-molecule technique performed at much lower protein concentrations than the present work. In a recent TR-SAXS study much more similar to ours, [START_REF] Asor | Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly[END_REF] Asor et al. obtained very similar results to ours but did find in their highest salt condition significant amounts of T = 3 capsids, which they estimated to plateau at 20% of the mass fraction. Unlike them, the position of the first minimum on our scattering patterns in varying salt conditions, which allows estimation of the T = 3 to T = 4 capsids ratio, remained remarkably fixed (see Table S2 in SI), close to the q-value expected for a T = 4 capsid. This first minimum is also close to the one expected for a solution with 20% (mass fraction) of T = 3 capsids (see Table S2 in SI), therefore we cannot rule out the presence of a small proportion of T = 3 capsids. However, unlike Asor et al. in a single experiment, 40 all our SVD analyses indicated an effective rank of 2 in all our experiments. These discrepancies, particularly the negligible variation of the fraction of T = 3 capsids in our data sets, may be due to the fact that the experiments of Asor et al. [START_REF] Asor | Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly[END_REF] were always performed below 0.5 M of ammonium acetate while ours were performed with 0.5 M of NaCl or more. Nevertheless, our assembly studies in accordance with recent work, 41 emphasized the rapid formation (in a few seconds) of capsid-like objects through a classical nucleation-growth mechanism in two phases, which could allow an almost instantaneous protection of the genome in vivo. These phases are then followed by a slow structural relaxation (in several minutes) of the capsid-like objects into icosahedral capsids while adding the few missing subunits. In vivo, the latter phase may allow the capsid to strengthen, providing thus an efficient and solid protection for the genome.

We were also able to confirm previous observations about the non-symmetrical dynamics of the assembly and disassembly of HBV empty capsids. [START_REF] Singh | Observed Hysteresis of Virus Capsid Disassembly Is Implicit in Kinetic Models of Assembly[END_REF] Unlike other viruses such as CCMV for which the disassembly pathway of empty capsids [START_REF] Law-Hine | Reconstruction of the Disassembly Pathway of an Icosahedral Viral Capsid and Shape Determination of Two Successive Intermediates[END_REF] is almost a mirror image of the assembly pathway, [START_REF] Law-Hine | Identification of a major intermediate along the self-assembly pathway of an icosahedral viral capsid by using an analytical model of a spherical patch[END_REF] the assembly of HBV empty capsids occurs quickly-over ten minuteswhile the disassembly requires more than ten hours, even in harsh non-physiological conditions (Fig. 6). In the case of an RNA virus like CCMV, the disassembly of the capsid is biologically relevant because the RNA has to be released into the cytoplasm of the infected cell. This is not the case with HBV for which there is no dissociation per se: Capsids loaded with viral DNA partially dissociate when transferred into the nucleus, but proteins remain partly associated with the genomic DNA (see Fig. S11 in SI). Despite the non-physiological conditions of our experiments, i.e., 3 M of urea at pH 9, the long and tough in vitro disassembly process is in adequacy with what happens in vivo. Indeed, this behaviour must be related to the resilience of the subunits that allow them to remain associated with genomic DNA, and consequently, harsh conditions are necessary to completely dissociate the capsid in vitro. Moreover, the capsid has to be robust enough to host partially double-stranded DNA during the HBV life cycle (see Fig. S11 in SI). There must be strong interactions between subunits and it explains why it is so difficult to completely dissociate them without the right cellular factors. It is also quite remarkable that in these conditions the process goes through a transient phase in which larger-than-capsid branching fractal clusters made of subunits form. This phenomenon is unusual with proteins under an X-ray beam, where aggregation is normally irreversible and due to radiation damage. Here it could be due to a change in protein conformation caused by urea, which first leads to form aggregates before the entropy finally plays its role by disassembling these into free subunits. These branching fractal clusters could reflect the ability of HBV subunits to self-organize in extended patterns suitable for their association with the genomic DNA in the nucleus. Time-resolved studies with fine structural information are increasingly required to better understand the dynamical pathways of viral assembly and disassembly. Elucidating how these pathways are linked to viral replication will hopefully be useful to combat viral infections and to halt outbreaks in their early stage.

Figure 1 :

 1 Figure 1: Thermal shift assay on empty HBV capsids. (A) A simple sub-viral particle consists of capsid proteins -associated in dimeric subunits -forming a shell and encasing the genome. The Cp149 subunits have hydrophobic sites on their sides (purple patches) and carry anionic charges (blue minus sign) on their surface. (B) Melting temperature T m as a function of Debye length κ -1 at pH 7.5 and different salinities. The red and black stars are experimental data replicates, and the red and black lines are linear regressions according to Eq. (1). The inset shows the derivative of the fluorescence intensity I F with respect to the temperature used to extract T m at pH 7.5 and different salinities: from 0 M (light blue curve) to 0.5 M (orange curve) by steps of 0.1 M.

nm - 1 ,

 1 close to the q-value expected for a T = 4 capsid, which indicates the formation of capsid-like objects where HBV forms T = 3 were in the minority (see Fig.S2in SI for the SAXS pattern of subunits and capsids). A SVD analysis was then performed on the matrix of scattering intensities I and revealed that each set of data could be approximated by a matrix of rank 2 (see Fig.S4in SI).It allowed us to reconstruct the time-resolved scattering intensities through a non-linear least-squares curve fitting by considering only two species coexisting in solution, i.e., T = 4 capsids and free subunits, and therefore, to estimate the evolution of the mass fractions.A typical reconstruction is presented on Fig.2.B, and the final mass fraction in capsids was estimated to be around 20%. All the final mass fractions are summarized in Fig.2.C.One can see first that there are a critical subunit concentration and a critical salinity to allow the formation of capsids. Secondly, the final mass fraction in capsids is a function of the initial subunit and salt concentrations. Both observations are consistent with previous experiments 11 as well as theoretical models based on the law of mass action and assuming the presence of only free subunits and capsids.[START_REF] Van Der Schoot | Kinetic theory of virus capsid assembly[END_REF]

Figure 2 :

 2 Figure 2: TR-SAXS data for the assembly of Cp149 empty capsids. (A) TR-SAXS patterns obtained at pH 9 and 0.9 g.L -1 of subunits. The assembly was triggered with 0.5 M of salt. The patterns are shifted for clarity. (B) Mass fractions of subunits (red) and capsids (blue) as a function of time. (C) Summary graph of the final mass fractions in capsids as a function of salt and subunit concentrations.

Figure 3 :

 3 Figure 3: Assembly phases. (A) Evolution of N w (blue) and R g (orange) as a function of time. The black and red curves show fits with a single exponential decay function. (B) Form factors P (q) at different time points. The gray dashed line indicates q = 0.2287 nm -1 . (C) Values of the form factors at q = 0.2287 nm -1 versus time. The red line is a single exponential decay fit yielding an estimate for the structural relaxation time τ P . (D) Summary graph of the ratios of the extracted characteristic timescales: τ P /τ N w .

Figure 4 :

 4 Figure 4: TR-SAXS data for the disassembly of Cp149 capsids. The final subunit and urea concentrations were 2.4 g.L -1 and 3 M, respectively. (A) Time evolution of the forward scattering intensity I(0) from 7 min to 16h30. The gray and red colored areas delimit the two phases of the disassembly. (b,c) Superimposed scattering patterns collected at early and late time steps. The patterns in red are the first and the last within each time range. The arrows in (B) point out isoscattering point.

Figure 4 .

 4 Figure 4.A depicts the time evolution of I(0), estimated by using the code DATRG, for the disassembly experiment. Two phases can be clearly seen: (i) An early short phase, up to 25 min (gray area), where the forward scattering intensities I(0) decreased over time; and (ii) a second longer phase (red area) with a rapid rise of I(0) at the beginning of the phase followed by a slow decrease to an equilibrium state. The superimposed patterns at the early stage of the kinetics are shown on Fig. 4.B and exhibited isoscattering (or isobestic) point (see black arrows), which suggested the presence of only two coexisting species in solution over this time range. The superimposed patterns at the late stage of the kinetics showed a rapid rise of the intensities at the beginning (Fig. 4.C). That rise of scattering intensity visible at low wavenumbers led to values exceeding those obtained initially with pure capsids, which suggested the formation of larger-than-capsid clusters.

Figure 5 :

 5 Figure 5: Species involved in the disassembly. (A) Scattering patterns of the three species in solution: subunits in blue, clusters in pink and capsids in red. (B) Structure factor S(q) of the clusters. The schematics represents the branching fractal structure. (C) Mass fractions of the three species as a function of time estimated by a least-squares minimization.

Figure 6 :

 6 Figure 6: Proposed assembly and disassembly pathways for Cp149 empty capsids.

  of subunits. Pierson et al. observed stable and structured late intermediates 16 made of 104, 111 or 117 dimers, while Katen et al. as well as Kondylis et al. pointed out labile and disordered late intermediates 17,18 containing defects or holes. The disassembly pathway is even more elusive, and a notable study was done by Singh and Zlotnick who combined chromatography and computer simulations to

Table 1 :

 1 Summary of the buffer solutions used in the sample preparations. Composition Lysis buffer (TN300) 300 mM NaCl; 5 mM DTT; 50 mM Tris pH 7.4 Purification buffer 5% sucrose; 5 mM EDTA; 1 mM DTT; 50 mM Tris pH 7.5 Sucrose buffer 300 mM NaCl; 5 mM DTT; 50 mM Tris pH 7.5 Purification disassembly buffer 3 M urea; 10 mM DTT; 20 mM Tris pH 7.5 Cp149 capsid buffer 1 mM DTT; 50 mM CHES pH 9 Cp149 subunit buffer 1 mM DTT; 50 mM CHES pH 9 Assembly triggering buffer 2 M NaCl; 1 mM DTT; 50 mM CHES pH 9 Disassembly triggering buffer 6 M urea; 1 mM DTT; 50 mM CHES pH 9

	Buffer

Acknowledgement

The authors thank Mehdi Zeghal, Anja Böckmann, Jéril Degrouard and Didier Law-Hine for fruitful advice. M.C. is supported by the "IDI 2016" project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02. G.T. and S.B. acknowledge financial support from the Agence Nationale de Recherches sur le Sida et les hépatites virales (ANRS). The electron microscopy imaging is supported by "Investissements d'Avenir" LabEx PALM (ANR-10-LABX-0039-PALM). We also acknowledge the European Synchrotron Radiation Facility (ESRF) and the synchrotron SOLEIL for allocation of synchrotron beam time on ID02 and SWING beamlines, respectively.

Supporting Information Available

Size distribution of Cp149 empty capsid, details on mean aggregation number, details on SVD analysis, characteristic timescales, scattering patterns of capsid, subunit and late intermediates, static light scattering and HBV life cycle.


Ronan Lebullenger
email: ronan.lebullenger@univ-rennes1.fr

Sébastien Chenu

Jean Rocherullé

Odile Merdrignac-Conanec

François Cheviré

Franck Tessier

A Bouzaza

S Brosillon

Glass foams for environmental applications

published or not. The documents may come

Introduction

Glass recycling is nowadays well implanted in worldwide quotidian lives. In each country, recuperation of glass alimentary containers, windows or cathode ray tube for example is encouraged by European laws. The case of glass waste from automotive industry is not so visible. In general, foam glass prepared from glass cullet needs a milling step to produce a glass powder. The conclusions of studies carried out on the influence of powder granulometry distribution on expanded resulting materials differ from one author to another. The foaming agent is commonly the calcium carbonate or chalk. Other expansion precursors such as sodium sulphate, mixture of iron oxide with carbon, and also silicium carbide were largely studied [START_REF] Scarinci | Glass foams[END_REF][START_REF] Rolland | [END_REF][START_REF] Tasserie | A new expanded material: optimization of the fabrication process[END_REF][START_REF] Tasserie | New expanded material based on industrial glass. I. Effect of the quality of powders and their mixing on properties of the material[END_REF][START_REF] Mear | Characterisation of porous glasses prepared from Cathode Ray Tube (CRT)[END_REF][6][7][START_REF] Bernardo | Reutilization and stabilization of wastes by the production of glass foams[END_REF][START_REF] Bernardo | Micro-and macro-cellular sintered glass-ceramics from wastes[END_REF][START_REF] Saburit Llaudis | Foaming of flat glass cullet using Si3N4 and MnO2 powders[END_REF][START_REF] Bernardo | Glass foams from dismantled cathode ray tubes[END_REF]. However, the use of nitride compound (Si 3N4 or AlN) which provide the formation of nitrogen bubbles is more "ecologically correct" [START_REF] Tasserie | New expanded material based on industrial glass. II. Role and effect of the amount of an expansive additive on the characteristics of the material[END_REF][START_REF] Garnier | Aluminosilicate monolithique expansé à double porosité ouverte[END_REF]. Expanded glass based materials are commercially available (Corning Pittsburg) for phonic or thermal insulation [START_REF] Shutov | Determination of practical properties of heat-insulating foam glass[END_REF][START_REF]Pittsburgh Corning Foamglass Insulation[END_REF][START_REF] Fernandes | Preparation and characterization of foams from sheet glass and fly ash using carbonates as foaming agents[END_REF][START_REF] Tulyaganov | Preparation and characterization of high compressive strength foams from sheet glass[END_REF][18][START_REF] Wu | Thermal and mechanical properties of a foamed glass-ceramic material produced from silicate wastes[END_REF]. The photo catalytic support approach could be an added value and a new use of these foam glasses in the civil and building engineering.

The semiconductor photocatalytic activity is based on the adsorption of an ultra band gap photon that promotes an electron from the valence band to the conduction band. In the case of titanium dioxide semiconductor, photon energy must be higher than 3.2 eV for anatase crystalline form that means a photon wavelength below 385 nanometers. The resulting electron-hole pair, after migration at the semiconductor surface, is then available for chemical redox reactions [START_REF] Mills | An overview of semiconductor photocatalysis[END_REF]. Particularly, the titanium dioxide modified materials have gained an increasing attention, due to the wide range of possible applications. Moreover, the relative low cost of the photocatalytic active TiO2 opened the way to scale applications, for example in the building sector. Studies have been reported in literature on various applications, including cementitious materials [START_REF] Mills | An overview of semiconductor photocatalysis[END_REF][START_REF] Calabria | Synthesis of sol-gel titania bactericide coatings on adobe brick[END_REF][START_REF] Wang | Volatile organic compounds in indoor environment and photocatalytic oxidation: state of the art[END_REF][START_REF] Strini | Measurement of benzene, toluene, ethylbenzene and o-xylene (BTEX) gas phase photodegradation by titanium dioxide dispersed in cementitious materials using a mixed flow reactor[END_REF].

In recent years, photocatalysis has proved to be a good technique for eliminating many water pollutants [START_REF] Thevenet | Photocatalytic degradation of acetylene over various titanium dioxide-based photocatalysts[END_REF][START_REF] Aguedach | Photocatalytic degradation of azo-dyes reactive black 5 and reactive yellow 145 in water over a newly deposited titanium dioxide[END_REF][START_REF] Boulinguiez | Photocatalytic degradation of ammonia and butyric acid in plug-flow reactor: degradation kinetic modeling with contribution of mass transfer[END_REF][START_REF] Brosillon | Gas phase photocatalysis and liquid phase photocatalysis: interdependence and influence of substrate concentration and photon flow on degradation reaction kinetics[END_REF] or air, such as volatile organic compounds (VOCs) [START_REF] Wang | Volatile organic compounds in indoor environment and photocatalytic oxidation: state of the art[END_REF]. These compounds may be emitted by human activities (transport, industry) but are also present in many products and materials within our homes. VOCs include a variety of substances that may be of biogenic origin (natural) or anthropogenic (human origin). They contain always the carbon element and other elements such as hydrogen, halogen, oxygen, and sulphur.

The aim of this present work is to prepare and characterise glass foams obtained from ordinary glass waste from automotive industry with the objective to be used as photocatalytic support. A preliminary comparison of the photocatalytic activity between TiO2 coated foam glasses and commercial impregnated cellulose support is also presented, studying the decomposition of gaseous toluene under UVA illumination.

Experimental procedure

Foam glass preparation

Previous research developed in our laboratory was realised on glass powdered and aluminium nitride [START_REF] Rolland | [END_REF][START_REF] Tasserie | A new expanded material: optimization of the fabrication process[END_REF][START_REF] Tasserie | New expanded material based on industrial glass. I. Effect of the quality of powders and their mixing on properties of the material[END_REF][START_REF] Tasserie | New expanded material based on industrial glass. II. Role and effect of the amount of an expansive additive on the characteristics of the material[END_REF][START_REF] Garnier | Aluminosilicate monolithique expansé à double porosité ouverte[END_REF]. In this present study, we used industrial glass waste formed by glass micro spheres of 250 μm diame m diameter. These glass micro balls are contaminated by oil and rubber impurities from the manufacturing process where they were used as heat transfer media for the rubber vulcanisation step in the automotive industry. The chemical glass sphere composition is in weight percent: 72.5 SiO2-13.7 Na2O-9.8 CaO-3.3 MgO-0.4 Al2O3-0.2 FeO/Fe2O3-0.1 K2O. The foaming agent used in the experiments is aluminium nitride from H.C. Starck GmbH. Glass micro balls are mixed with aluminium nitride, and the resulted initial batch of 1 kg weight is introduced in a refractory nickel steel mould. Some foam samples were prepared by adding to the initial batch, titanium dioxide P25 from Degussa or dust residues from blast furnaces provided by Arcelor Mittal Dunkerque (France). The thermal treatment of the mixtures is performed in a conventional electrical furnace. The heating rate is about 15 K min -1 and the dwell temperature is maintained for one to four hours. The cooling rate of the obtained foam material is governed by the furnace inertia.

Foam glass characterisation techniques

Differential thermal and gravimetric analyses (DTA-TGA) were carried out on TA Instruments Model SDT 2960 equipment. Measurements were done under synthetic air, using platinum crucibles and a 10 K min -1 heating rate. X-ray diffraction characterisation conducted on crushed samples was realised at room temperature with a Philips PW3710 diffractometer operating with Cu Kα radiation (λ = 1.5418 Å), the counting step and time were 0.02 ° and 1 second respectively. X'PERT softwares -Data Collector and Graphics and Identify -were used, respectively, for recording, analysis, and phase matching of the patterns. Helium picnometer AccuPyc 1330 Micromeritics was used to determine the samples density. Nitrogen and oxygen content in foam glasses was determined with a LECO TC-436 analyzer using the inert gas fusion method. Oxygen is measured as CO2 by infrared spectroscopy, while the nitrogen released as N2 , is determined by thermal conductivity.

Catalyst supports

The glass foams previously prepared (sample#8 ones, see Table 1) were used as support for photocatalysis tests. The amount of titanium dioxide required to deposit on glass foam is placed in a water/alcohol mixture (50/50) to form a slurry solution [START_REF] Lebrette | Stability of aqueous TiO2 suspensions: influence of ethanol[END_REF]. Three different slurries for deposit were prepared to coat 350 cm² of foam plates. That means quantities of 0.7, 1.4 and 2.1 g of TiO2 PC500 from Millenium were dispersed in a 50 ml volume of a water/alcohol mixture to prepare coated samples with 20, 40 and 60 g of TiO2/m², named Foam20, Foam40 and Foam60 respectively. The slurry is wholly deposited on each foam samples with a brush. We verified that the TiO2 coating was better controlled with the brush method than the spray application. In our study, the titanium dioxide used is PC500 reference provided by the Millennium Society (pure anatase crystalline phase). The coated foam glass pieces are then heat treated at 560 °C to insure a good TiO2 adhesion. The commercial media used for comparison is the "media 1049", composed of cellulose fibres coated with silica and titanium dioxide (PC500). This catalyst support is flexible and provided by Alhstrom Paper Group. The quantity of catalyst deposited on the media is equal to 25.5 g m -2 . A 480 cm 2 sheet impregnated commercial paper is placed in the reactor for this study. Specific area of studied powders was measured by BET technique with Micromeritics Flowsorb II 2300 equipment.

Photocatalysis experimental setup

The reactor used in this study is a batch reactor type of 1.5 l capacity. The commercial media catalyst or the coated foam glass is placed in the reactor. The UV lamp used for catalyst illumination is a compact fluorescent lamp provided by Philips under the reference "PL-L 24 W/10/4P", its spectrum is centred at λmax = 365 nm for a power average of 27 W/m 2 measured with a radiometer (Vilber Lourmat, VLX-3W). The reactor is sealed, and a small volume (micro litre, μm diame l) of liquid toluene (Carlo Erba Reagenti) is injected through the septum using a syringe. The vaporisation of toluene occurs instantaneously. Before irradiation, the air-toluene mixture is stirred with a magnetic bar during at least 1 h in the dark. We note a decrease of the concentration during the first minutes. This is due to the adsorption, on the catalyst surface, which is the first step of the heterogeneous catalysis. After 50 min, the equilibrium adsorption is reached. The concentration of gaseous toluene in the reactor is followed by sampling and gas chromatography analysis. Then the UV lamp is switched on to initiate the photo degradation. Toluene samples are taken every 3 min using 1000 μm diame L chromatographic syringe. The analysis is done by gas chromatography (Fisons GC 9000 series) equipped with a capillary column (Chrompact FFAP-CB) and a flame ionization detector. Nitrogen is used as a gas-carrier (P = 50 kPa). The temperature conditions for the oven, the injection chamber and the detector are respectively 115, 200 and 250 °C. Under these conditions of analysis, the retention time of toluene is 1.30 min.

Results

Thermal and structural characterisation of glass foams

Fig. 1 shows the curves obtained for the DTA-TGA measurement performed under air on aluminium nitride used as foaming agent. We have observed a first small exothermic peak with onset temperature about 800 °C followed by a second high one with a maximum at 1200 °C. These peaks correspond to AlN oxidation as explained in the discussion part. Fig. 2 presents the DTA curve obtained on a 50 mg mixture of glass micro balls waste with 2% weight of aluminium nitride. The glass transition is observed at 560 °C and an exothermic peak is present at 850 °C revealing the decomposition reaction of AlN with the viscous glass melt. We have also realised thermal analysis (not showed here) on foam samples and its glassy nature is confirmed by the presence of an endothermic step (glass transition) around 560 °C. For the sample prepared with a dwell of 4 h, a partial devitrification is highlighted by the presence of diffraction peaks on XRD patterns (Fig. 3). The crystallised phases identification with X'PERT software revealed the presence of numerous possible phases including mainly wollastonite (CaSiO3 -ICDD-PDF#27-0088) and SiO2 (#14-0654 and #11-0695) [START_REF]JCPDS, International Centre for Diffraction data[END_REF]. Table 1 summarizes the values of density and porosity as well as the chemical composition (nitrogen analysis) of foam glasses prepared at different temperatures and times. The density values were obtained by helium pycnometry (dpyc) as well as from weight and apparent volume measurements (dapp). If we consider that the total volume (Vf) of a foam sample is the sum of glass matter volume (Vg), open pores volume (Vo) and close pores volume (Vc), we propose to express the different densities (in g cm -3 ) as following. For pycnometric density, we obtain dpyc = m/(Vg + Vc), where m is the weight of the foam sample. For apparent density, we get dapp = m/Vf or dapp = m/(Vg + Vc + Vo). Open porosity, i.e. Vo/Vf (%) can be described by the following formula: Open porosity = (1 -dapp/dpyc) × 100. Closed porosity, i.e. Vc/Vf, (%) can be expressed by: Closed porosity = (dapp/dpyc -dapp/2.5) × 100, where 2.5 is the estimated medium value of density in g cm -3 of the glass without pores (m/V g = 2.5). In Table 1 are reported the calculated values of open and closed porosity. For samples with the same initial composition (sample#1, #2, #4 and #11), the pycnometric values tends to increase with the temperature from 800 to 880 °C whereas the apparent density is decreasing from 1.18 to 0.37 g cm -3 . These results lead to an increase of open porosity from 3 to 78%, meaning the connection of nitrogen bubbles in the viscous melt with temperature increase. It can be observed that the increase of heat treatment time has the same effect than the temperature increase (#2 and #3 treated at 820 °C; #4, #5 and #6 treated at 850 °C). The addition of TiO2 (#8), or steel dust (#9) or both (#10) treated in the same conditions (850 °C for 240 min) also lead to high porosity, 82, 80 and 82% respectively. However, the highest porosity (86%) was obtained for the sample with 6% TiO2 heated at 900 °C during 240 min (#12). In addition, the highest pycnometric values are close to 2.3 but are lower than of initial glass beads (dglass = 2.48 g cm -3 ) revealing the presence of closed pores inside the foamed samples.

Density and chemical composition of glass foams

The oxygen and nitrogen analysis was performed on crushed foam samples. The nitrogen content measured is from the N 3-ion nitrides still present in the foam material. As shown in Table 1, only 20 to 30% of the nitrogen introduced with AlN in the initial batch has reacted and participated in the expansion of the glass. An increase in reaction time yields for better use of the pore-forming agent. Similarly, the addition of titanium dioxide promotes the decomposition of aluminium nitride. Fig. 4 shows photography of some foam samples prepared in the same conditions (850 °C for 4 h). Sample #6 presents a white colour while, sample #9 containing iron oxide is grey and a yellowish tint is observed for sample #8 containing TiO2. It can be also observed that iron and titanium doped foams present bigger pores (few millimetres diameter) for identical experimental parameters such as time and temperature.

Characterisation of TiO2 used for the coating of glass foams

The catalyst powder TiO2 PC500 from Millenium was dispersed in water/ethanol slurry, and then was dried up to 550 °C. This operation was realised with the aim to know the influence of thermal treatment of coated foam on its catalyst properties. X-ray diffraction analysis showed that the anatase structure of PC500 TiO2 is kept even after the 550 °C treatment. We observed a narrowing of the width at half height for the diffraction peaks. The specific area measured by BET analysis confirmed the thermal effect and we observed a drastic decrease of the specific area value from 260 to 60 m² g -1 . On the other hand, it was not possible to measure the specific area of the commercial media 1049, because this material cannot support a treatment above 250 °C, this drying step being necessary before BET analysis.

The coated foams were observed by scanning electronic microscopy (Fig. 5). The coating presents some cracks, but for catalysis applications it is an advantage because these defects will increase the contact surface with toluene. The nature of the solution used to prepare the slurry had influence of the coating adhesion. Adhesive screen test revealed that the mixture H2O/ethanol (50/50) was the best compared with pure solution of water or alcohol.

Photocatalysis of toluene

To study UVA photocatalytic degradation of toluene, various initial concentrations of toluene were tested with the different catalyst supports. For each toluene degradation runs, we wait systematically 1 h before initiating the UV illumination of the catalyst, and we observed that a portion of introduced toluene was adsorbed by the catalyst. The adsorption capacity at the equilibrium, Qe (mg g -1 ), is equal to (C0 -Ce)•V/w, where C0 is the initial injected toluene concentration (mg m -3 ), C e is the equilibrium toluene concentration (mg m -3 ), V is the volume of the batch reactor (1.5 litre) and w is the mass (g) of TiO2 deposited on the considered support. Fig. 6 presents the evolution of Qe in function of initial toluene concentration Ce for the three studied supports (Foam20, Foam40 and Media1049). We note that the adsorption capacity increases with the concentration of toluene in the reactor. This behaviour seems to be a Langmuir type. One can note that the adsorption on coated foams is negligible when compared with media 1049. Fig. 6. Adsorption capacity at the equilibrium Qe (mg g -1 ) versus equilibrium toluene concentration Ce (mg m -3 ) for three supports (Foam20, Foam40 and Media 1049).

Fig. 7 shows the evolution of toluene concentration with illumination time for the four studied supports. The initial concentration at time equal to zero is the one measured after the 60 min of the adsorption step. For Foam20 support (20 g of TiO2 by m²), an initial toluene concentration of 1500 mg m -3 was completely degraded after 30 min (Fig. 7a). Regarding support Foam60 (60 g of TiO2 by m²), the degradation time is reduced to 20 min (Fig. 7c). Therefore, the higher the catalyst coating concentration is, the faster is the toluene degradation. This observation is in accordance with an heterogeneous photocatalysis mechanism. For commercial media 1049 (25.5 g of TiO2 by m²), 25 min are necessary to decompose the same toluene initial concentration (1500 mg m -3 ) (Fig. 7d). However, the different supports did not contain the same amount of catalyst depending on the TiO2 concentration and size of the support. For better comparison, we calculate the apparent rate of degradation, taking into account the total amount of titanium dioxide for each support. Using the Langmuir-Hinshelwood model, described in details elsewhere [START_REF] Aguedach | Photocatalytic degradation of azo-dyes reactive black 5 and reactive yellow 145 in water over a newly deposited titanium dioxide[END_REF][START_REF] Boulinguiez | Photocatalytic degradation of ammonia and butyric acid in plug-flow reactor: degradation kinetic modeling with contribution of mass transfer[END_REF][START_REF] Brosillon | Gas phase photocatalysis and liquid phase photocatalysis: interdependence and influence of substrate concentration and photon flow on degradation reaction kinetics[END_REF], and applying it to the results obtained for different initial concentration of toluene (mg m -3 ) and different TiO2 catalyst concentration (g m -2 ), we determined the apparent rate of toluene degradation, k2, expressed in mg m -3 min -1 g -1 . For commercial support, the quantity of titanium dioxide was 1.2 g (480 cm² × 25.5 g m -2 ). For coated foams, we used a surface of 350 cm² with 20, 40 or 60 g m -2 TiO2 concentration. The k2 values obtained are listed in Table 2. Thus, it may be observed that support foam (60 g m -2 ) presents an apparent constant rate of degradation of toluene comparable to TiO2 Media 1049, namely 400 (mg m -3 min -1 g -1 ). However, it is possible that all the TiO2 deposited on the foam is not used for photocatalysis. Therefore, additional tests are needed to confirm the efficiency of these coated supports.

Discussion

The foaming process results of the AlN decomposition reaction occurring between 800 and 1200 °C (Fig. 1) and can be written as following: 2AlN(s) →2Al(s) + N2(g).

(

The reduced aluminium Al is oxidized by the oxygen present in the glass, and the alumina produced is dissolved in the viscous glass melt. Previous works described that the aluminium nitride oxidation occurs when alkali elements (Na, K) or transition metals (Fe, Mn, Ti) are present as oxide compounds in the melt [START_REF] Garnier | Aluminosilicate monolithique expansé à double porosité ouverte[END_REF]. Fig. 8 shows the Ellingham diagram for various redox couples.

More generally, the foaming reaction can be described as: Regarding the influence of experimental parameters on the values of porosity, several comments can be made. For foams prepared with AlN at 820 °C, the heating time has an important influence on the closed and open porosity (samples #2 and #3, Table 1). At this temperature, the aluminium nitride oxidation is weakly exothermic as observed in DTA analysis (Fig. 1). For temperatures above 820 °C, the soda-lime silicate glass viscosity is below 10 8 Poises, it corresponds to the working or blowing glass region. So, the nitrogen bubbles from aluminium nitride oxidation can expand more easily and connect themselves. Besides, when increasing process temperature, the aluminium nitride oxidation is also improved (see Fig. 1). The samples prepared at 850 °C present a high open porosity (>70%), available for the penetration of the slurry, also the connection of the pores allows the flow of fluids through the prepared foams, important for the future catalytic performance. At this temperature or above, an increase time does not change drastically porosity because the pore connectivity is yet achieved, and for longer time, devitrification is occurring (Fig. 3). Thus, for catalytic tests, we used foam glasses prepared at 850 °C which is also favourable for the energy balance of the process.

3 M n+ + nN 3-→3 M + n/2 N2(g). (2)
For samples prepared with a mixture of aluminium nitride and titanium dioxide, the presence of TiO2 enhanced the foaming process (samples #5 and #7 (850 °C -2 h) and samples #6 and #8 (850 °C -4 h)).

3 TiO2 + 4 AlN→2 Al2O3 + 3 TiN + 1/2 N2 (3)
The same improvement is observed for sample containing prepared fly ash. It is due to the presence of iron oxide Fe2O3 as reported elsewhere [START_REF] Fernandes | Preparation and characterization of foams from sheet glass and fly ash using carbonates as foaming agents[END_REF].

Concerning the TiO2 coating process of expanded glasses, investigations are in progress to perform a heat treatment at lower temperature and to study its influence on catalyst adhesion and toluene degradation. Indeed, in heterogeneous catalysis, the catalyst surface in contact with the reactants (active surface) plays an important role on the kinetics of degradation. In addition, the irradiated surface must be the more important as possible since the catalytic reaction is activated by the UV irradiations. So, a catalyst will be more efficient than its active surface is large. The influence of coating parameters such as temperature preparation on catalyst TiO2 structure (anatase or rutile) or specific area must be implemented to improve these new catalyst supports which are glass foams prepared from industrial wastes.

Conclusion

We prepared foam glasses using glass micro balls waste from automotive industry and aluminium nitride as foaming agent. The incorporation of blast furnace smoke or titanium dioxide in the initial batch improves the foaming process. Prepared expanded glasses presented open porosity higher than 70%. Temperature and time influences on foam characteristics were checked and explained. Medium temperature such as 850 °C is sufficient to prepare cellular glasses which were then coated by TiO2 using a water/alcohol slurry. These coated foams were compared to a commercial catalyst media for the toluene degradation under UV illumination. By analyzing these different materials, we determined that the coated foam glasses are photoactive. The coated foams, that we analyzed, present a similar effectiveness than commercial photocatalyst paper, but for higher catalyst concentration. However, these first results are very encouraging, and it can be underlined that the glass support presents a strong advantage on cellulose media: after a number of efficient uses, heat treatment or other cleaning treatment are possible on foam glass to potentially restore their photocatalysis power, which is more delicate to realise with the cellulose support.

Therefore, this work shows the real possibility to use industrial waste glass to transform them into photocatalyst support for environmental applications.

Fig. 1 .

 1 Fig. 1. DTA-TGA curves obtained for AlN under air.

Fig. 2 .

 2 Fig. 2. DTA curve (in function of time) for a glass-AlN mixture (98-2 wt.%).

Fig. 3 .

 3 Fig. 3. X-ray diffractograms for samples prepared at 850 °C for 2 and 4 h.

Fig. 4 .

 4 Fig. 4. Photography of foam glasses prepared at 850 °C for 4 h, (#6: glass + AlN; #8: glass + AlN + TiO2 ; #9: glass + AlN + steel waste).

Fig. 5 .

 5 Fig. 5. SEM picture of a TiO2 coated glass foam.

Fig. 7 .Table 2 .

 72 Fig. 7. Evolution of toluene concentration in function of UVA illumination time for the four studied support (Foam20, Foam40, Foam60 and Media1049). The initial volume (microlitre, μm diame l) of toluene injected in the batch reactor is indicated in the graph inserts.

Fig. 8 .

 8 Fig. 8. Ellingham diagram for the oxidation of aluminium nitride and various metals.

Table 1 .

 1 Initial batch composition, process parameters, and characteristics of prepared foam samples.

	Sample	Initial batch				T (°C) Time	Foam sample
	#	Glass	AlN	N (wt.%)	TiO2	Steel waste		(min)	Dpyc	Dapp	Closed	Open	Nresidual/Ninitial
		(wt.%)	(wt.%)	calcul.	(wt%)	(wt.%)			(g cm -3 )	(g cm -3 )	porosity	porosity	(wt.%)
											(vol%)	(vol%)
	1	98	2				800	90	1.215	1.18	50	3
	2	98	2				820	90	0.971	0.80	50	18
	3	98	2				820	240	2.293	0.70	3	69
	4	98	2				850	90	1.369	0.49	16	64
	5	98	2	0.68			850	120	2.222	0.63	3	72	80
	6	98	2	0.68			850	240	2.310	0.66	2	71	74
	7	95.5	1.5	0.51	3		850	120	2.278	0.69	3	70	74
	8	95.5	1.5	0.51	3		850	240	2.316	0.42	1	82	66
	9	95.5	1.5			3	850	240	2.308	0.47	2	80
	10	95.5	1.5		1.5	1.5	850	240	2.303	0.41	1	82
	11	98	2				880	90	1.704	0.37	7	78
	12	91	3		6		900	240	2.108	0.29	2	86
	dpyc : pycnometric density.
	dapp : apparent density.

Acknowledgements

We thank Ahlstrom research and service (C. Vallet) for supplying photocatalytic non-woven paper media 1049, Cooper Standard Automotive (JM Veillé) Vitré France for glass waste supplying, Arcelor Mittal Dunkerque France (Th. Desmonts) for steel-making ash and smoke, and JF Coulon, ECAM-Rennes for SEM analysis. The undergraduate students F. Boivent, N. Freslon, Th. Reynaldo, M. Toutirais, L. Mougenot, J. Tamakusu are thanked here.


Arun Dhaka

Dr Olivier Jeannin

Ie-Rang Jeon

Dr Emmanuel Aubert

Enrique Espinosa

Marc Fourmigué
email: marc.fourmigue@univ-rennes1.fr

Dr ] A Dhaka

Dr I.-R Jeon

Pr E Espinosa

Activating chalcogen bonding (ChB) in alkylseleno/ alkyltelluroacetylenes toward ChB directionality control

Activation of a deep electron-deficient area on chalcogen atoms (Ch = Se, Te) is demonstrated here in alkynyl chalcogen derivatives, in the prolongation of the (C≡)C-Ch bond. The solidstate structures of 1,4-bis(methylselenoethynyl)perfluorobenzene (1Se) show the formation of recurrent chalcogen-bonded (ChB) motifs. Association of 1Se and the tellurium analog 1Te with 4,4'-bipyridine and with the stronger Lewis base 1,4-di(4-pyridyl)piperazine gives 1:1 cocrystals with 1D extended structures linked by short and directional ChB interactions, comparable to those observed with the corresponding halogen bond (XB) donor, 1,4bis(iodoethynyl)-perfluorobenzene. This "alkynyl" approach for chalcogen activation provides the crystal engineering community with efficient, and neutral ChB donors for the elaboration of supramolecular 1D (and potentially 2D or 3D) architectures, with a degree of strength and predictability comparable to that of halogen bonding in iodoacetylene derivatives.

Introduction

Crystal engineering strategies are rooted in our ability to manipulate intermolecular interactions with a high degree of prediction about the expected outcome of the attempted intermolecular associations. [1] This predictability is not only a direct consequence of the strength of the interaction, but also of its directionality. [2,3] Besides hydrogen bonding, [4,5] the so-called sigmahole interactions have raised in the last 20 years a very strong interest. For example, the success of halogen bonding [6] and its applications in a wide variety of domains, [7,8,9] is essentially based not only on its strength, but also on its strong directionality as the charge-depleted area which develops in the prolongation of a C-X bond is concentrated within a limited area.

Besides halogen bonding, chalcogen bonding also enters in this category of sigma-hole interactions. [10] First investigated by theoretical methods, [11,12,13] and on the basis of highresolution diffraction studies, [14,15] ChB has been known and identified for decades in the crystal structures of many chalcogenated derivatives, [16,17] but its involvement in crystal engineering strategies still struggles to make a strong mark as its XB analog, due mainly to a lack of control of directionality. Indeed, at variance with halogens, the presence of two σ-bonds on the divalent chalcogen atom generates two σ-holes. Different strategies have been reported recently however, aiming at controlling in some way the ChB interactions for a specific goal. We can mention first the association on the same molecule of strong ChB donor and acceptor sites, as in 1,2,5-telluradiazoles, [18] 1,2-chalcogenazole N-oxide, [19,20] , benzo-1,3-chalcogenazole, [21] favoring the formation of infinite ribbons [18,22] or discrete supramolecular assemblies. [23] The use of ChB donors in organocatalysis [24,25] or anion recognition [26,27] processes involves the preparation of bidentate chelating molecules bearing two activated chalcogen atoms, able to interact with one single Lewis base, neutral or anionic, as found in molecules linking two tellurophenes, [28] two 5-(methylchalcogeno)-1,2,3-triazole moieties, [START_REF] Aj | [END_REF] two thiophene units bearing Electron Withdrawing Groups (EWG), [30] or two selenocyanate groups. [31] In several examples, one of the two substituents linked to the chalcogen atom has a strong EWG character, favoring the formation of a stronger σ-hole in the prolongation of this EWG-Ch bond. This strategy to recover part of the directionality characteristic of XB has been explored with parabis(selenocyanatomethyl)benzene (Scheme 1a), which co-crystallizes with 4,4'-bipyridine to form a ChB chain motif through very short and directional Se•••N≡C contacts. [32] This 1D structure mimics those obtained with ditopic XB donors such as 1,4-diiodoperfluorobenzene (Scheme 1b), or diiodoacetylene. Looking for more rigid ditopic ChB donors than these selenocyanate derivatives, we considered the possibility to replace the two iodine atoms in rigid Several linear oligoalkynes, α,ω-substituted with chalcogenomethyl groups, MeCh-(C≡C)n-ChMe (Ch = Se, Te; n = 2-4), were described in 2002. [33,34] Among them, one (Ch = Te, n = 2) was shown to organize into tubular nanostructure stabilized by Ch•••Ch intermolecular interactions slightly below the van der Waals contact distance, [35] but their potential to form co-crystals with Lewis bases through ChB interactions had not been addressed.

To answer this question, we investigated the ability of 1Se or 1Te to co-crystallize with linear, ditopic Lewis bases such as the prototypical 4,4'-bipyridine. The success of this approach, as shown below, provides us with extremely efficient and directional ChB donors for the elaboration of supramolecular architectures, with a degree of strength and predictability comparable to that of halogen bonding.

The ChB donor ability of 1Se and 1Te has been first evaluated from the calculated values of the extrema of the electrostatic potential surfaces (ESP), the largest the positive ESP value, the more important the σ-hole at the chalcogen atom and therefore the ChB donor ability. The preparation of 1Se (Scheme 2) is based on the metalation of the bis(alkynyl) derivative 4 with BuLi, followed by reaction with grey selenium and alkylation with MeI. This procedure failed in our hands with tellurium. An alternative route to 1Te involves the reaction of the bis(alkynylsilver) derivative 5 with methyltelluroniumbromide MeTe-Br. [29c] The diiodo derivative 2 was prepared as reported earlier from the reaction of the bis(trimethylsilylalkynyl) compound 3, through reaction with NIS and AgNO3. [36] A c c e p t e d M a n u s c r i p t ). [37] Phase B (tetragonal, SG I41/a) is characterized by 10 independent 1Se molecules, including two 1Se molecules inserted inside channels (see below) with a refined 2/3 occupancy. Molecules are organized through highly directional Type II Se•••Se contacts (Fig. 2) with facing electrophilic•••nucleophilic regions to generate tetrahedral motifs, with Se•••Se distances in a 3.63-3.66 Å range (RR = 0.96) (see also Fig. S4 and Table S2). S2 and Fig. S4).

F F I I F F F F F F TMS TMS F F F F Se Se F F F F Ag Ag F F F F Te Te H TMS Pd catalyst, CuI NEt 3 , 65°C 80% F F F F H H K 2 CO 3 t BuOH/MeOH i BuLi,
These motifs stack along the c-axis to delineate a tubular square-lattice network (Fig. 3a, Fig. S5) organized into helical chains running along c (Fig. 3b). At the center of these helical stacks, a large volume is occupied by two other molecules (in red and black in Fig. 3) interacting with each other within the channels into a double helix through Type I, slightly shorter (RR = 0.92) Se•••Se interactions (Fig. 3b, Fig. S7, Table S2). With these two new 1Se and 1Te derivatives at hand, we can now evaluate their ability to act as ChB donors in supramolecular assemblies as well-known iodoacetylene derivatives (as 2) do with halogen bonding. As shown in Figure 5a, we found that cocrystallization of 2 with bipy leads indeed to the formation of chains with a short and directional I•••N contact (RR = 0.79). Using the ditopic ChB donors 1Se and 1Te leads to a very similar 1D motif, with the formation of 1Se•bipy and 1Te•bipy co-crystals which exhibit the sought-after, short and directional ChB interactions (Table 1), demonstrating the efficiency of the alkynyl substituent to activate chalcogen atoms toward ChB interactions, with a strength almost comparable to that of the iodinated analog 2. In both co-crystals, the ChB interaction involves the σ-hole in the prolongation of the alkynyl-chalcogen bond and the reduction ratio is almost comparable between iodine (0.79) and tellurium (0.82). In other words, alkynyl-tellurium derivatives can be as efficient as prototypical alkynyl-iodine derivatives to enter into strong and directional σhole interactions toward Lewis bases. In order to further strengthen these ChB interactions, we considered bipyridine analogs which could exhibit a stronger Lewis base character, as for example observed when one replaces pyridine with the more electro-rich 4-dimethylaminopyridine (DMAP). To reach this goal, we envisioned the piperazine derivative [38] hereafter abbreviated as bipy-pip (Scheme 3) which combines the ditopic character of 4,4'-bipyridine with the stronger Lewis-base character of DMAP. To our surprise, this interesting molecule has never been used as XB (nor ChB)

acceptor. [START_REF] Henling | Only one reported example of hydrogen-bonded structure with carboxylic acids[END_REF] Scheme 3. Combining the electron donating effect of -NMe2 with the ditopic character of bipyridine.

Its co-crystallization with 1Se and 1Te (and 2) was as successful as with bipy and the three 1:1 co-crystals were isolated and structurally characterized. They all exhibit short and directional σ-hole interactions, in the prolongation of the alkynyl-chalcogen bond, notably shorter than with bipy itself (see Table 1), with RR value down to 0.79 in 1Te•bipy-pip, and leading to the recurrent formation of 1D structures (Fig. 6). The success of this "alkynyl" approach provides the crystal engineering community with efficient, and neutral, ChB donors for the elaboration of supramolecular 1D (and potentially 2D or 3D) architectures, with a degree of strength and predictability comparable to that of halogen bonding.

For Table of Content

Chalcogen bond activation by alkynyl substitution is realized in bis(selenomethyl-alkynyl)

and bis(telluromethyl-alkynyl) derivatives, as evidenced in co-crystals with ditopic Lewis

  Scheme 1.

  A c c e p t e d M a n u s c r i p t As shown in Fig. 1 (see calculation details in ESI), both Se and Te derivatives exhibit a notable σ-hole in the prolongation of the (C≡)C-Ch bond, much stronger than that in the prolongation of the other H3C-Ch bond (Fig. S1 in ESI). This points already for a potential good directionality of ChB interactions involving these atoms. Comparison with the analogous iodo derivative 2 shows that, albeit slightly smaller (-12%), 1Te exhibits a comparable σ-hole extremum.

Fig. 1 .

 1 Fig. 1. Details of the ESP maps of (from left to right) 1Se, 1Te and 2 at optimized geometries, plotted on the 0.002 electron/bohr 3 isosurface of the electronic density. The extrema values Vs,max of the electropositive (blue) area are indicated. Potential scale ranges from 0 (red) to 37.7 (blue) kcal/mol.

  Scheme 2. Synthetic paths to the 1Se, 1Te and 2.

  Scheme 3. Comparison of X•••X and Ch•••Ch interaction motifs. Type II interactions refer to the so-called halogen bonding (XB) or chalcogen bonding (ChB).

Fig. 2 .

 2 Fig. 2. One tetrahedral motif formed by directional, Type II (C≡)C-Se•••Se ChB in 1Se (phase B) (See TableS2and Fig.S4).

Fig. 3 .

 3 Fig. 3. Detail of the solid-state arrangement in 1Se (Phase B) showing the helical organization of molecules (only one helix out of six is shown in green, see Fig. S7 for all helices), and two other molecules inserted inside channels (in red and black).

Figure 5 .

 5 Figure 5. Details of the solid-state structures of the 1:1 co-crystals of bipy with 2 (a), 1Se (b)and 1Te(c) (see also Fig.S8).

Figure 6 .

 6 Figure 6. Details of the solid-state structures of the 1:1 co-crystals of bipy-pip with 2 (a), 1Se (b) and 1Te (c).

  bases such as 4,4'-bipyridine and 1,4-di(pyridin-4-yl)piperazine, with Te•••N interactions as short as I•••N halogen bonds with analogous iodo-alkynyl derivatives.

Table 1 .

 1 Pertinent structural characteristics of the ChB (XB) interactions in co-crystals (Ch = Se, Te; X = I).

	Co-crystal	Ch/X•••N dist. (Å) RR	C-(Ch/X)•••N angle (°)
	2•bipy	2.778(4)	0.79	173.5(1)
	1Se•bipy	3.055(4)	0.89	176.1(1)
	1Te•bipy	2.952(4)	0.82	173.9(1)
	2•bipy-pip	2.718(9)	0.77	176.9(1)
		2.700(8)	0.76	178.9(1)
	1Se•bipy-pip	2.995(11)	0.87	171.6(1)
	1Te•bipy-pip	2.855(4)	0.79	171.8(1)

Acknowledgements

This work has been supported by ANR (Paris) as ANR-17-CE07-0025-01 (Nancy) and ANR-17-CE07-0025-02 (Rennes). The EXPLOR mesocentre is thanked for computing facilities (Project 2019CPMXX0984). Keywords: Alkynes • Chalcogens • Crystal Engineering • Lewis bases A c c e p t e d M a n u s c r i p t