N Olivi-Tran
email: nathalie.olivi-tran@umontpellier.fr

Nuclear and Particle

Keywords:

. We make the hypothesis that the fermions of the 2nd and 3rd families are excited states of the fermions of the 1st family. Indeed, the fermions of the 2nd and 3rd families have masses equal to 2 n .(p 2 )/2 where n is an integer [1] calculated for the first family of fermions and p is another integer. p is an integer which corresponds to the excited states of the elementary wavefunctions (the energy of the excited elementary wave functions are equal to p 2 /2; using normalized units).

Introduction

I make the assumption that our threedimensional universe is embedded in a four dimensional euclidean space. Time is a function of the fourth dimension of this space [START_REF] Olivi-Tran | The FLRW cosmological model revisited: Relation on the local time with the local curvature and consequences on the Heisenberg uncertainty principle[END_REF][START_REF] Olivi-Tran | What if our three dimensional curved universe was embedded in four dimensional space? Consequences on the EPR paradox[END_REF][START_REF] Olivi-Tran | Dimensional analysis of Einstein's fields equations[END_REF]. If we apply this hypothesis to particle physics, we may say that elementary particles are fourdimensional, threedimensional and twodimensional.

The coordinates (x, y, z, t) are not orthonormal.Indeed, time t evolves as log(r) where r is the comoving distance in cosmology [START_REF] Olivi-Tran | The FLRW cosmological model revisited: Relation on the local time with the local curvature and consequences on the Heisenberg uncertainty principle[END_REF].

To obtain the first family of fermions from the Standard Model ( i.e. quark up, electron, electron neutrino) one may say that [START_REF] Olivi-Tran | Gottiniaux A classification of elementary particles in d = 4 following a simple geometrical hypothesis in real space[END_REF]:

• the electron is fourdimensional (t, x, y, z)

• the quark is three dimensional (t, x, y).

• finally, the electronic neutrino is twodimensional (t, x) and x, y and z are equivalent.

To obtain the remaining fermions (elementary particles), one has to modify the quantum number p (similar to the quantum number of a particle in a box). Thus, the remaining fermions of the Standard Model may be seen as excited states of the first fermion family.

Straightforwardly, we make the following hypotheses:

• Spacetime has an underlying hypersquare array of edge length

• Elementary wave functions ( in (x, y, z, t) space)are eigenfunctions of a particle in a square potential (reduced parameters)

√ 2exp(-ix) for space √ 2exp(-it) for time
• The eigenvalues of the elementary wave functions are equal to p 2 /2 (with p an integer number)

Masses of the electron, muon and tau

For electrons, we have The Dirac matrices are representative of infinitesimal rotations within the wavefunction of a given elementary particle.

iγ µ ∂ µ ψ = mψ (2)       ∂ 1 Ψ ∂ 2 Ψ ∂ 3 Ψ ∂ 1 Ψ ∂ 2 Ψ ∂ 3 Ψ ∂ 1 Ψ ∂ 2 Ψ ∂ 3 Ψ ∂ 0 Ψ                                               = m.                                               Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ                                               (
Using combinatorial analyzis we obtain equation (1) (using the fact that electrons are 4d [START_REF] Olivi-Tran | Gottiniaux A classification of elementary particles in d = 4 following a simple geometrical hypothesis in real space[END_REF] and that all space dimensions are equivalent).

There are 3 possibilities of arranging γ 1 , γ 2 , γ 3 (the Dirac matrices) over x, y and z (all space dimensions are equivalent) and one possibility to arrange σ 0 (temporal Pauli matrix: half of γ 0 ; because time does not go backward).

The large matrix M (see equation ( 1) ) containing all combinations has a dimension 9X4 + 2 = 38. We see that, with the coordinate vectors √ 2exp(-it) and √ 2exp(-ix) (eigenfunctions of a particle in a square potential), we have to multiply the modified Dirac equation by the Jacobian corresponding to these new coordinates. This Jacobian is equal to

√ 2 38
where 38 is the dimension of the large matrix [START_REF] Olivi-Tran | The masses of the first family of fermions and of the Higgs boson are equal to integer powers of 2 Nuclear and Particle Physics Proceedings[END_REF]. We multiply the mass of the first particle of this family by the eigenvalues of the eigenfunctions (of the particle).

We decompose the eigenvalues into prime numbers. The number of eigenvalues for the ground state (electron) is 38 (the dimension of the large matrix M). For the other particles, we take into account the spinor (1, 0) T corresponding to the σ 0 Pauli matrix. So except for the electron, there are 37 eigenvalues for each particle.

• The mass of the electron is equal to The values in italic are the experimental masses [6]. We see that for the tau particle, one of the eigenvalues ( 41 2 2 ) is much larger than the others. This may explain the short lifetime of this particle.

√ 2 38 =2 19 eV/c 2 =2 19 .( 1 2
The masses (theoretical and experimental) of the electron, muon and tau are summarized in Table 1.

Masses of the quarks

For quarks, we have

iγ µ ∂ µ ψ = mψ (4)
The Dirac matrices are representative of infinitesimal rotations within the wavefunction of a given elementary particle.

Using combinatorial analyzis we obtain equation (3) (using the fact that quarks are 3d [START_REF] Olivi-Tran | Gottiniaux A classification of elementary particles in d = 4 following a simple geometrical hypothesis in real space[END_REF] and that all space dimensions are equivalent).

There are 3 possibilities of arranging γ 1 , γ 2 , γ 3 (the Dirac matrices) over x, y and z (all space dimensions are equivalent). There is one possibility to arrange σ 0

                                                       
γ 1 0 0 0 0 0 0 0 0 0 0 0 0 γ 2 0 0 0 0 0 0 0 0 0 0 0 0 γ 3 0 0 0 0 0 0 0 0 0 0 0 0 σ 0 0 0 0 0 0 0 0 0 0 0 0 0 γ 2 0 0 0 0 0 0 0 0 0 0 0 0 γ 3 0 0 0 0 0 0 0 0 0 0 0 0 γ 1 0 0 0 0 0 0 0 0 0 0 0 0 σ 0 0 0 0 0 0 0 0 0 0 0 0 0 γ 3 0 0 0 0 0 0 0 0 0 0 0 0 γ 1 0 0 0 0 0 0 0 0 0 0 0 0 γ 2 0 0 0 0 0 0 0 0 0 0 0 0 (temporal Pauli matrix; half of γ 0 , because time does not go backward ) for each combination of spatial Dirac matrices (x, y; x, z and y, z). We have to take into account that the quarks are 3 dimensional. So, the matrix M containing all combinations has a dimension equal to 9X4 + 3X2 = 42. We see that, with the coordinate vectors √ 2exp(-it) and √ 2exp(-ix) (eigenfunctions of the underlying hypersquare array), we have to multiply the modified Dirac equation by the Jacobian corresponding to these new coordinates. This Jacobian is equal to √ 2 42 where 42 is the dimension of the matrix [START_REF] Olivi-Tran | The masses of the first family of fermions and of the Higgs boson are equal to integer powers of 2 Nuclear and Particle Physics Proceedings[END_REF].

σ 0       ∂ 1 Ψ ∂ 2 Ψ ∂ 3 Ψ ∂ 0 Ψ ∂ 1 Ψ ∂ 2 Ψ ∂ 3 Ψ ∂ 0 Ψ ∂ 1 Ψ ∂ 2 Ψ ∂ 3 Ψ ∂ 0 Ψ       Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ                                                         (3)
We multiply the mass of the first particle of the quarks family by the eigenvalues of the eigenfunctions (of the particle). We decompose the eigenvalues into prime numbers. The number of eigenvalues for the ground state (quark up) is 42 (the dimension of the large matrix M, see equation ( 3)). For the other quarks, we take into account the spinor (1, 0) T corresponding to the 3 σ 0 Pauli matrices. So except for the quark up, there are 39 eigenvalues for each quark. The values in italic are the experimental masses [6]. The theoretical and experimental masses of the quarks family are summarized in table 2.

Masses of the neutrinos

Up to now, there is no theoretical propagation equation for the neutrinos. If we use the eigenvalues of the elementary wave functions like for quarks and electrons, muons and taus, we may write:

• The mass of the electron neutrino is equal to 2eV/c 2

• The mass of the muon neutrino is equal to 2. 412 2 2 = 412 2 eV/c 2 = 169keV/c 2

• The mass of the tau neutrino is equal to 2. 3937 2 2 = 3937 2 eV/c 2 = 15.4MeV/c 2 Hence, we found theoretical values of the masses of the neutrinos which are in good agreement with the experimental masses.

Conclusion

We found the theoretical values of masses for all the elementary fermions (1st, 2nd and 3rd families of fermions). These theoretical masses are in good agreement with the experimental masses (the differences between theoretical and experimental masses are less than 10% except for the quarks down and strange). There is a possibility to analyze the symmetries of these particles and compare them to the symmetries of the Standard Model.

Table 1 :

 1 Theoretical and experimental masses of the electron, muon and tau

	1)

Table 2 :

 2 Theoretical and experimental masses of the quarks family.

Table 3 :

 3 Theoretical masses of the neutrinos and upper limits of experimental masses


domain: spi phys

text:
Adeline Kabacinski

Julie Armougom

Jean-Michel Melkonian
email: jean-michel.melkonian@onera.fr

Myriam Raybaut

Jean-Baptiste Dherbecourt

Antoine Godard

Ruslan Vasilyeu

Vadim Smirnov

Single-Frequency Operation of a Near-degenerate Optical Parametric Oscillator Using a Transversally Chirped Volume Bragg Grating

We report on single-frequency emission near 2.2 µm with an optical parametric oscillator. The OPO wavelength is tuned over 22 nm using a Bragg reflector incorporating a transverse chirp of the grating period.

Introduction

Spectral selection in an Optical Parametric Oscillator (OPO) behaves very differently than in a laser. It is essentially driven by the phase difference between the generated signal and idler waves and the nonlinear polarization created by the pump. This so-called phase-matching condition writes, in the collinear case:

- - < Δ 2 ⁄
, where n p,s,i are the index of refraction at wavenumbers σ p,s,i , L the crystal length, and Δ is the maximum dephasing allowed by the parametric gain. Derivation of this relation leads to the total first-order gain bandwidth:

2Δ = , , , (1)
where n g is the group velocity index. Under pulsed pumping, several longitudinal modes oscillate within the gain bandwidth and, since the oscillation starts from parametric noise, these modes will differ from one pulse to another. This problem is the worst in OPOs using near-degenerate signal and idler waves ( = = 2 ⁄ ) with identical polarizations (type 0 or type I phase-matching), because in this case !, = !, , so that the gain bandwidth becomes very broad. We circumvented this issue by introducing Vernier spectral filtering in doubly-resonant cavities, in which spectral selection is achieved by the coincidence between signal and idler cavity modes [START_REF] Hardy | Compact, single-frequency, doubly resonant optical parametric oscillator pumped in an achromatic phase-adapted double-pass geometry[END_REF]. For this scheme to be still effective near degeneracy, we had to resort to periodically-poled lithium niobate (PPLN) with crossed polarizations such that !, ≠ !, (type II phase-matching) [START_REF] Raybaut | Highenergy single-longitudinal mode nearly diffraction-limited optical parametric source with 3 MHz frequency stability for CO2 DIAL[END_REF]. The low non-linear coefficient of PPLN with crossed polarizations was partially balanced by the very low threshold offered by the doubly-resonant cavity.

Recently, Volume Bragg Gratings (VBGs) have emerged as very-narrow, high-efficiency spectral filters for laser applications. They have been used in OPOs to provide narrowband tunable emission [START_REF] Jacobsson | Tunable narrowband optical parametric oscillator using a transversely chirped Bragg grating[END_REF], and single-frequency operation at a fixed wavelength off degeneracy [4]. In this work, we use a VBG to produce tunable single-frequency radiation very close to degeneracy, while benefiting from the high gain of PPLN with identical polarizations.

Design of the transversally chirped Volume Bragg Grating

VBGs fabricated in photo-thermo-refractive (PTR) glass have outstanding properties in the near infrared providing extremely high spectral and angular selectivity with no secondary peak, and diffraction efficiency up to 99.99% [START_REF] Efimov | High-efficiency Bragg gratings in photothermorefractive glass[END_REF]. Unlike other holographic materials, PTR glass-based elements have robust performance in harsh environmental condition, unrestricted life time and high laser damage threshold. All above pave the way for their usage as intracavity mode filters in various laser systems. A transversally chirped volume Bragg grating (TC-BG) is a reflecting VBG in which the transverse period varies across one lateral dimension. Nowadays, state-of-the-art technology allows fabrication of such gratings with lateral dimensions up to 25 mm. For this experiment, we designed a TC-BG which is 20 mm wide, with a chirp rate of 1.1 nm/mm. The FWHM spectral acceptance is 1.2 nm around 2.2 µm and the maximum diffraction efficiency is 80%. The TC-BG is AR-coated at 1.064 µm + 2-2.2 µm. The angular acceptance was checked to be much larger than the mode divergence inside the cavity.

Experimental results

The OPO is doubly-resonant with nested signal and idler cavities (Fig. 1, left). The non-linear crystal is a 4.2-mmlong MgO:PPLN crystal with a quasi-phase-matching period of 32.03 µm for identical pump, signal, and idler polarizations. The two-pass first-order gain bandwidth given by Eq. 1 is 724 cm -1 (spanning 1800 longitudinal modes). The signal cavity is formed by a gold mirror with a 50 mm radius of curvature (M 3 ) and a highly reflective dielectric mirror deposited on the input crystal facet (M 2 ). The idler cavity is formed by the gold mirror and the TC-BG which acts as a plane output coupler. The TC-BG is mounted on a transverse translation stage to shift the peak wavelength of the reflectivity curve. The distance between the TC-BG and the signal mirror has been chosen to allow only one signal/idler mode coincidence within the TC-BG bandwidth (Fig. 1, right). The TC-BG and the back mirror are mounted on PZT actuators to match the signal and idler combs and finely tune the output wavelength. The oscillation threshold with the TC-BG is 7.5 µJ, identical to the one obtained with a dielectric mirror of the same Fig. 2 shows the emission spectrum of the OPO when translating the TC-BG, and tuning the PZT actuators to maximize the signal/idler mode overlap. A total tunability of 17 nm was achieved, compliant with the TC-BG specifications. As observed with our previous nested-cavity OPOs, several modes oscillate when the signal and idler combs are mismatched. What is remarkable here is that, despite the huge gain bandwidth, only two neighboring modes are allowed to oscillate, thanks to the high selectivity of the TC-BG. When the signal and idler combs are correctly matched using the PZTs, the OPO emits single-frequency radiation.

Fig. 2 .

 2 Fig. 2. a) Spectrum at different TC-BG positions. Spectrum at one TC-BG position for b) mismatched and c) matched signal/idler combs.The peak width is limited by the spectrometer resolution. The black dashed line is the calculated reflectivity curve of the TC-BG.

Left: Scheme of the nested-cavity OPO cavity with the TC-BG. Right: Spectral filtering is a combination of signal/idler combs coincidence and selection by the reflectivity of the TC-BG.


text:
Jean-Baptiste Dherbecourt

Jean-Michel Melkonian

Antoine Godard

Vincent Lebat

Nicolas Tanguy

Cédric Blanchard

Xavier Watremez

Dominique Dubucq

Stéphanie Doz

Pierre-Yves Foucher

Myriam Raybaut
email: myriam.raybaut@onera.fr

The NAOMI GAZL multispecies differential absorption lidar: realization and testing on the TADI gas leak simulation facility

  L'archive ouverte pluridisciplinaire

Introduction

Differential absorption lidars (DIAL) are valuable tools for remote detection, localization, and quantification of a gaseous species, for safety applications, as well as for environmental monitoring. DIAL can be tailored to detect species such as CO 2 and CH 4 in the infrared, where they display characteristic absorption features, linked to their vibration modes. In a DIAL, two laser pulses are emitted, at two wavelengths called ON (tuned to the absorption band) and OFF (on an absorption minimum). The laser pulses are backscattered by atmospheric aerosols, collected by a telescope and focused on a photodetector. A gas plume can be localized and quantified by comparing the range resolved ON and OFF signals.

Several systems have been and are currently in development for such applications [1,2]. Here, we aim at developing a compact, range resolved, multi-species system for both CO 2 and CH 4 , based a widely tunable, single frequency emitter, with a high conversion efficiency. The emitter is based on a pulsed, nanosecond, single frequency, Nested Cavity Optical Parametric Oscillator (NesCOPO) [3], amplified to 16 mJ, and implemented in a direct detection Lidar system. This Lidar, NAOMI GAZL, is tested on a gas leak tests facility, called TADI for Transverse Anomaly Detection Infrastructure, in the frame of NAOMI project (for New Advanced Observation Method Integration), along with other instruments (for instance hyperspectral imaging).

GAZL instrument

Fig. 1 .

 1 Fig. 1. NAOMI GAZL NesCOPO emitted wavelength as a function of the temperature, for three different PPLN periods a). The atmospheric transmission for CO2 (for 400 ppm) and CH4 (for 2 ppm) over 1 km are given. Picture of the NAOMI GAZL lidar b) and deployment of the Lidar on TADI facility c).

TOTAL and Onera NAOMI project.

The emitter is a NesCOPO emitting in the 1.57-1.65µm range, based on a multi-track periodically-poled LiNbO 3 (PPLN) crystal, pumped by a 10 ns, 100 Hz, injection-seeded Q-switched Nd:YAG laser. Given the wide tunability of the NesCOPO, several absorption lines for CO 2 and CH 4 can be targeted (Fig. 1.a)).

The single frequency radiation is amplified up to 16 mJ, using a PPLN preamplifier and KTA amplifiers. The emitter is then integrated in a DIAL system (Fig. 1.b). The receiver unit is a home-build Newtonian telescope, coupled to a commercial amplified PIN photodiode. The maximum achievable detection bandwidth is 14.5 MHz, corresponding approximately to 10 m spatial range resolution cells along the line of sight.

TADI facility

Located in Lacq in France, TADI facility is an open-air site measuring 2,000 m² for qualifying systems designed to detect, localize and quantify remotely CO 2 and CH 4 releases. Equipped with surface facilities (pipelines, columns, recovered wellheads, etc.), this test area can reproduce around 30 scenarios of controlled emissions from 0.3 to 300 g/s of gas in an industrial environment.

GAZL testing on TADI facility

NAOMI GAZL was deployed on the TADI facility during a test campaign in October 2018. The DIAL was located 250 m away from the gas release system. Fig. 2 a) and b) show an example of remote detection, quantification and localization of a CH 4 plume generated by TADI. The system was tested for different fluxes of CH 4 and CO 2 . Comparisons with integrated concentration in ppm.m retrieved from LWIR imaging hyperspectral data acquired during this campaign can also be used then to analyse and validate GAZL results (Fig. 2 c).


Erwan Paineau
email: erwan-nicolas.paineau@u-psud.fr

Pascale Launois
email: pascale.launois@u-psud.fr

Chapter 5 Nanomaterials From Imogolite: Structure, Properties and Functional Materials

Keywords: Imogolite, nanotube, structure, monodisperse diameter, synthesis, functionalization, charged interface, self-organization, nanocomposite, molecular sieving, adsorbent 5

Hollow cylinders with a diameter in the nanometer range are carving out prime positions in nanoscience. Thanks to their physico-chemical properties, they could be key elements for next-generation nanofluidics devices, for selective molecular sieving, energy conversion or as catalytic nanoreactors. Several difficult problems such as fine diameter and interface control are solved for imogolite nanotubes. This chapter will present an overview of this unique class of clay nanotubes, from their geological occurrence to their synthesis and their applications. In particular, emphasis will be put on providing an up-to-date description of their structure and properties, their synthesis and the strategies developed to modify their interfaces in a controlled manner. Developments on their applications, in particular for polymer/imogolite nanotubes composites, molecular confinement or catalysis, are presented.

 Japan, (b-c) Optical observations of gel films (white arrows) found in the 2Bw1 and 3Bw5 horizons, respectively, (d) Typical transmission electron microscopy (TEM) micrograph of imogolite extracted from the gel-like film, in association with allophane (spherical particles). Adapted with permission from [START_REF] Nanzyo | Non-crystalline Inorganic Constituents of Soil[END_REF].

Since its first description in 1962, imogolite was found to occur worldwide either in almost pure form as macroscopic gel-like films in weathered pumice beds [START_REF] Miyauchi | Mineralogy of gel-like substance in the pumice bed in Kanuma and Kitakami districts[END_REF][START_REF] Jaritz | Ein Vorkommen von Imogolit in Bimsböden Westdeutschlands[END_REF][START_REF] Yoshinaga | Identification of imogolite in the filmy gel materials in the imaichi and shichihonzakura purlice beds[END_REF][START_REF] Yoshinaga | Occurrence of imogolite as gel film in the pumice and scoria deds of western and central Honshu and Hokkaido[END_REF] or in B horizons of allophanic Andosols as a typical weathering product of pyroclastic materials under a humid climate and well-drained conditions [START_REF] Besoain | Imogolite in volcanic soils of Chile[END_REF][START_REF] Gense | Conditions de formation de l'imogolite dans les produits d'altération de roches volcaniques basiques de l'Ile de la Réunion[END_REF][START_REF] Yoshinaga | Occurrence of imogolite in some volcanic ash soils of New Zealand[END_REF][START_REF] Parfitt | Imogolite from New Guinea[END_REF][START_REF] Wada | Allophane and imogolite[END_REF][START_REF] Violante | Identification of imogolite in some volcanic soils from Italy[END_REF][START_REF] Panichini | Understanding carbon storage in volcanic soils under selectively logged temperate rainforests[END_REF]. However, the occurrence of natural imogolite is not restricted to volcanic ash soils since it was later recognized in podzolized horizons of Spodosol, formed from non-volcanic parent materials in colder regions of the world [START_REF] Tait | Occurrence of imogolite in some scottish soils[END_REF][START_REF] Ross | Evidence for imogolite in canadian soils[END_REF][START_REF] Dahlgren | Formation and stability of imogolite in a tephritic spodosol, Cascade Range, Washington, USA[END_REF][START_REF] Gustafsson | Aluminium solubility characteristics of spodic B horizons containing imogolite-type materials[END_REF][START_REF] Gustafsson | Mineralogy of poorly crystalline aluminium phases in the B horizon of Podzols in southern Sweden[END_REF]. Although the mechanisms of imogolite formation in natural environment are not fully elucidated, it is well admitted that the presence of volcanic ash in these soils may enhance their formation since the dissolution of volcanic glass provides a readily available source of soluble silicic acid (H 4 SiO 4 ) [START_REF] Dahlgren | Formation and stability of imogolite in a tephritic spodosol, Cascade Range, Washington, USA[END_REF]. Beyond Earth deposits, imogolite was recently found in the layered outcrops at Mawrth Vallis in Mars, suggesting a period of rapid weathering and it is believed that it could be used as a marker in the evolution of the Martian climate [START_REF] Bishop | Evidence for a changing Martian climate from the mineralogy at Mawrth Vallis[END_REF][START_REF] Bishop | Surface clay formation during short-term warmer and wetter conditions on a largely cold ancient Mars[END_REF].

Prior to use, natural imogolite needs to be extracted from parent material, which usually contains organic and inorganic impurities, as schematically described in Figure 5.2 [START_REF] Ma | Surface functionalization of aluminosilicate nanotubes with organic molecules[END_REF]. Typically, soils samples are treated with an aqueous solution of hydrogen peroxide to remove organic contaminants, followed by citrate-bicarbonatedithionite treatment to dissolve extractable oxides. Purified imogolite gels are then washed by centrifugation and redispersed in weak acidic solution. Finally, air-drying or freeze-drying processes are often applied to obtain a cotton-like substance for further characterization but packing of nanotubes in bundles may occur during such processes, which may impede their full dissociation afterwards.

Transmission Electron Microscopy (TEM) observations remain the most common approach to identify imogolite minerals in soil samples. Typical TEM micrograph is presented in Figure 5.1d, showing the characteristic thread-like morphology of imogolite bundles, each thread consisting of bundled "fibre" units with diameter between 2 and 3 nm [START_REF] Yoshinaga | Identification of imogolite in the filmy gel materials in the imaichi and shichihonzakura purlice beds[END_REF][START_REF] Yoshinaga | An electron microscopic study of soil allophane with an ordered structure[END_REF][START_REF] Russell | Imogolite: a unique aluminosilicate[END_REF]. In 1970, Wada et al. [START_REF] Wada | High resolution electron micrographs of imogolite[END_REF] were the first to propose, thanks to improvements in TEM experiments, that the parallel lines observed in TEM micrographs represent the walls of a hollow tube rather than a fibre structure.

Structure and Physico-Chemical Properties of Imogolite 5.2.1. Structure of imogolite

During the ten years following the observation of fine fibrous imogolite particles in soils, their structure remained unclear. Due to the presence of broad modulations in X-ray scattering diagrams, imogolite was claimed to be a non-crystalline or poorly crystalline mineral. Different structural models were proposed based on X-ray scattering and electron diffraction [START_REF] Russell | Imogolite: a unique aluminosilicate[END_REF][START_REF] Wada | A structural scheme of soil allophane[END_REF][START_REF] Wada | The structure of "imogolite[END_REF], involving paracrystalline order as well as various chains of AlO 6 octahedra linked sideways by SiO 4 tetrahedra. As mentioned above, in 1970, Wada et al. [START_REF] Wada | High resolution electron micrographs of imogolite[END_REF] showed, on the basis of high resolution electron micrographs, that the unit fibre is a hollow tube, opening new perspectives in the determination of the imogolite structure.

The structure of imogolite nanotubes (INT) was solved in 1972, in an article which brought together the different teams previously involved in its structural analysis [START_REF] Cradwick | Imogolite, a hydrated aluminum silicate of tubular structure[END_REF]. Its nominal composition is (OH) 3 Al 2 O 3 Si(OH), where hydroxyls groups and atoms are labelled here from outside to inside the nanotube. Imogolite nanotube consists of a curved di-octahedral gibbsite-like layer (Al(OH) 3 ) with isolated (SiO 3 )OH tetrahedron units connected via covalent bonding between three mutual oxygen atoms, as it is shown in Figure 5.3a. The curvature effect can be understood in a ultra simplified way by noting that the distance between adjacent oxygen atoms on the tetrahedron is shorter than that on the planar gibbsite-like sheet. Rolling would thus allow adjusting the distances. The gibbsite-like sheet is rolled in such a way that aluminium octahedra have a zig-zag arrangement perpendicularly to the nanotube axis, as it is highlighted in Figure 5.3a. The nanotube structure is characterized by the number N of octahedra along such a zig-zag circumference. In their seminal article on the structure of natural imogolites [START_REF] Cradwick | Imogolite, a hydrated aluminum silicate of tubular structure[END_REF], Cradwick and co-workers could not determine the exact value of N between N = 10, 11 and 12. It has not yet been done unambiguously since then, despite intensive research. The diameter of imogolite nanotubes obtained artificially (see section 5.3) is slightly larger than that of natural imogolite nanotubes, indicating larger N values.

As already mentioned, X-ray scattering diagrams of imogolite nanotube samples consist of a limited number of broad modulations. It is not due to a poor crystallinity of imogolite, as it was first assumed, but to the nanometric lateral extend of the nanotubes. A methodogy was recently proposed to determine their atomic structure determination from wide-angle X-ray scattering experiments [START_REF] Monet | Structural resolution of inorganic nanotubes with complex stoichiometry[END_REF]. Monet et al. applied the methodology to methylated imogolite nanotubes, where methyl groups replace the inner hydroxyl groups (see section 5.3). They evidenced a different rolling mode for these modified imogolite nanotubes, with an 'armchair' arrangement of the aluminium octahedra along the tube circumference, as it is illustrated in Figure 5.3b [START_REF] Monet | Structural resolution of inorganic nanotubes with complex stoichiometry[END_REF]. The family of imogolite nanotubes can be extended to methylated imogolite nanotubes or to germanium-based imogolite nanotubes, where silicon is replaced by germanium (see Section 5.3). With diameters of the order of the nanometer, INTs can be considered as true inorganic analogs of the well-known carbon nanotubes. But contrary to single-walled carbon nanotubes or other inorganic single-walled nanotubes such as BN or MoS 2 ones [START_REF] Hernandez | Elastic properties of C and B x C y N z composite nanotubes[END_REF][START_REF] Seifert | Structure and electronic properties of MoS 2 nanotubes[END_REF], whose strain energy decreases monotonically with increasing diameter, INTs present a well-defined energy minimum as a function of their diameter or of their chirality [START_REF] Monet | Structural resolution of inorganic nanotubes with complex stoichiometry[END_REF][START_REF] Tamura | Molecular dynamics modeling of tubular aluminum silicate: Imogolite[END_REF][START_REF] Konduri | Strain energy minimum and vibrational properties of single-walled aluminosilicate nanotubes[END_REF][START_REF] Guimaraes | Imogolite nanotubes: Stability, electronic, and mechanical properties[END_REF][START_REF] Konduri | Controlling nanotube dimensions: Correlation between composition, diameter, and internal energy of single-walled mixed oxide nanotubes[END_REF][START_REF] Teobaldi | Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes[END_REF][START_REF] Poli | Large-scale density functional theory simulation of inorganic nanotubes: a case study on Imogolite nanotubes[END_REF].

It is worth concluding this paragraph by emphasizing the singularity of imogolite compared to other clays. Let's briefly compare it here to halloysite presented in Figure 5.4 (for a review article about halloysite, see e.g. [START_REF] Joussein | Halloysite clay minerals-a review[END_REF]). Halloysite is generally polydisperse and does not form single-walled nanotube like imogolite. The wall of an halloysite multi-walled nanotube (or nanoscroll, see Figure 5.4b) has nominal formula Al 2 Si 2 O 5 (OH) 4 . It consists in a gibbsite-like sheet with which SiO 4 tetrahedra share only one oxygen atom (Figure 5.4a). In other words, tetrahedra are head to toe in imogolite and in halloysite. Tetrahedron orientation in imogolite is exceptional for a clay mineral. The external surface of halloysite is covered by polymerized SiO 4 tetrahedra forming a true layer [START_REF] Yuan | Properties and applications of halloysite nanotubes: recent research advances and future prospects[END_REF], while it is the internal surface of imogolite, which consists in a silicon-based sheet. It is covered by isolated SiO 3 (OH) tetrahedra, a unique feature for a clay.

Physico-chemical Properties of Imogolite

The structure of imogolite is at the origin of its peculiar properties. Probably the most significant behavior of imogolite nanotubes is their monodispersity in diameter and chirality [START_REF] Cradwick | Imogolite, a hydrated aluminum silicate of tubular structure[END_REF][START_REF] Monet | Structural resolution of inorganic nanotubes with complex stoichiometry[END_REF]. It is a major advantage for the detailed study of their physicochemical properties or the development of some targeted applications (see section 5.4). Concerning their electronic properties, Bursill et al. were the first to suggest a large electronic band gap structure for imogolite [START_REF] Bursill | Imogolite: an aluminosilicate nanotube material[END_REF]. According to different simulations, aluminosilicate nanotubes are insulators with a calculated band gaps higher than 4 eV [START_REF] Guimaraes | Imogolite nanotubes: Stability, electronic, and mechanical properties[END_REF][START_REF] Teobaldi | Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes[END_REF][START_REF] Lourenco | Nanotubes with well-defined structure: single-and double-walled imogolites[END_REF][START_REF] Elliott | Chemically selective alternatives to photoferroelectrics for polarization-enhanced photocatalysis: the untapped potential of hybrid inorganic nanotubes[END_REF]. Several efforts have therefore been prompted recently to reduce the band gap, in particular by doping the imogolite structure via isomorphic substitution [START_REF] Alvarez-Ramirez | First principles studies of Fe-containing aluminosilicate and aluminogermanate nanotubes[END_REF][START_REF] Avellan | Structural incorporation of iron into Ge-imogolite nanotubes: a promising step for innovative nanomaterials[END_REF][START_REF] Shafia | Al/Fe isomorphic substitution versus Fe 2 O 3 clusters formation in Fe-doped aluminosilicate nanotubes (imogolite)[END_REF] (see section 5.3).

Like other clay minerals, imogolite is subject to dehydroxylation and high temperature structural transformations. Its thermal stability is relatively low with dehydroxylation occurring at temperatures above T > 300°C [START_REF] Yoshinaga | Imogolite in some Ando soils[END_REF][START_REF] Yoshinaga | Identification of imogolite in the filmy gel materials in the imaichi and shichihonzakura purlice beds[END_REF][START_REF] Van Der Gaast | Small-angle X-ray powder diffraction, morphology, and structure of allophane and imogolite[END_REF][START_REF] Mackenzie | Structure and thermal transformations of imogolite studied by Si 29 and Al 27 high-resolution solid-state nuclear magnetic-resonance[END_REF][START_REF] Kang | Dehydration, dehydroxylation, and rehydroxylation of single-walled aluminosilicate nanotubes[END_REF]. Dehydroxylation process actually preludes to subsequent structural collapse. Further heating treatment led either to the occurrence of an X-ray amorphous phase [START_REF] Farmer | Synthetic imogolite -properties, synthesis, and possible applications[END_REF][START_REF] Donkai | Preparation of transparent mullite silica film by heat-treatment of imogolite[END_REF] or to a lamellar phase [START_REF] Mackenzie | Structure and thermal transformations of imogolite studied by Si 29 and Al 27 high-resolution solid-state nuclear magnetic-resonance[END_REF][START_REF] Zanzottera | Thermal collapse of single-walled alumino-silicate nanotubes: transformation mechanisms and morphology of the resulting lamellar phases[END_REF], corresponding to the partial breakdown of the nanotube structure. At even higher temperatures, thermogravimetric analysis (TGA) of INTs exhibits an exothermic peak above 950°C. It was first related to the formation of -alumina [START_REF] Yoshinaga | Imogolite in some Ando soils[END_REF]. It seems however to correspond to a mullite crystalline phase (3Al 2 O 3 .2SiO 2 ) [START_REF] Donkai | Preparation of transparent mullite silica film by heat-treatment of imogolite[END_REF].

As far as the imogolite stability is concerned, knowledge of its mechanical properties is of prime importance towards future developments in material science. Several computational studies have reported that the Young modulus of INTs, characterizing the stiffness of the nanotube, is in the range 100-300 GPa [START_REF] Guimaraes | Imogolite nanotubes: Stability, electronic, and mechanical properties[END_REF][START_REF] Teobaldi | Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes[END_REF][START_REF] Liou | Relationships among the structural topology, bond strength, and mechanical properties of single-walled aluminosilicate nanotubes[END_REF][START_REF] Liou | Relationships among the structural topology, bond strength, and mechanical properties of single-walled aluminosilicate nanotubes[END_REF], i.e. it is of the same order of magnitude as for halloysite (140 GPa) [START_REF] Lecouvet | Elastic modulus of halloysite nanotubes[END_REF], MoS 2 nanotubes (150 GPa) [START_REF] Li | Strain-tunable electronic and transport properties of MoS 2 nanotubes[END_REF] or chrysotile (160-280 GPa) [START_REF] Piperno | Characterization of geoinspired and synthetic chrysotile nanotubes by atomic force microscopy and transmission electron microscopy[END_REF]. However, experimental studies of INT mechanical properties are still missing. Moreover, the possible existence of various types of defects in the imogolite wall [START_REF] Yucelen | Defect structures in aluminosilicate single-walled nanotubes: a solid-state nuclear magnetic resonance investigation[END_REF] may strongly modify the mechanical properties of the nanotubes [START_REF] Da Silva | Structural, electronic, and mechanical properties of inner surface modified imogolite nanotubes[END_REF][START_REF] Liou | Defective Single-walled aluminosilicate nanotubes: structural stability and mechanical properties[END_REF]. There are several indications that imogolite nanotubes can easily deform, more specifically when they are assembled in bundles. Molecular dynamic calculations performed on aluminosilicate imogolites show that the basis of interacting nanotubes can deform to become oval [START_REF] Tamura | Molecular dynamics modeling of tubular aluminum silicate: Imogolite[END_REF][START_REF] Creton | Molecular dynamics study of hydrated imogolite -2. Structure and dynamics of confined water[END_REF]. Recent numerical calculations [START_REF] Da Silva | Structural, electronic, and mechanical properties of inner surface modified imogolite nanotubes[END_REF] also indicate that partial dehydroxylation of the inner surface silanols of the aluminosilicate nanotube should induce substantial deformations of the nanotubes. The authors concluded that the control of the degree of dehydroxylation by heat treatment may allow one to tune the electronic and mechanical properties of imogolite nanotubes [START_REF] Da Silva | Structural, electronic, and mechanical properties of inner surface modified imogolite nanotubes[END_REF]. From an experimental point of view, Amara et al. [START_REF] Amara | Hexagonalization of aluminogermanate imogolite nanotubes organized into closed-packed bundles[END_REF] gave the first evidence of a deformation, namely hexagonalization, of imogolite nanotubes at room temperature, when they are assembled in bundles, thanks to a systematic method developed to analyze X-ray scattering diagrams as a function of the nanotube shape.

It was early recognized that imogolite nanotubes present interesting colloidal properties. In their seminal paper, Yoshinaga and Aomine evidenced that INTs aggregate in concentrated NaCl solutions with a jelly-like appearance, while air-dried INTs recover their swelling properties in weak acidic suspensions (pH < 4) [START_REF] Yoshinaga | Imogolite in some Ando soils[END_REF]. It is now well proved that imogolite can form transparent gels, which generally fill instantaneously the whole suspension volume by fast coagulation mechanisms [START_REF] Philipse | On the density and structure formation in gels and clusters of colloidal rods and fibers[END_REF]. Furthermore, suspensions of imogolite nanotubes form a true liquid-crystalline nematic phase at very low volume fractions, either for natural [START_REF] Donkai | Dilute-solution properties of imogolite[END_REF][START_REF] Kajiwara | Lyotropic mesophase of imogolite,1. Effect of polydispersity on phase-diagram[END_REF][START_REF] Kajiwara | Lyotropic mesophase of imogolite. 2. Microscopic observation of imogolite mesophase[END_REF][START_REF] Donkai | Lyotropic mesophase of imogolite. 3. Observation of liquid-crystal structure by scanning electron and novel polarized optical microscopy[END_REF] or synthetic imogolite nanotubes [START_REF] Levitz | Intermittent Brownian dynamics over a rigid strand: Heavily tailed relocation statistics in a simple geometry[END_REF][START_REF] Paineau | A liquid-crystalline hexagonal columnar phase in highly-dilute suspensions of imogolite nanotubes[END_REF], as expected for highly elongated colloidal nanorods. Moreover, Paineau et al. discovered that, at slightly higher imogolite concentration, INTs also form a liquid-crystalline hexagonal columnar phase (Figure 5.5a), which is much more stable to dilution than reported so far in literature [START_REF] Paineau | A liquid-crystalline hexagonal columnar phase in highly-dilute suspensions of imogolite nanotubes[END_REF]. Thanks to its low visco-elasticity, this columnar phase is easily aligned in an alternating electric field, in contrast with usual columnar liquid-crystal phases [START_REF] Ramos | Swelling of a lyotropic hexagonal phase by monitoring the radius of the cylinders[END_REF][START_REF] Grelet | Hard-rod behavior in dense mesophases of semiflexible and rigid charged viruses[END_REF] (Figure 5.5b). This significant advantage could be exploited for the elaboration of anisotropic nanocomposite materials (see section 5.4). Furthermore, imogolite nanotubes present high capacity to bind anions as originally evidenced in geological context [START_REF] Parfitt | Adsorption of phosphate on imogolite[END_REF][START_REF] Harsh | Adsorption of cations on imogolite and their effect on surface-charge characteristics[END_REF][START_REF] Su | Sodium and chloride sorption by imogolite and allophanes[END_REF][START_REF] Parfitt | Allophane and imogolite: role in soil biogeochemical processes[END_REF]. Electrophoretic measurements reveal that the outer-surface charge of imogolite is positive over a wide range of pH, with point of zero charge (PZC) values higher than 7 [START_REF] Harsh | Adsorption of cations on imogolite and their effect on surface-charge characteristics[END_REF][START_REF] Karube | Electrophoretic behavior of imogolite under alkaline conditions[END_REF][START_REF] Su | The electrophoretic mobility of imogolite and allophane in the presence of inorganic anions and citrate[END_REF][START_REF] Tsuchida | Effects of pH and ionic strength on electrokinetic properties of imogolite[END_REF], which can be used to control nanotubes bundling by anion condensation. Recent X-ray scattering measurements confirmed this assumption [START_REF] Paineau | Effect of ionic strength on the bundling of metal oxide imogolite nanotubes[END_REF]. It was shown that, even at low ionic strength, imogolite nanotubes tend to organize in small bundles after solvent evaporation. Altogether, experimental observations on liquid crystal phases [START_REF] Paineau | A liquid-crystalline hexagonal columnar phase in highly-dilute suspensions of imogolite nanotubes[END_REF] as well as those on nanotube bundling [START_REF] Paineau | Effect of ionic strength on the bundling of metal oxide imogolite nanotubes[END_REF] strongly suggest the dominant role of electrostatic interactions between imogolite nanotubes. Gustafsson proposed that the structural charge may arise from elongations of Al-O bonds or shortening of Si-O ones, inducing a weak positive (negative) charge on the outer (inner) surface of imogolite [START_REF] Gustafsson | The surface chemistry of imogolite[END_REF], an hypothesis confirmed with density functional theory (DFT) simulations [START_REF] Guimaraes | Imogolite nanotubes: Stability, electronic, and mechanical properties[END_REF][START_REF] Teobaldi | Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes[END_REF][START_REF] Poli | Large-scale density functional theory simulation of inorganic nanotubes: a case study on Imogolite nanotubes[END_REF][START_REF] Elliott | Chemically selective alternatives to photoferroelectrics for polarization-enhanced photocatalysis: the untapped potential of hybrid inorganic nanotubes[END_REF].

Synthesis and Modification of Imogolite 5.3.1. Synthesis of Imogolite Nanotubes

From an industrial point of view, the main drawback of natural imogolite is that they do not form large deposits compared to other natural one-dimensional clay minerals, such as halloysite, sepiolite or palygorskyte [START_REF] Joussein | Halloysite clay minerals-a review[END_REF][START_REF] Pasbakhsh | Characterisation of properties of various halloysites relevant to their use as nanotubes and microfibre fillers[END_REF][START_REF] Pasbakhsh | Natural mineral nanotubes: properties and applications[END_REF]. But their synthesis was developed quite quickly after their discovery. Farmer et al. [START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF] proposed in 1977 a sol-gel method to achieve synthesis of INTs in aqueous suspension and under mild conditions around 100°C. Typically, the synthesis of INTs can be divided in four steps as summarized in Figure 5.6. [START_REF] Denaix | Structure and affinity towards Cd2+, Cu2+, Pb2+ of synthetic colloidal amorphous aluminosilicates and their precursors[END_REF]. The third step consists in ageing the solution under hydrothermal conditions either by reflux or in autoclave to allow the growth of nanotubes. After sufficient time, the product is recovered at room temperature and purified by washing against water (step 4) (Figure 5.6). It should be underlined that compared to carbon nanotubes synthesis, the synthesis of imogolite is a low temperature process.

Since Farmer et al. article [START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF], several improvements have been proposed to increase the purity and the yield of the synthetic product by changing either the nature of the precursors, their concentration or their stoichiometric ratios [START_REF] Barrett | The synthesis and characterization of imogolite[END_REF][START_REF] Marzan | Synthesis of platinum nanoparticles in aqueous host dispersions of inorganic (imogolite) rods[END_REF][START_REF] Abidin | A new method for nano tube imogolite synthesis[END_REF][START_REF] Levard | Synthesis of imogolite fibers from decimolar concentration at low temperature and ambient pressure: a promising route for inexpensive nanotubes[END_REF][START_REF] Chemmi | A novel fluoride route for the synthesis of aluminosilicate nanotubes[END_REF][START_REF] Chemmi | Key steps influencing the formation of aluminosilicate nanotubes by the fluoride route[END_REF][START_REF] Arancibia-Miranda | Advancements in the synthesis of building block materials: experimental evidence and modeled interpretations of the effect of Na and K on imogolite synthesis[END_REF]. Furthermore, several authors reported that the formation of imogolite nanotubes might depend on the step durations [START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF][START_REF] Yang | Growth mechanism. of synthetic imogolite nanotubes[END_REF][START_REF] Yucelen | A generalized kinetic model for the formation and growth of single-walled metal oxide nanotubes[END_REF], by changing the temperature of the synthesis [START_REF] Wada | Imogolite synthesis at 25-degrees[END_REF][START_REF] Lee | Thermodynamic control of diameter-modulated aluminosilicate nanotubes[END_REF] or by modifying the method of heating [START_REF] Lam | Microwaveassisted synthesis of highly monodispersed single-walled aluminosilicate nanotubes[END_REF][START_REF] Avellan | Accelerated microwave assisted synthesis of alumino-germanate imogolite nanotubes[END_REF].

Imogolite synthesis is commonly performed with Al alkoxide (ASB: aluminum trisec-butoxide), AlCl 3 or Al(ClO 4 ) 3 precursors, the latter offering a lower complexity ability, hence reducing the formation of by-products [START_REF] Farmer | Synthetic imogolite, a tubular hydroxyaluminium silicate[END_REF]. Although different Si sources have been explored [START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF][START_REF] Abidin | A new method for nano tube imogolite synthesis[END_REF][START_REF] Ohashi | Characterization of synthetic imogolite nanotubes as gas storage[END_REF][START_REF] Hongo | Synthesis of imogolite from rice husk ash and evaluation of its acetaldehyde adsorption ability[END_REF], the use of alkoxide such as tetraethoxysilane (TEOS) is recognized to promote imogolite growth [START_REF] Farmer | Synthetic imogolite -properties, synthesis, and possible applications[END_REF] due to its slow condensation kinetics. In addition, it was shown that a slight excess of Si precursor could inhibit the formation of aluminium hydroxides such as gibbsite or boehmite [START_REF] Barrett | The synthesis and characterization of imogolite[END_REF][START_REF] Levard | Synthesis of Ge-imogolite: influence of the hydrolysis ratio on the structure of the nanotubes[END_REF][START_REF] Mukherjee | Phenomenology of the growth of singlewalled aluminosilicate and aluminogermanate nanotubes of precise dimensions[END_REF][START_REF] Picot | Exploring hybrid imogolite nanotubes formation via Si/Al stoichiometry control[END_REF]. Moreover, several authors suggested that higher concentration of precursors or the nature of the counter-ions could prevent tube formation while promoting spherical-like nanostructures such as allophanes [START_REF] Arancibia-Miranda | Advancements in the synthesis of building block materials: experimental evidence and modeled interpretations of the effect of Na and K on imogolite synthesis[END_REF][START_REF] Picot | Exploring hybrid imogolite nanotubes formation via Si/Al stoichiometry control[END_REF][START_REF] Inoue | Influence of citric-acid on the natural formation of imogolite[END_REF][START_REF] Inoue | Influence of citric acid on the formation of short-range ordered aluminosilicates[END_REF][START_REF] Nakanishi | Heat-induced gelation of hydroxy-aluminosilicate synthesized by instantaneous mixing of sodium silicate and aluminum chloride[END_REF]. The synthesis of INTs thus requires careful adjustments.

Modification of Imogolite Nanotubes

An advantage of INTs over other nanotubes is that one can tune its morphology and wall chemistry by straightforward approaches. Yucelen et al. [START_REF] Yucelen | Shaping single-walled metal oxide nanotubes from precursors of controlled curvature[END_REF] suggested that the diameter of imogolite nanotubes can be changed by controlling the shape of nanometer-scale precursors formed in the early stage of the synthesis by changing the nature of the protic acid used (HCl, HClO 4 , CH 3 COOH) (Figure 5.7a). One of the most blatant progress in INT synthesis is probably the replacement of silicon by germanium through isomorphic substitution (Figure 5.7b). Initially explored by Wada [START_REF] Wada | Effects of substitution of germanium for silicon in imogolite[END_REF], the synthesis of aluminogermanate INTs (Ge-INT) has mainly risen in recent years [START_REF] Levard | Synthesis of Ge-imogolite: influence of the hydrolysis ratio on the structure of the nanotubes[END_REF][START_REF] Mukherjee | Phenomenology of the growth of singlewalled aluminosilicate and aluminogermanate nanotubes of precise dimensions[END_REF][START_REF] Levard | Synthesis of large quantities of single-walled aluminogermanate nanotube[END_REF]. Ge-analogues are produced in large quantities from decimolar initial concentrations [START_REF] Levard | Synthesis of large quantities of single-walled aluminogermanate nanotube[END_REF]. Furthermore, Maillet et al. [START_REF] Maillet | Evidence of double-walled Al-Ge imogolite-like nanotubes. a cryo-TEM and SAXS investigation[END_REF][START_REF] Maillet | Growth kinetic of single and double-walled aluminogermanate imogolite-like nanotubes: an experimental and modeling approach[END_REF] evidenced that Ge-INTs could exist not only as single-walled (SWINT) but also as double-walled imogolite nanotubes (DWINT) depending of the initial concentration of aluminum precursor [START_REF] Thill | Physico-chemical control over the single-or double-wall structure of aluminogermanate imogolite-like nanotubes[END_REF]. The produced Ge-based imogolite nanotubes were shorter than Sibased ones but Amara et al. [START_REF] Amara | Single-step formation of micron long (OH) 3 Al 2 O 3 Ge(OH) imogolite-like nanotubes[END_REF] recently reported the synthesis of micron-long germanium-based imogolite nanotubes by producing the hydroxyl ions by thermal decomposition of urea (CO(NH 2 ) 2 ), bypassing the process of slow injection of NaOH. The inner diameter increases from ~ 1.5 to 3 nm from Si to Ge single-walled INTs. SWINT diameter can be tuned finely by adjusting the concentrations in initial Si and Ge precursors, thus changing the substitution ratio [Si]/([Si]+[Ge]) [START_REF] Konduri | Controlling nanotube dimensions: Correlation between composition, diameter, and internal energy of single-walled mixed oxide nanotubes[END_REF][START_REF] Thill | How the diameter and structure of (OH) 3 Al 2 O 3 Si x Ge 1-x OH imogolite nanotubes are controlled by an adhesion versus curvature competition[END_REF][START_REF] Alvarez-Ramirez | Ab initio simulation of the structural and electronic properties of aluminosilicate and aluminogermanate natotubes with imogolitelike structure[END_REF]. Based on these promising results, other isomorphic substitutions have been recently investigated, in particular by partially replacing Al 3+ by Fe 3+ in the outer wall [START_REF] Avellan | Structural incorporation of iron into Ge-imogolite nanotubes: a promising step for innovative nanomaterials[END_REF][START_REF] Shafia | Al/Fe isomorphic substitution versus Fe 2 O 3 clusters formation in Fe-doped aluminosilicate nanotubes (imogolite)[END_REF][START_REF] Ookawa | Synthesis and characterization of Fe containing imogolite[END_REF][START_REF] Shafia | Isomorphic substitution of aluminium by iron into single-walled alumino-silicate nanotubes: A physico-chemical insight into the structural and adsorption properties of Fe-doped imogolite[END_REF]. Although these improvements do not imply significant change of the nanotube diameter (up to 1% of doping rate) [START_REF] Shafia | Al/Fe isomorphic substitution versus Fe 2 O 3 clusters formation in Fe-doped aluminosilicate nanotubes (imogolite)[END_REF], the effect of Fe incorporation acts as specific coordination centers for organic moieties and modifies the electronic properties of the nanotubes by decreasing the band gap, even for low substitution rates [START_REF] Alvarez-Ramirez | First principles studies of Fe-containing aluminosilicate and aluminogermanate nanotubes[END_REF]. Other isomorphic substitutions have been proposed from the point of view of theory, either by replacing both Al and Si atoms by elements of groups III (Ga, In) and IV (C, Ge, Sn) [START_REF] Alvarez-Ramirez | Theoretical study of (OH) 3 N 2 O 3 MOH[END_REF] or by substituting the inner tetrahedrons by phosphorous and arsenite derivatives [START_REF] Guimaraes | Imogolite-like nanotubes: structure, stability, electronic and mechanical properties of the phosphorous and arsenic derivatives[END_REF], but it remains to be implemented experimentally.

Surface Functionalization of Imogolite Nanotubes

An interesting feature of INTs is the high density of hydroxyl groups on their outer surface (~18 OH/nm 2 ), offering multiple binding sites for external surface functionalization. Depending on the intended application, it is often necessary to make INTs compatible with organic matrix. Hence, surface functionalization of INTs has been widely explored, as compiled in recent reviews [START_REF] Ma | Surface functionalization of aluminosilicate nanotubes with organic molecules[END_REF][START_REF] Shikinaka | Design of stimuli-responsive materials consisting of the rigid cylindrical inorganic polymer "imogolite[END_REF][START_REF] Paineau | Imogolite nanotubes: a flexible nanoplatform with multipurpose applications[END_REF]]. An efficient way to modify a metal oxide surface is to use phosphonate derivatives [START_REF] Neouze | Surface modification and functionalization of metal and metal oxide nanoparticles by organic ligands[END_REF]. This issue has been extensively studied [START_REF] Yamamoto | Surface modification of aluminosilicate nanofiber "imogolite[END_REF][START_REF] Yamamoto | Preparation of a novel (polymer/inorganic nanofiber) composite through surface modification of natural aluminosilicate nanofiber[END_REF][START_REF] Yamamoto | Transparent polymer nanohybrid prepared by in situ synthesis of aluminosilicate nanofibers in poly(vinyl alcohol) solution[END_REF][START_REF] Park | Twodimensional alignment of imogolite on a solid surface[END_REF][START_REF] Bac | Surface-modified aluminogermanate nanotube by OPA: Synthesis and characterization[END_REF][START_REF] Ma | Surface modification of individual imogolite nanotubes with alkyl phosphate from an aqueous solution[END_REF][START_REF] Yah | Molecular aggregation state and electrical properties of terthiophenes/imogolite nanohybrids[END_REF][START_REF] Ma | Poly(methyl methacrylate) grafted imogolite nanotubes prepared through surface-initiated ARGET ATRP[END_REF][START_REF] Picot | Behaviour of hybrid inside/out Janus nanotubes at an oil/water interface. A route to self-assembled nanofluidics?[END_REF][START_REF] Li | Dispersing surface-modified imogolite nanotubes in polar and non-polar solvents[END_REF] since 2001 and the first report of the chemisorption of octadecylphosphonic acid onto the outer surface of imogolite nanotubes [START_REF] Yamamoto | Surface modification of aluminosilicate nanofiber "imogolite[END_REF]. Successful grafting of organic moieties can be evidenced by dispersing unmodified and modified nanotubes in organic solvents (Figure 5.8) [START_REF] Bac | Surface-modified aluminogermanate nanotube by OPA: Synthesis and characterization[END_REF][START_REF] Picot | Behaviour of hybrid inside/out Janus nanotubes at an oil/water interface. A route to self-assembled nanofluidics?[END_REF][START_REF] Yamamoto | Preparation and properties of [poly(methyl methacrylate)/imogolite] hybrid via surface modification using phosphoric acid ester[END_REF]. Grafting of carboxylates [START_REF] Yamamoto | Preparation of a novel (polymer/inorganic nanofiber) composite through surface modification of natural aluminosilicate nanofiber[END_REF][START_REF] Shikinaka | Direct evidence for structural transition promoting shear thinning in cylindrical colloid assemblies[END_REF][START_REF] Shikinaka | Chirallinkage-induced hierarchical ordering of colloidal achiral nanotubes in their thixotropic gel[END_REF] and sulfonates [START_REF] Jiravanichanun | Preparation of hybrid films of aluminosilicate nanofiber and conjugated polymer[END_REF] groups have also been reported with similar results as with phosphonates. Otherwise, the use of silane as coupling agent appears to be controversial because the moieties remain hydrolytically labile and are totally removed after several days of dialysis [START_REF] Johnson | Silylation of a tubular aluminosilicate polymer (imogolite) by reaction with hydrolyzed (-aminopropyl)triethoxysilane[END_REF][START_REF] Johnson | Hydrolysis of (-aminopropyl)triethoxysilane-silylated imogolite and formation of a silylated tubular silicate-layered nanocomposite[END_REF]. Beyond chemisorption, chemical vapor deposition (CVD) [START_REF] Lee | Conducting properties of polypyrrole coated imogolite[END_REF][START_REF] Chang | Effect of UV irradiation during synthesis of polypyrrole by a one-step deposition/polymerization process[END_REF] or -ray irradiation [START_REF] Lee | Preparation of an imogolite/poly(acrylic acid) hybrid gel[END_REF][START_REF] Ryu | Dynamic behavior of hybrid poly (acrylic acid) gel prepared by -ray irradiated imogolite[END_REF] have also been considered.

The inner hydrophilic cavity of INTs can also be functionalized by a post-synthesis chemical modification. Post-functionalization can be obtained with different silane agents such as (3-aminopropyl)triethoxysilane (APTES), methyltrimethoxysilane (MTMS) or trichlorosilane (TCIS) but also with acetyl chloride after dehydration of the hydrophilic INT samples at sufficiently high temperature [START_REF] Johnson | Hydrolysis of (-aminopropyl)triethoxysilane-silylated imogolite and formation of a silylated tubular silicate-layered nanocomposite[END_REF][START_REF] Kang | Single-walled aluminosilicate nanotubes with organic-modified interiors[END_REF]. However, the degree of inner surface substitution is lower than 35% [START_REF] Kang | Single-walled aluminosilicate nanotubes with organic-modified interiors[END_REF]. On can also use direct, template-free, synthesis route by replacing, the initial alkoxide (prefiguring the tetrahedral layer) by a functionalized one (Figure 5.7c). Hydroxyl groups can be replaced by methyl [START_REF] Bottero | Synthesis and characterization of hybrid organic/inorganic nanotubes of the imogolite type and their behaviour towards methane adsorption[END_REF] or amino [START_REF] Kang | Direct synthesis of single-walled aminoaluminosilicate nanotubes with enhanced molecular adsorption selectivity[END_REF] groups. Like for unmodified INTs, a dependence of the inner cavity diameter with the substitution of Si by Ge could be expected in hybrid nanotubes. Amara et al. [START_REF] Amara | Hybrid, tunable-diameter, metal oxide nanotubes for trapping of organic molecules[END_REF] demonstrated that hybrid imogolite with methylated inner cavities can be obtained with Si to Ge endmembers (Figure 5.9) and that the inner diameter increases progressively with decreasing the ratio [Si]/([Si]+[Ge]), from 1.8 and 2.4 nm. Methylation of the inner cavity not only offers control over the surface properties but it also leads to a drastic structural change of the chirality of the nanotube (see section 5.2) [START_REF] Monet | Structural resolution of inorganic nanotubes with complex stoichiometry[END_REF]. Interestingly, Bahadori et al. recently considered the possibility to prepare novel Fe-doped imogolite nanotubes with methylated inner cavity, combining two type of isomorphic substitution [START_REF] Bahadori | Photoactivated degradation of tartrazine by H 2 O 2 as catalyzed by both bare and Fedoped methyl-imogolite nanotubes[END_REF].

In brief, the synthesis of imogolite-like nanostructures of the type (OH) 3 (Al 2- x M x )O 3 (Ge 1-y Si y )R (with M = Fe 3+ , Ga 3+ …; R = -OH, -CH 3 , -CH 2 NH 2 …) offers a unique system of 1D nanostructures with monodisperse sizes and adjustable aspect ratio.

Applications in Functional Materials

Reinforcement of Polymer Materials

With their well-defined morphologies and their easy surface functionalization, imogolite nanotubes have emerged during the last decades as serious candidates for reinforcing polymer nanocomposites by using various type of polymers in the form of films or membranes and very recently in the form of fibres (Table 5.1). Imogolite nanotubes have often been mixed with poly(vinyl alcohol) (PVOH) since PVOH/INT mixtures can be processed readily from aqueous solutions. PVOH/INT blend films were successfully prepared but the incorporation of imogolite nanotubes has only a slight influence on both Young modulus and tensile strength properties of the nanocomposite [START_REF] Hoshino | Lyotropic mesophase formation in PVA/imogolite mixture[END_REF][START_REF] Choi | Preparation and characterization of syndiotacticity-rich ultra-high molecular weight poly(vinyl alcohol) imogolite blend film[END_REF]. Similar enhancement of mechanical properties was also observed with poly(methyl methacrylate) (PMMA) [START_REF] Yamamoto | Preparation and properties of [poly(methyl methacrylate)/imogolite] hybrid via surface modification using phosphoric acid ester[END_REF] and poly(acrylic acid) (PAA) nanocomposites [START_REF] Lee | Preparation of an imogolite/poly(acrylic acid) hybrid gel[END_REF][START_REF] Ryu | Dynamic behavior of hybrid poly (acrylic acid) gel prepared by -ray irradiated imogolite[END_REF][START_REF] Ryu | Structural response of imogolitepoly(acrylic acid) hydrogel under deformation[END_REF][START_REF] Shikinaka | Robust imogolite hydrogels with tunable physical properties[END_REF]. However, incorporation of PMMA grafted INT into poly(vinyl chloride) (PVC) films reveal that the reinforcement is strongly dependent on the interfacial adhesion between the functionalized nanotubes and the polymer matrix [START_REF] Ma | Preparation and properties of PVC/PMMA-gimogolite nanohybrid via surface-initiated radical polymerization[END_REF]. In addition to reinforcement in solid materials, the combination of imogolite with various polymers also yields homogeneous hydrogels exhibiting thixotropic behaviour, hierarchical ordering as well as reversible isotropicanisotropic structural transitions in response to strain [START_REF] Shikinaka | Direct evidence for structural transition promoting shear thinning in cylindrical colloid assemblies[END_REF][START_REF] Shikinaka | Chirallinkage-induced hierarchical ordering of colloidal achiral nanotubes in their thixotropic gel[END_REF][START_REF] Shikinaka | Robust imogolite hydrogels with tunable physical properties[END_REF][START_REF] Shikinaka | Nanohybrid film consisted of hydrophobized imogolite and various aliphatic polyesters[END_REF][START_REF] Shikinaka | Reinforcement of hydrogel by addition of fiber-like nanofiller[END_REF][START_REF] Shikinaka | Strain-induced reversible isotropic-anisotropic structural transition of imogolite hydrogels[END_REF][START_REF] Shikinaka | Quasi-solid electrolyte: a thixotropic gel of imogolite and an ionic liquid[END_REF]. Imogolite hydrogels can also be prepared with biomacromolecules [START_REF] Jiravanichanun | Preparation and characterization of imogolite/DNA hybrid hydrogels[END_REF][START_REF] Thomas | Biosurfactant-mediated one-step synthesis of hydrophobic functional imogolite nanotubes[END_REF] for encapsulation and/or for sustained release of enzymes or model drugs [START_REF] Kato | Effective encapsulation of laccase in an aluminium silicate nanotube hydrogel[END_REF][START_REF] Gelli | Enhanced formation of hydroxyapatites in gelatin/imogolite macroporous hydrogels[END_REF].

Molecular Selectivity and Storage

Beyond their use as fillers for reinforced materials, imogolite nanotubes also present a promising potential for molecular confinement applications thanks to their well-defined diameters and interfaces. Imogolite nanotubes were proposed as an efficient molecular sieving material, especially for gas adsorption and storage [START_REF] Ohashi | Characterization of synthetic imogolite nanotubes as gas storage[END_REF][START_REF] Karube | Water retention by colloidal allophane and imogolite with different charges[END_REF][START_REF] Wilson | Benzene displacement on imogolite[END_REF][START_REF] Bonelli | IR spectroscopic and catalytic characterization of the acidity of imogolite-based systems[END_REF][START_REF] Bonelli | IR spectroscopic study of the acidic properties of alumino-silicate single-walled nanotubes of the imogolite type[END_REF]. Interestingly, the selective functionalization of the inner interface (see section 5.3.3) results in dramatically enhanced molecular selectivity over CO 2 /CH 4 and CO 2 /N 2 [START_REF] Kang | Direct synthesis of single-walled aminoaluminosilicate nanotubes with enhanced molecular adsorption selectivity[END_REF]. Methylated-modified imogolite nanotubes can also be used in aqueous suspensions for trapping organic molecules [START_REF] Picot | Behaviour of hybrid inside/out Janus nanotubes at an oil/water interface. A route to self-assembled nanofluidics?[END_REF][START_REF] Amara | Hybrid, tunable-diameter, metal oxide nanotubes for trapping of organic molecules[END_REF]. INTs could finally be employed as tuneable building blocks for filtration applications by reverse osmosis [START_REF] Liou | Investigating the potential of single-walled aluminosilicate nanotubes in water desalination[END_REF]. In combination with their compatibility with different polymer matrix, the fabrication of imogolite-based membranes has started to receive more intention recently. In this framework, several studies reported that addition of imogolite nanotubes in water filtration membranes (Figure 5.11) induces a substantial increase of the water flux while achieving significant ion exclusion [START_REF] Kang | Single-walled aluminosilicate nanotube/poly(vinyl alcohol) nanocomposite membranes[END_REF][START_REF] Barona | High permeate flux of PVA/PSf thin film composite nanofiltration membrane with aluminosilicate single-walled nanotubes[END_REF][START_REF] Barona | Interfacial polymerization of polyamidealuminosilicate SWNT nanocomposite membranes for reverse osmosis[END_REF][START_REF] Pan | Thin film nanocomposite membranes based on imogolite nanotubes blended substrates for forward osmosis desalination[END_REF][START_REF] Li | Synthesis of Polyamide Thin-film nanocomposite membranes using surface modified imogolite nanotubes[END_REF]. However, the mechanisms involved in the enhancement of the membranes performance remain to be carefully investigated from the viewpoint of fundamental science. In particular, no studies has clearly established whether water molecules diffuse through or around imogolite nanotubes incorporated in the matrix.

Environment Field

Imogolite nanotubes were recognized as good adsorbents very early on, especially in environmental context where they present high capacity to bind anions and metallic cations. Parfitt et al. [START_REF] Parfitt | Adsorption of phosphate on imogolite[END_REF] reported that natural imogolite (pumice beds) are capable of fixing large amounts of phosphates up to 120-250 µmol.g -1 . They suggested that the adsorption mechanism is related to a ligand-exchange reaction at the surface of imogolite nanotubes. Similar mechanisms have been invoked for the adsorption of metallic cations (Cu 2+ , Pb 2+ , UO 2 2+ ) on the outer surface of INTs [START_REF] Denaix | Structure and affinity towards Cd2+, Cu2+, Pb2+ of synthetic colloidal amorphous aluminosilicates and their precursors[END_REF][START_REF] Arai | Uranyl adsorption and surface speciation at the imogolite-water interface: Self-consistent spectroscopic and surface complexation models[END_REF]. On the other hand, Levard et al. [START_REF] Levard | Role of natural nanoparticles on the speciation of Ni in andosols of la Reunion[END_REF] revealed incorporation of Ni species into the octahedral vacancies of the external INT wall.

The immobilization of different noble metals nanoparticles on specific sites of the external surfaces was also investigates by Liz-Marzan and Philipse [START_REF] Marzan | Synthesis of platinum nanoparticles in aqueous host dispersions of inorganic (imogolite) rods[END_REF]. In that case, imogolite nanotubes in aqueous media act as a solid support, being effective to stabilize the formation of Pt, Au, Ag and bimetallic nanoparticles [START_REF] Liz-Marzán | Stable hydrosols of metallic and bimetallic nanoparticles immobilized on imogolite fibers[END_REF][START_REF] Kuroda | Uniform and high dispersion of gold nanoparticles on imogolite nanotubes and assembly into morphologically controlled materials[END_REF]. These results pave the way towards potential uses of imogolite nanotubes for water treatment [START_REF] Guilment | Hybrid organic-inorganic materials designed to clean wash water in photographic processing: Genesis of a sol-gel industrial product the Kodak Water Saving Treatment System[END_REF][START_REF] Guerra | Adsorption of rubidium on raw and MTZ-and MBI-imogolite hybrid surfaces: An evidence of the chelate effect[END_REF][START_REF] Arancibia-Miranda | Preparation and characterization of a single-walled aluminosilicate nanotube-iron oxide composite: Its applications to removal of aqueous arsenate[END_REF][START_REF] Shafia | Reactivity of bare and Fe-doped alumino-silicate nanotubes (imogolite) with H 2 O 2 and the azo-dye Acid Orange 7[END_REF], antimicrobial agents [START_REF] Geraldo | Synthesis of CdTe QDs/single-walled aluminosilicate nanotubes hybrid compound and their antimicrobial activity on bacteria[END_REF][START_REF] Yucelen | Synthesis and immobilization of silver nanoparticles on aluminosilicate nanotubes and their antibacterial properties[END_REF], transparent dressings [START_REF] Lerat | Dressing and antiseptic agent containing silver[END_REF] and for catalysis applications [START_REF] Imamura | Shapeselective copper-loaded imogolite catalyst[END_REF].

Catalysis

It was suggested early that INT may act as a catalyst [START_REF] Farmer | Synthetic imogolite -properties, synthesis, and possible applications[END_REF]. But, despite the many progresses achieved in the synthesis of imogolite nanostructures, this field remains relatively unexplored. The first published example is probably the one on the coupling of Cu species with INT [START_REF] Imamura | Shapeselective copper-loaded imogolite catalyst[END_REF] that induces a higher activity in the decomposition of tert-butyl hydroperoxide than with unloaded imogolite or with Cu-SiO 2 materials. Katsumata et al. investigated complex Cu 2+ -grafted TiO 2 /INT composites which exhibit very efficient absorption and photodecomposition rate of acetaldehyde [START_REF] Katsumata | Visible-light-driven photodegradation of acetaldehyde gas catalyzed by aluminosilicate nanotubes and Cu(II)-grafted TiO 2 composites[END_REF]. Imogolite nanotubes and their derivatives have also been used for hydroxylation of olefins [START_REF] Qi | Surface-modified imogolite by 3-APS-OsO 4 complex: Synthesis, characterization and its application in the dihydroxylation of olefins[END_REF], catalytic oxidation of aromatic hydrocarbon [START_REF] Ookawa | Oxidation of aromatic hydrocarbons with H 2 O 2 catalyzed by a nano-scale tubular aluminosilicate, Fe-containing imogolite[END_REF] isomerization of glucose to fructose [START_REF] Olson | Utilizing imogolite nanotubes as a tunable catalytic material for the selective isomerization of glucose to fructose[END_REF] or photo-degradation of azo-dyes [START_REF] Bahadori | Photoactivated degradation of tartrazine by H 2 O 2 as catalyzed by both bare and Fedoped methyl-imogolite nanotubes[END_REF][START_REF] Shafia | Reactivity of bare and Fe-doped alumino-silicate nanotubes (imogolite) with H 2 O 2 and the azo-dye Acid Orange 7[END_REF], although using dyes for evaluating photocatalytic properties remain controversial [START_REF] Rochkind | Using dyes for evaluating photocatalytic properties: a critical review[END_REF].

On the theoretical background, DFT calculations reveal a most interesting feature specific to imogolite structure. INTs bear a tunable permanent polarization of their wall and a real-space separation of the valence and conduction band edges is highlighted [START_REF] Teobaldi | Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes[END_REF][START_REF] Poli | Large-scale density functional theory simulation of inorganic nanotubes: a case study on Imogolite nanotubes[END_REF]. Characterization of the nanotube band separation and optical properties reveal the occurrence of near UV inside-outside charge-transfer excitations, which may be effective for enhanced photocatalytic activity [START_REF] Elliott | Chemically selective alternatives to photoferroelectrics for polarization-enhanced photocatalysis: the untapped potential of hybrid inorganic nanotubes[END_REF][START_REF] Poli | The potential of imogolite nanotubes as (co-)photocatalysts: a linear-scaling density functional theory study[END_REF]. In spite of previous use of INTs as catalyst support (see section 5.4.3) and preliminary results on the performance of INTs for photo-catalytic decomposition of organic dyes [START_REF] Bahadori | Photoactivated degradation of tartrazine by H 2 O 2 as catalyzed by both bare and Fedoped methyl-imogolite nanotubes[END_REF][START_REF] Shafia | Reactivity of bare and Fe-doped alumino-silicate nanotubes (imogolite) with H 2 O 2 and the azo-dye Acid Orange 7[END_REF], to date this subject is still to be explored.

Environmental Health and Safety

Only few experimental studies have been performed on the cytotoxicity and genotoxicity of natural and synthetic imogolite nanotubes compared to carbon nanotubes for instance. In vitro tests performed on aluminosilicate nanotubes reveal that imogolite are internalised into murine macrophage cells and induce a low dose and time-dependent cytotoxicity, but to a lesser extent than single-and multi-walled carbon nanotubes [START_REF] Rotoli | Imogolite: an aluminosilicate nanotube endowed with low cytotoxicity and genotoxicity[END_REF]. A high toxicity effect of INT to lung cell cultures was reported by Farmer et al 1983 but without mentioning the dose administered [START_REF] Farmer | Synthetic imogolite -properties, synthesis, and possible applications[END_REF]. Recent investigations do not show any genotoxic effect except for a decrease in DNA integrity observed in airway epithelial cells and for the highest dose (80 μg.cm -2 ) [START_REF] Rotoli | Imogolite: an aluminosilicate nanotube endowed with low cytotoxicity and genotoxicity[END_REF]. By contrast, Liu et al. investigated the effect of Ge-imogolite nanotubes (average length: 6 and 51 nm long) on human fibroblast culture [START_REF] Liu | Influence of the length of imogolite-like nanotubes on their cytotoxicity and genotoxicity toward human dermal cells[END_REF]. The authors observed higher internalization rates in the case of low aspect ratio Ge-INTs without decreasing the cell viability. However, these short nanotubes seem to induce significant lesions of DNA, mainly through oxidative stress while INTs with higher aspect ratio exhibit a weaker genotoxicity [START_REF] Liu | Influence of the length of imogolite-like nanotubes on their cytotoxicity and genotoxicity toward human dermal cells[END_REF]. To go further, the respiratory biopersistence and lung toxicity of Ge-SWINT and Ge-DWINT with length of ~70 nm were evaluated in vivo and compared with crocidolite particles [START_REF] Van Den Brule | Nanometer-long Ge-imogolite nanotubes cause sustained lung inflammation and fibrosis in rats[END_REF]. The results showed that Ge-INT are biopersistent and promote genotoxicity, sustained inflammation and fibrosis in lung cells, with effects more severe than those induced by crocidolite [START_REF] Van Den Brule | Nanometer-long Ge-imogolite nanotubes cause sustained lung inflammation and fibrosis in rats[END_REF]. Care should be exercised in handling powders or freeze-dried imogolite samples, which are readily dispersed in air.

Attention should also be paid to the fact that the biological medium can strongly modify the physico-chemical properties of imogolite. Indeed, hydroxyl groups on the outer wall of imogolite nanotubes may interact either by bonding ionic species [START_REF] Harsh | Adsorption of cations on imogolite and their effect on surface-charge characteristics[END_REF][START_REF] Paineau | Effect of ionic strength on the bundling of metal oxide imogolite nanotubes[END_REF], present in the biological medium or by interacting directly with phosphonic acid groups of biological polymers [START_REF] Jiravanichanun | Preparation and characterization of imogolite/DNA hybrid hydrogels[END_REF]. Future research is necessary to confirm these hypotheses and they will rely on the recent progress made on the synthesis of various imogolite-like nanostructures with well-defined morphologies.

Suggestions and Future Prospects

We have shown in the previous sections that imogolite is naturally present but widely dispersed in environment, thus limiting its applications. The major breakthrough for using INTs was certainly their easy synthesis by sol-gel methods under mild conditions, a prerequisite for developing green materials. Such approach induces some drawbacks. Indeed, in the case of aluminosilicate imogolite nanotubes, the starting precursors are easily accessible and inexpensive, but often yielding low quantities of nanotubes. The situation is reversed in the case of aluminogermanate INTs.

It is now possible designing innovative INTs with modular interfaces in a predictive way, which has recently led to some progress the field of imogolite-based functional materials. Imogolite-like nanotubes can be considered as a flexible building block with multipurpose applications (nanocomposites, stimuli-responsive materials, (photo)catalysis, ion adsorption, molecular separation and storage…). It is interesting to note also that most of the applications explored up to now do not fully exploit all properties (controlled morphology, tuneable interfaces and colloidal proeperties) of these peculiar nanostructures. For instance, a future trend could be to combine the well-defined morphology of INTs with their ease to self-organize to produce novel nanocomposites and artificial ion channel devices, as was done recently with carbon nanotubes [START_REF] Geng | Stochastic transport through carbon nanotubes in lipid bilayers and live cell membranes[END_REF][START_REF] Tunuguntla | Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins[END_REF]. Finally, recent DFT calculations [START_REF] Elliott | Chemically selective alternatives to photoferroelectrics for polarization-enhanced photocatalysis: the untapped potential of hybrid inorganic nanotubes[END_REF][START_REF] Poli | The potential of imogolite nanotubes as (co-)photocatalysts: a linear-scaling density functional theory study[END_REF] showed that imogolite nanotubes display a real-space separation of the valence and conduction bands, which may be effective for electron-hole pair (e*-h) separation and enhanced photocatalytic activity, an interesting alternative to photoferroelectrics materials [START_REF] Bhavanasi | Polarization orientation, piezoelectricity, and energy harvesting performance of ferroelectric PVDF-TrFE nanotubes synthesized by nanoconfinement[END_REF][START_REF] Su | Silver-modified nanosized ferroelectrics as a novel photocatalyst[END_REF][START_REF] Sastre | Selective, room-temperature transformation of methane to C1 oxygenates by deep UV photolysis over zeolites[END_REF]. Coupled with molecular confinement, the promising use of polarized 1D nanotubes for photocatalysis applications deserves to be explored experimentally.

Figure 5 . 1 .

 51 Figure 5.1. (a) Soil profile from Kiwadashima, Tochigi, Japan, (b-c) Optical observations of gel films (white arrows) found in the 2Bw1 and 3Bw5 horizons, respectively, (d) Typical transmission electron microscopy (TEM) micrograph of imogolite extracted from the gel-like film, in association with allophane (spherical particles). Adapted with permission from [3].

Figure 5 . 2 .

 52 Figure 5.2. Schematic representation of the different purification steps of natural imogolite. Reproduced with permissions from [24] © 2012 Ma et al; licensee Beilstein-Institut.

Figure 5 . 3 .

 53 Figure 5.3. (a) Schematic top and side view of a N=13 imogolite nanotube. Ochre, blue, red and white atoms are Si, Al, O and H atoms, respectively. Ochre tetrahedra (blue octahedrons) are SiO 4 tetrahedra (AlO 6 octahedrons), with O atoms at the top and Si (Al) atom at the center. The dashed black line on the right view illustrates the zig-zag configuration. (b) Top and side view of a methylated imogolite nanotube. Dark atoms are C atoms and ochre tetrahedra are now SiO 3 C tetrahedra. The dashed black line on the right view illustrates the armchair configuration.

Figure 5 . 4 .

 54 Figure 5.4. Schematic representation of (a) the wall structure of halloysite and (b) its tubular morphology. Typical (c) transmission electron microscopy (TEM) and (d) atomic force microscopy (AFM) images of halloysite nanotubes. Adapted with permissions from [41].

Figure 5 . 5 .

 55 Figure 5.5. (a) Optical observation between crossed polarizers (white arrows) of a hexagonal columnar phase (Col H ) in aqueous suspensions of aluminogermanate imogolite nanotubes (volume fraction = 0.22%). (b) Two-dimensional small-angle Xray scattering image of the Col H phase aligned under electric field. Adapted with permissions from [69].

Figure 5 . 6 .

 56 Figure 5.6. Flowchart for the two main synthesis methods of imogolite nanotubes.From Farmer et al. in[START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF] and Denaix et al. in[START_REF] Denaix | Structure and affinity towards Cd2+, Cu2+, Pb2+ of synthetic colloidal amorphous aluminosilicates and their precursors[END_REF].The first one consists in the hydrolysis of Al and Si precursors by the addition of a NaOH solution under vigorous stirring. In a second step, the pH is adjusted to 4.5 by addition of a mixture of HCl and acetic acid promoting condensation of Al and formation of roof-tiled imogolite precursors, also referenced as proto-imogolite[85- 89]. Let's note here that Denaix et al. showed that this step can be skipped by controlling the NaOH concentration up to an hydrolysis ratio [OH]/[Al] = 2[START_REF] Denaix | Structure and affinity towards Cd2+, Cu2+, Pb2+ of synthetic colloidal amorphous aluminosilicates and their precursors[END_REF]. The third step consists in ageing the solution under hydrothermal conditions either by reflux or in autoclave to allow the growth of nanotubes. After sufficient time, the product is recovered at room temperature and purified by washing against water (step 4) (Figure5.6). It should be underlined that compared to carbon nanotubes synthesis, the synthesis of imogolite is a low temperature process.Since Farmer et al. article[START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF], several improvements have been proposed to increase the purity and the yield of the synthetic product by changing either the nature of the precursors, their concentration or their stoichiometric ratios[START_REF] Barrett | The synthesis and characterization of imogolite[END_REF][START_REF] Marzan | Synthesis of platinum nanoparticles in aqueous host dispersions of inorganic (imogolite) rods[END_REF][START_REF] Abidin | A new method for nano tube imogolite synthesis[END_REF][START_REF] Levard | Synthesis of imogolite fibers from decimolar concentration at low temperature and ambient pressure: a promising route for inexpensive nanotubes[END_REF][START_REF] Chemmi | A novel fluoride route for the synthesis of aluminosilicate nanotubes[END_REF][START_REF] Chemmi | Key steps influencing the formation of aluminosilicate nanotubes by the fluoride route[END_REF][START_REF] Arancibia-Miranda | Advancements in the synthesis of building block materials: experimental evidence and modeled interpretations of the effect of Na and K on imogolite synthesis[END_REF]. Furthermore, several authors reported that the formation of imogolite nanotubes might depend on the step durations[START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF][START_REF] Yang | Growth mechanism. of synthetic imogolite nanotubes[END_REF][START_REF] Yucelen | A generalized kinetic model for the formation and growth of single-walled metal oxide nanotubes[END_REF], by changing the temperature of the synthesis[START_REF] Wada | Imogolite synthesis at 25-degrees[END_REF][START_REF] Lee | Thermodynamic control of diameter-modulated aluminosilicate nanotubes[END_REF] or by modifying the method of heating[START_REF] Lam | Microwaveassisted synthesis of highly monodispersed single-walled aluminosilicate nanotubes[END_REF][START_REF] Avellan | Accelerated microwave assisted synthesis of alumino-germanate imogolite nanotubes[END_REF].Imogolite synthesis is commonly performed with Al alkoxide (ASB: aluminum trisec-butoxide), AlCl 3 or Al(ClO 4 ) 3 precursors, the latter offering a lower complexity ability, hence reducing the formation of by-products[START_REF] Farmer | Synthetic imogolite, a tubular hydroxyaluminium silicate[END_REF]. Although different Si sources have been explored[START_REF] Farmer | Synthesis of imogolite -tubular aluminum silicate polymer[END_REF][START_REF] Abidin | A new method for nano tube imogolite synthesis[END_REF][START_REF] Ohashi | Characterization of synthetic imogolite nanotubes as gas storage[END_REF][START_REF] Hongo | Synthesis of imogolite from rice husk ash and evaluation of its acetaldehyde adsorption ability[END_REF], the use of alkoxide such as tetraethoxysilane (TEOS) is recognized to promote imogolite growth[START_REF] Farmer | Synthetic imogolite -properties, synthesis, and possible applications[END_REF] due to its slow condensation kinetics. In addition, it was shown that a slight excess of Si precursor could inhibit the formation of aluminium hydroxides such as gibbsite or boehmite[START_REF] Barrett | The synthesis and characterization of imogolite[END_REF][START_REF] Levard | Synthesis of Ge-imogolite: influence of the hydrolysis ratio on the structure of the nanotubes[END_REF][START_REF] Mukherjee | Phenomenology of the growth of singlewalled aluminosilicate and aluminogermanate nanotubes of precise dimensions[END_REF][START_REF] Picot | Exploring hybrid imogolite nanotubes formation via Si/Al stoichiometry control[END_REF]. Moreover, several authors suggested that higher concentration of precursors or the nature of the counter-ions could prevent tube formation while promoting spherical-like nanostructures such as allophanes[96,108- 111]. The synthesis of INTs thus requires careful adjustments.

Figure 5 . 7 .

 57 Figure 5.7. Schematic representation of shape control of imogolite nanotubes. (A) Anion complexation during the hydrolysis step; (B) isomorphic substitution; (C) inner functionalization by using specific organosilicate (or germane) tetrahedra. Reprinted with permissions from [88] © 2012 American Chemical Society.

Figure 5 . 8 .

 58 Figure 5.8. Illustration of the dispersion state of poly(methyl methacrylate) (PMMA) grafted aluminosilicate nanotubes and of unmodified ones in water/chloroform phase. Reprinted with permissions from [137].

Figure 5 . 9 .

 59 Figure 5.9. X-ray scattering (XRS) diagrams obtained on methyl-modified imogolite nanotubes of nominal composition (OH) 3 Al 2 O 3 Si x Ge 1-x (CH 3 ) prepared at different substitution ratio x = [Si]/([Si] + [Ge]). Analysis of XRS diagrams upon substitution of Si by Ge shows an increase of the nanotube diameter. Reprinted with permissions from [150].

  Instead of preparing films by a solution blend of imogolite powder, Yamamoto et al. made composites in situ by synthesis of INT in presence of the PVOH [129]. It improves the dispersion of INTs in the resulting film and enhances their optical and mechanical properties (Figure 5.10) [129].

Figure 5 . 10 .

 510 Figure 5.10. Optical transparency of in situ hybrid (upper) and blend (lower) imogolite/PVOH films. The thickness of films is ~ 100 mm. Reprinted with permissions from [129].

Figure 5 . 11 .

 511 Figure 5.11. Schematic diagram of (a) pristine and (b) modified filtration membranes by incorporation of aluminosilicate imogolite nanotubes. (c) Mechanism proposed for water filtration and salt rejection (ID: internal diameter). Reprinted with permissions from [156].

Table 5 . 1 .

 51 Class and type of polymer used for imogolite-reinforced nanocomposites.

	Class of	Type	Acronym Final form Ref.
	polymer
	Vinyl	Poly(vinyl alcohol) PVOH	Film	[128,129,152-154]
				Membrane [155-157]
				Fibre	[158]
		Poly(vinyl	PVC	Film	[159]
		chloride)
	Acrylate Poly(methyl	PMMA	Film	[137]
		methacrylate)
		Poly(acrylic acid)	PAA	Hydrogel	[145,146,160,161]
		Poly(hydroxyethyl	PHEA	Hydrogel	[161]
		acrylate)
	Ester	Poly(-	PCL	Film	[162]
		caprolactone)		Hydrogel	[163]
		Poly(lactic acid)	PLA	Hydrogel	[163]
		Poly(butylene	PBS	Hydrogel	[163]
		succinate)
		Polyamide	PA	Membrane [164-166]
				Hydrogel	[161,167,168]
	Others	Dicarboxilic acid	DA	Hydrogel	[138,139,169]

Acknowledgement

We would like to thank our collaborators who share our interest in imogolite nanotubes and in their properties: Geoffrey Monet (PhD student), Rajesh Bandhary (post-doctoral researcher), Stéphane Rols, Stéphan Rouzière, Pierre Levitz, Laurent Michot, Anne-Laure Rollet, Gilberto Teobaldi and Milo Shaffer.