Dynamics of the freezing front during the solidification of a colloidal alumina aqueous suspension: in situ X-ray radiography, tomography and modeling

Ice templating of colloidal suspension is gaining interest in material science because it offers the possibility to shape advanced materials, and in particular porous ceramics. Recent investigations on this peculiar process show that a correlation between the morphology of the frozen suspension and the velocity of the freezing front do exist. The dynamics of the freezing front of a colloidal suspension of alumina is investigated in the present study by experimental tests, finite element numerical analysis and theoretical analytical calculations. The experimental tests are carried out by in situ X-ray radiography (investigation of the dynamics of the freezing front) and tomography (investigation of the resulting morphology of the frozen suspension). The finite element model is a continuous properties model; it is used for investigating the dynamics and the shape of the freezing front. The analytical model is based on the two-phase Stefan problem. We propose a solution for the dynamics of the solidification front based on the calculation of the diffusivity as a function of the particle fraction and local temperature.

INTRODUCTION

Since 1954, ice templating, also known as freeze casting, is known as an environmental friendly and cost effective shaping process for fabricating advanced ceramic materials [START_REF] Maxwell | Preliminary investigation of the freeze-casting method for forming refractory powders[END_REF] . This shaping technique offers the possibility to introduce a certain amount of open porosity with interconnecting pore channels or pore gradients in ceramic bodies [START_REF] Araki | Porous ceramic codies with interconnected pore channels by a novel freeze casting technique[END_REF] . Recent publications [START_REF] Araki | New freeze-casting technique for ceramics with sublimable vehicles[END_REF][START_REF] Soltmann | Freeze gelation: a new option for the production of biological ceramic composites (biocers)[END_REF] show the wide range of application of ice templating, including separation filters, catalyst supports, biosensors, gas distributors and implantable bone scaffolds. For introducing the pore structures in bulk ceramic bodies, suspensions with a low solid content are first frozen to obtain vehicle ice crystals which are often connected with each other in dendritic shapes, surrounded by the frozen concentrated ceramic suspension [START_REF] Araki | Porous ceramic codies with interconnected pore channels by a novel freeze casting technique[END_REF] . After freeze drying (removal of the ice by sublimation), porous channels remain, replicating the shape of the interconnected ice crystals. Ongoing research shows that the shape of the frozen structures and the porosity is particularly dependent on the speed of the freezing front [START_REF] Deville | Freeze-casting of porous ceramics: a review of current achievements and issues[END_REF] . Sintered bodies of Al2O3 with aligned channels fabricated by unidirectional ice templating of conventional aqueous ceramic slurries were reported in numerous papers [START_REF] Fukasawa | Synthesis of porous silicon nitride with unidirectionally aligned channels using freeze-drying process[END_REF][START_REF] Fukasawa | Synthesis of porous ceramics with complex pore structure by freeze-dry processing[END_REF][START_REF] Deville | Ice-templated porous alumina structures[END_REF] . These studies investigate the microstructure of the interconnected crystals of alumina, in relation to the velocity of the freezing front. The microstructure corresponding to the initial instants of solidification has been described in terms of crystal shape (R-crystals for the random structures, Z-crystals for the lamellar structures) [START_REF] Deville | In situ x-ray radiography and tomography observations of the solidification of aqueous alumina particle suspensions-part I: initial instants[END_REF] . This study also describes the structural periodicity of the lamellar texture obtained in the resulting microstructure. These investigations were carried out by high resolution in situ X-ray radiography and tomography. The purpose of the present work is to investigate the kinetics of the freezing front of colloidal suspensions of alumina by X-ray radiography and tomography. The experimental observations are compared to the results obtained with a thermal finite element model of the system (mould and colloidal suspension) and to the solution of the system of ordinary differential equation generated by the two-phase Stefan problem.

MATERIALS AND METHODS

Experimental setup

The experimental part of this study focuses on the use of two non-destructive imaging techniques, i.e. the high-resolution X-ray absorption radiography and tomography. We directly image the growth of the crystals in the suspension and the redistribution of the corresponding particles. X-ray attenuation radiography is a very well known technique used for years for the non-destructive imaging of samples. It is fast but the information coming from the bulk of the sample are sometimes difficult to interpret, because projected on a 2D plane. The use of tomography in materials science is newer [START_REF] Maire | X-ray Tomography applied to the characterization of cellular materials. Related Finite Element modeling problems[END_REF] . X ray tomography combines information from a large number of X-ray radiographs taken with different viewing angles of the sample. The technique includes a computed step, i.e., a recalculation step during which a 3D map of the local absorption coefficients in each elementary volume of the sample is retrieved from the set of absorption radiographs. The reconstructed map gives an indirect image of the microstructure. X-ray tomography was performed in the present study at a voxel size of (3.62 μm) [START_REF] Araki | New freeze-casting technique for ceramics with sublimable vehicles[END_REF] . A set of 900 projections was taken within 180°. The complete technical description of the tomograph used can be found in [START_REF] Buffiere | In situ experiments with x ray tomography: an attractive tool for experimental mechanics[END_REF] . To summarize, this tomograph is equipped with a tungsten transmission target to produce a small size X-ray source, operated at 116 kV and 50 µA without filtering in the present study. The detector is an amorphous silicon flat panel made of 1900 * 1500 square pixels of 127 µm in lateral size.

Slurries were prepared by mixing distilled water with a small amount (0.2 wt% of the suspension) of ammonium polymethacrylate anionic dispersant (Darvan C, R. T. Vanderbilt Co., Norwalk, CT) and 32%vol of alumina powder (Ceralox SPA 0.5, Sasol, Tucson, AZ, USA, D50=0.3 μm, SSA 8 m²/g).

Freezing experiments were performed by pouring the suspensions into a polypropylene cylindrical mould, invisible to X-rays, placed at the tip of a copper cold finger inside a cryogenic cell (see Fig. 1 -right hand side-for a scheme of the setup). The copper finger is cooled at its bottom using liquid nitrogen. This finger is 6 cm long so that the sample can be placed close to the X-ray tube for the highresolution tomography measurement. The conduction of cold along the copper rod induces a decrease of the temperature at the bottom of the colloidal suspension, eventually leading to its freezing. The cryogenic cell is composed of a double wall PMMA envelope which prevents condensation or frost to accumulate and perturb the X-ray measurement. The atmosphere of the chamber is not refrigerated so that the suspension is forced to freeze directionally from the bottom. Freezing kinetics is controlled by a resistance heater placed at the bottom of the copper rod using the information of the temperature measured by a thermocouple at the tip of the copper rod (close to the point where the solution touches the copper). The left side of the Figure 1 shows a close up of the sample, and the arrows indicate the heat flux and the temperature at the base of the sample. These boundary conditions are used in the thermal finite element model. The experimental setup was equipped with a PID controller for setting different temperature profiles to the mould. The PID controller was connected to a PC for recording the temperature profile during the solidification process. Five different temperature profiles were used: constant, linear, and three parabolic profiles. Radiographies were acquired during freezing in order to record the evolution of the freezing front. The acquisition frequency in the radiography was 1.4 Hz, therefore the minimal time span between two images was 0.7 sec. The spatial resolution of radiography was chosen to be 11 μm. At this resolution, the entire sample was visible on the CCD screen. The maximal height of the polypropylene mould was 16 mm and the internal diameter of the mould was 3 mm. As soon as the solidification process was completed and all the information about the kinetics of the freezing front recorded in terms of temperature and radiography as a function of time, the microstructure of the frozen sample was investigated by tomography. In order to keep the full width of the sample inside the field of view of the detector, a resolution of 3.62 μm was used. Two tomographic reconstructions were necessary to analyse the morphology of the full height of each frozen sample.

Finite element modelling

Incremental thermo-mechanical finite element simulations were used for simulating the kinematics of the freezing front. Since the experimental configuration is fully axial symmetric, 2D axial symmetrical geometry was chosen for representing the problem. The Figure 1 (left hand side) shows a sketch of the corresponding finite element model. The equations solved in the finite element model are the conduction equation (Fourier's law) and the convection equation. A thermal conductivity was defined for each component of the system and h = 20 W/m²K was used to represent the heat transfer coefficient to air. In order to simulate the thermal behaviour of the suspension, a continuous properties model was considered. If the region of the continuous phase transition is chosen to be small in the temperature/enthalpy density diagram, the model is also a good approximation to the dynamics of substances with discontinuous phase transitions [START_REF] Egolf | Theory and modelling of phase change materials with and without mushy regions[END_REF] . Since experimental tests show a relatively small zone of coexistence of the liquid and solid phases (and a well defined ice front), this approximation is suitable for describing the overall thermodynamic behaviour of the phase transition. In general, the thermal properties depend on local particle concentration. The results from X-ray tomography (Figure 3) show the relative fraction of the concentrated particle zone (black zones), in comparison to the pure ice (white zones). The particle concentration is limited between the nominal volumetric concentration (fvol=0.32) and the maximum concentration (fp= 0.58 is the breakthrough concentration), and between these limits the variation of the suspension properties due to the particle rich phase fraction is relatively small. According to Peppin [START_REF] Peppin | Solidification of colloidal suspensions[END_REF] , the diffusivity and the freezing temperature depend on the particle fraction, as shown in paragraph 2. , as shown by Table 1. The properties of the suspension were calculated according to the equations presented in the following section (Analytical modelling), the thermal conductivity in particular was estimated by the model of Jeffrey [START_REF] Jeffrey | Conduction through a random suspension of spheres[END_REF] . The main limitation of the continuous property model consists in the inability of reproducing fluctuations effects. In fact, the continuous property model does not account the rapid dendritic freezing occurring in the system; only planar and parabolic freezing front are predicted. Also, the Stefan model described in the next paragraph applies to slow planar freezing and not to the rapid dendritic freezing. Such effect can be included by particle-based simulation methods as shown by Barr [START_REF] Barr | Structural properties of materials created through freeze casting[END_REF] .

Analytical modelling

In this paragraph, an extended Stefan model of the solidification of the colloidal suspension described in the paragraph 2.1 is presented. The problem is named after Jožef Stefan, the Slovene physicist who introduced the general class of such problems around 1890, in relation to problems of ice formation [START_REF] Rubinstein | The Stefan Problem[END_REF] . The purpose of the model is to calculate the dynamics of the freezing front depending on the temperature profiles imposed at the base of the suspension. The temperature profiles are polynomials of the sixth order and reproduce the profiles used in the experimental tests. The Stefan problem is a two-phase moving boundary problem that allows the calculation of the temperature field and the position of the interface between two phases in a melting or freezing process. The physical assumptions for the application of the Stefan problem are: conduction only, constant latent heat of fusion Lf, fixed melting temperature Tm, the interface between the two phases has no thickness, surface tension and ice nucleation are not considered (uniform freezing only).

The Stefan problem requires the estimation of the numbers of Stefan (St) and Lewis (Le). The two numbers can be estimated by using the dimensionless compressibility factor z as a function of particle fraction, which accounts for particle-particle interactions. The literature shows several attempts of estimating z(f) [START_REF] Thiele | Equation of state for hard spheres[END_REF][START_REF] Mcquarrie | Statistical Mechanics[END_REF][START_REF] Russel | Colloidal Dispersions[END_REF][START_REF] Ree | Fifth and sixth virial coefficients for hard spheres and hard disks[END_REF][START_REF] Woodcock | Glass transition in the hard-sphere model and Kauzmann»s paradox[END_REF] . An approximation proposed by Peppin [START_REF] Peppin | Solidification of colloidal suspensions[END_REF] , valid over the entire concentration range, merges the results obtained by Woodcock [START_REF] Woodcock | Glass transition in the hard-sphere model and Kauzmann»s paradox[END_REF] for concentration up to packing concentration, and the results by Carnahan and Starling 22 for low concentration. The freezing temperature is also obtained as a function of the particle fraction. The Figure 2 shows the plot of the compressibility factor z(f)(upper side) and the freezing temperature as a function of the particle fraction (lower side). Details on the analytical model are provided in the Appendix. The properties of the solution, such as the heat capacity and the density, depend on the particle fraction, as shown by Figure 3 (upper side). The solution of the Stefan problem is strongly dependent on the St and Le numbers, plotted in Figure 3 (lower side) as a function of the particle fraction. The problem depends also on the estimation of the diffusivity coefficient D, plotted in Figure 4 as a function of the temperature of the suspension and the particle fraction. The number of Lewis indicates the influence of the Brownian diffusion on the motion of particles. At relatively small particle radius (0.5-1 μm) a Lewis number Le = 230-250 is expected [START_REF] Davis | Disorder-to-order transition in settling suspensions of colloidal silica: X-ray measurements[END_REF][START_REF] Worster | Solidification of fluids[END_REF] . At this value the velocity of the freezing front is small, compared to the velocity at which the particles can migrate by Brownian diffusion, quite strong for small particles. Peppin observed that at small Lewis number, the concentration and the temperature profiles resemble those observed during alloy solidification, while for high Lewis number the weak or absent Brownian diffusion allows the formation of a porous medium ahead of the freezing front and the possibility of a morphological instability. In certain cases, the interface can become unstable owing to supercooling and particle engulfment at high front velocity [START_REF] Coriell | Oscillatory morphological instabilities due to non-equilibrium segregation[END_REF] . If such instability is present during the solidification of a colloidal suspension, a variation in the freezing front velocity ∂ h ∂ t and a variation in the quantity fl are induced. In other words, when the instability occurs, an acceleration (or deceleration) of the front and a discontinuity in the particle fraction occurs.

RESULTS AND DISCUSSION

The results of experimental tests consist in morphological observation and quantitative information on the dynamics of the solidification process of the colloidal suspension considered in this research. The morphology was experimentally investigated by X-ray tomography, and the results about dynamics, obtained by radiography, was compared to the results obtained by finite element modeling (FEM) and to the solution of the Stefan problem obtained by numerical solved ordinary differential equation (ODE).

Morphology

Four zones can be morphologically distinguished in the frozen suspension [START_REF] Deville | In situ x-ray radiography and tomography observations of the solidification of aqueous alumina particle suspensions-part I: initial instants[END_REF] . The Figure 3 shows a sample of the frozen suspension and the four zone qualitatively identified by the morphology of the crystals (on the left) and the corresponding slices obtained by X-ray tomography (black and white, on the right). The grey level images obtained by X-ray tomography were filtered with a median filter and a specifically designed threshold was used for obtaining black and white images that preserve the morphology of the crystals. In these images, the white part represents the ice, and the black part represents the alumina particle rich regions. Morphologically speaking, the crystals can be classified in "R-crystals" (random symmetry) and "Z-crystals" (vertically aligned with the axis of the mould). This distinction is important from a morphological point of view since the R-crystals reject the alumina particles in the z-direction, and the Z-crystals reject the particles in the x and y-direction. The goal of a directional ice templating technique is to obtain a structure mainly composed of Z-crystals. According to the qualitative observation [START_REF] Deville | In situ x-ray radiography and tomography observations of the solidification of aqueous alumina particle suspensions-part I: initial instants[END_REF] , only the last zone of the sample (D) is purely composed of Z-crystals. The Table 2 synthetically shows the morphological zone in the frozen alumina suspensions.

In the zone between 0 and 3 mm of distance from the base of the mould, the resolution of the tomography was not good enough to image the crystals and particles distribution, therefore the actual microstructure is unknown. However, the freezing front is detectable and the measured interface velocity is particularly high (approximately 0.5-1 mm/s).

The Zone A starts as the resolution of the tomograph (voxel size: 3.62 3 µm 3 ) allows us to obtain quantitative information on the size of the crystals. This zone is characterized by a rapid growth of the R-crystals. The velocity of the freezing front is diminishing to approximately 0.15 mm/s. The Zone B corresponds to the transition between the zone A populated by Rcrystals only and the region that shows both R-crystals and Z-crystals (zone C).

At the beginning of zone C the entrapped particles reach a local maximum corresponding to the packing of particles obtained with Z-crystals at this particular interface velocity. The recently stopped R-crystals are occupying a large fraction of the xy-plane. The thickness of this zone is strongly dependent on the temperature gradient and the cooling temperature profile. If the temperature gradient is not present (constant temperature) the zone D extends until the end of the solidification process.

The zone D represents a steady state condition, morphologically speaking, since it is composed mainly of Z-crystals that extend vertically until the end of the solidification process. Particles redistribution is occurring in the xy plane. The particle fraction is reducing almost linearly. The zone D presents thin vertical ice structures, separated by alumina packed particles, interconnected by thin horizontal alumina structures. Morphologically speaking, it is the only stable zone in the ice templating technique.

The Figure 6 shows the samples frozen using five different cooling profiles. The diagram shows the repartition of the morphological zone for each sample. It can be observed immediately that the crystals in the sample with a constant cooling profile do not reach a purely vertical morphology (pure Z-crystals are present only in zone D), and the vertical structure in this sample are quite rare. This is due to a limited resolution in the X-ray tomography. The exact position of the zone B was identified by the measurement of the particle fraction, rather than using the visual analysis. The darkening corresponds to a rapid increase of the particle rich phase fraction, followed by a morphological mutation of the crystals: the R-crystals stop growing and they are progressively being replaced by Z-crystals. The positions and the extensions of the zone B for each sample are easily identified by the curves of the particle fraction as a function of distance from the copper cold surface, shown in the second diagram of Figure 7, while the first diagram shows the temperature profiles as a function of time. In the diagram of the particle fraction the curve par3 is not represented since it shows extremely little or no difference compared to the curve par1. The zone B is defined as being comprised between the local minimum and the local maximum of the particle fraction. The extension of the zone B seems to be larger in the curves than in the Figure 6. In the case considered, the solidification front is not a planar surface, but a parabolic surface that present a local maximum at the axis of the cylindrical mould. Since in Figure 6 the intersection of the conical surface with the mould is visible, the zone B appears smaller than in the tomographic reconstructions. The particle rich phase fraction at the beginning of zone A is approximately 0.57 for all the samples, and then it diminishes with different inclination to a local minimum. The behaviour of the particle fraction obtained with the constant temperature profile is quite different from the others in terms of extension of the zone B (the distance between local minimum and maximum particle fraction in the transition zone) and particle fraction at the end of the solidification process. Since the transition zone is associated with the reduction of the population of R-crystals and the growth of the population of Z-crystals, a weak transition zone, i.e. when the difference between the minimum and maximum particle fraction is relatively small (such as in the case of constant temperature profile) lead to an extended zone C. The sample with constant temperature profile does not show any zone with Z-crystals. In the case of constant temperature profile the velocity of the interface after the transition zone is so low that the Z-crystals can not grow. It should also be noted that the value of the constant temperature profile is close to the theoretical freezing temperature calculated in the analytical model section (Eq. 8). As the temperature profile approaches the freezing temperature, the transition zone became weaker. Deville et al. [START_REF] Deville | In situ x-ray radiography and tomography observations of the solidification of aqueous alumina particle suspensions-part I: initial instants[END_REF] observed that the transition to Z-crystals is possible only with a particular range of velocities of the freezing front. Therefore, out of this range it is not possible to describe the morphology of the frozen suspension in terms of Zcrystals and R-crystals, as done for the linear and parabolic temperature profiles used in this paper. The maximum extension of the transition zone is obtained with parabolic profiles ("par1" in particular). The steepness of parabolic profiles par1 and par3 maximizes the extension of the zone D by a large size of the transition zone, which reduces the extension of the zone B. A low temperature also tends to shift the transition zone backward to the cold finger, allowing more space for the steady state zone D. Not surprisingly, the condition that maximizes the zone D is a steep supercooled temperature profile, possibly parabolic.

Dynamics

In the experimental tests the error is generated by the resolution of the in-situ radiography (11 μm). A systematic error is also generated by the shape of the solidification front. In the initial phase of solidification, the front is a planar surface. As it strays from the copper surface, the solidification front becomes a parabolic surface. The parabolic shape of the solidification front is due to the limited insulation of the suspension from the air surrounding the polypropylene tube, almost invisible to X-ray. In order to limit the perturbation of the images in the radiography and tomography, it was chosen to provide minimal insulation. The radiography shows the solidification front in the xz plane, that becomes thicker and thicker as the distance from the copper surface increases. Finite element analysis was used for estimating the shape of the solidification front, and correcting the systematic error. The Figure 8 shows the shape of the front during three instants of the solidification with the temperature profile "par1". In order to minimize the error due to the shape of the solidification front, a reference position for the solidification front was estimated at -2/3 err from the upper limit, as shown in Figure 8 on the left. Due to this correction, the error on the position of the front is 11 μm. When differentiating in order to obtain the velocity of the freezing front, this error approximately represents 1% of the measured velocity.

The velocity of the solidification front was measured by in situ radiographies of the suspension during solidification. The images were recorded at a fixed time span of 0.7 seconds. The Figure 9 shows the plots of velocity of the freezing front as a function of time. The experimental results (test, solid line) are compared to the results by finite elements (FE, dashed line) and analytical model (ODE, meshed pattern line). The velocity was calculated by the position of the freezing front, considered as the projection of the front on the mould, and corrected according to the error estimation described at the beginning of the paragraph. It can be observed that the predictions by finite elements approximately follow the results by experimental tests, with a slight underestimation compared to the tests. On the other hand, the analytical model overestimates the velocity of the freezing front. A perfect fit of the analytical results with the tests was not expected. However, the finite element model based on the continuous properties model of the colloidal suspension and an analytical model based on the extended Stefan problem, that includes the calculations of the diffusion coefficient as a function of the particle fraction, provide two different approaches to the solidification problem. The parabolic profiles of temperature at the copper finger were used in order to minimize the decrease of the velocity of the freezing front as the distance between the copper finger and the front increases. This is in principle useful to obtain as soon as possible the steady state morphology of the crystals (zone D). According to the Figure 9 the velocity profiles "par1" and "par3" are the most efficient, and this is confirmed by the finite element analysis and by the analytical model. By comparing the velocities profiles of Figure 9 to the positions of zone B in the samples "par1" and "par3" in Figure 6, it can be observed that the most efficient velocity profiles shift backward the transition zone, leaving more space for developing the zone D. This behaviour can be explained by the analytical model. For a Lewis number of 200-230 (Figure 3), Brownian diffusion is quite high. The driving force for solidification is the undercooling at the base of the suspension. At slow solidification rates the particles easily diffuse away from the interface. The temperature of the suspension ahead of the interface is always warmer than the freezing temperature. However, at faster solidification rates the concentration and concentration gradient increase at the interface. When the concentration gradient at the interface is steep enough that the gradient in the freezing temperature is larger than the temperature gradient (that in the diagram of the particle fraction in Figure 7 corresponds to a minimum of the particle fraction), the suspension ahead of the interface is below its freezing temperature (constitutionally supercooled). In analogy with binary alloys, constitutional supercooling is closely related to morphological instability, according to Davis [START_REF] Davis | Theory of Solidification[END_REF] .

CONCLUSIONS

This paper investigates the dynamics of the solidification front in the ice templating of alumina colloidal suspension. The methods used include experimental tests, finite element modeling and analytical modeling. The three approaches and the comparison of the results provide a deep insight in the problem of obtaining packed alumina structures in the vertical direction. X-ray tomography allows recognizing four zones in the final product of the ice templating process. In terms of morphology, the objective of ice templating is to obtain spatially uniform lamellar structures, interconnected by bridges (interconnected Z-crystals). This condition is reached in the last zone of the frozen suspension, after a transition zone. The analytical model shows that in the transition zone, if the Lewis number is relatively high (Le = 200-230), the rejected particle form a packed layer, followed by a zone characterized by a variation of the morphology: the random shape crystals (R-crystals) stop growing and the Zcrystals start to develop. The extension of the Z-crystals zone depends on the size and the extension of the transition zone. By 3D reconstruction of data by X-ray tomography it is possible to plot the particle fraction as a function of the vertical position. The transition zone is identified by a two local singular points (minimum and maximum) of the particle fraction, and the distance between these singular points indicates the extension of the transition zone. By controlling the temperature at the base of the suspension it is possible to control the extension of the Z-crystals zone. A steep parabolic profile of the temperature maximizes the extension of the Z-crystals zone by a strong reduction of the transition zone (that also reduces the extension of the zone B). The lower parabolic temperature profile at the base of the suspension is associated with a shift of the transition zone towards the base of the suspension, leaving more space for the Z-crystals to develop. In terms of modeling, the thermal properties of a colloidal suspension in a solidification process depend on the particle fraction. However, results from finite elements show that a model based on constant properties is sufficient to provide reliable results. In principle, the thermal properties depend on the particle concentration, however constant properties can be used since the actual concentration range of the suspension considered in this paper is limited (0.32-0.58). A model for calculating each property should be chosen carefully in the literature, with particular attention to the specific heat capacity. The parameter that should be checked for choosing an appropriate model is the Lewis number, which represents the importance of the Brownian motion. The equations used in this paper for predicting the thermal properties are fitted on small particles (0.5-1 μm).

The analytical model provides results in terms of velocity of the freezing front. The model can be used to compare the responses of the system to different temperature profiles, thus it has to be properly tuned in order to obtain the actual velocity profile. Therefore, the analytical model can be used to provide guidelines in the choice of the temperature profile, in order to maximize the extension of the zone characterized by vertical lamellar structures (Z-crystal zone). In conclusion, the morphology of ceramics shaped with the technique of ice templating can be partially controlled by choosing the profile of the temperature at the base of the suspension. The dynamics of the freezing process of alumina colloidal suspension can be modeled by analytical calculations and finite elements. The two approaches complementary contribute to the modeling of the problem: the analytical model estimate the thermal properties of the colloidal suspension that have to be used in the finite element model. Also, the analytical model provides the estimation of the number of Lewis Le and the diffusion coefficient D, that resulted to be the most important parameters to predict the morphological behavior of colloidal suspension [START_REF] Mcquarrie | Statistical Mechanics[END_REF][START_REF] Davis | Theory of Solidification[END_REF] . The analytical works presented in this paper allow estimating Le and D as a function of the medium properties, the particle radius, and the concentration of alumina. Future works should investigate the impact of the dispersant on the number of Lewis. According to the experimental tests, to the finite element analysis and to the solution of the Stefan problem, a successful approach consists in applying a cooling rate approximately between 2 and 4°C/min; as the transition zone occurs, it is worth increasing the cooling rate following a parabolic profile. Since the position of the transition zone is a priori unknown, it is convenient to apply a parabolic profile since the beginning of the process.

µ R 6π 0 T k = D B (Eq.2)
with kB the Boltzmann's constant, R the radius of the alumina particle, µ the dynamic viscosity of the carrying fluid. In order to calculate the numbers of Stefan and Lewis, the thermal properties of the suspension were estimated for the liquid and the solid phases.

The thermal conductivity was estimated by the equation of Jeffrey [START_REF] Jeffrey | Conduction through a random suspension of spheres[END_REF] used for modeling the thermal conductivity of the suspension (Eq.3):

( )

2 1 3 2α 2 16 3β 4 1 3Φ 3C 1 2 2 + α α = β , k k = α , + + α + β + = γ γ β + β + k = k fluid ice vol vol fluid TS - Eq.3
With kice, fluid the thermal conductivities of the medium (water) in the solid and in the liquid phase, and f vol the nominal volumetric concentration of the alumina particles:

k ice = 2. 2 W mK , k fluid = 0. 6 W mK , Φ vol = 0 . 32 ,
The thermal conductivity of the suspension after freezing can be obtained by Eq.3

and is equal to k TS = 0. 9187 W mK . The thermal conductivity of the suspension before freezing can be approximated by the thermal conductivity of the medium (liquid water) [START_REF] Egolf | Theory and modelling of phase change materials with and without mushy regions[END_REF] : k TL = 0 .6 W mK . For concentrations Cvol<0.5, the specific heat capacity and the density of the suspension (Cp and ρ) can be estimated by the following relation:

( ) ( ) part P S) water(L, P S L, ρ Cp, Φ + ρ Cp, Φ = ρ Cp, - 1
Eq.4

Where f p =0.58 is the packing fraction of particle in the suspension in the concentrated region between the ice crystals at ambient temperature and pressure. The Stokes-Einstein diffusivity has also been used by Peppin et al. [START_REF] Peppin | Solidification of colloidal suspensions[END_REF] for writing the diffusion coefficient as a function of the local absolute temperature T and the local particle fraction f (Eq. 5)

( ) ( ) ( ) ( ) ( ) dΦ Φz d Φ = Φ D , Φ D D = T Φ, D 6 0 1 ˆ- (Eq. 5)
where z is the dimensionless compressibility factor which accounts for the effect of particle-particle interactions on the osmotic pressure ( ) Φ Π , which can be written as ( ) ( )

Φ Tz k v Φ = Φ Π B p (Eq. 6)
The expression of the osmotic pressure as a function of the particle fraction is a fundamental result from statistical mechanics 29 which states that the osmotic pressure of a suspension of particles and the pressure of a perfect gas are the same functions of volume fraction if the particle-particle interaction potential is the same. Peppin [START_REF] Peppin | Solidification of colloidal suspensions[END_REF] propose the following estimation of the compressibility factor: Peppin [START_REF] Peppin | Solidification of colloidal suspensions[END_REF] obtain the freezing temperature by utilising the conditions for local thermodynamic equilibrium between the liquid phase and the solid phase, assuming a planar interface and isotropic stress between the two phases, and the latent heat of fusion approximately constant in the temperature range considered. From these assumptions Peppin obtains the value of the freezing temperature ( )

Φ T f : ( ) f L p m B m f L ρ v T k = m mz + T = T 1 1 - f (Eq. 8)
with Tm=273K, the melting temperature of water.

Once the thermal properties of the suspension (kT, Cp and r) the diffusion coefficient D and the freezing temperatureTf have been estimated, the Stefan problem for unidirectional solidification of the suspension of hard-sphere colloids can be formulated. The Figure 2 shows the quantities involved in the formulation of the Stefan problem as a function of f. The Stefan problem is a system of two ordinary differential equations (ODE) and its solution represents the temperature field and the position h(t) of the solidification front. The Equation 9shows the ODEs of the Stefan problem with the boundary conditions. The problem was solved by using the MATLAB ODE suite, according to the methods illustrated by Shampine and Reichelt [START_REF] Shampine | The MATLAB ODE suite[END_REF] . By substituting the results for Φ in the Stephan condition ( )

λ = η
, it is possible to obtain the expression of λ for each boundary condition:

( ) ( ) λ = η | η θ | η θ St Le = t λ + λ = η λ = η 2 ÷ ÷ ø ö ç ç è ae ¶ ¶ - ¶ ¶ - - Eq. 12

3 .

 3 By considering a mean value of the suspension properties as a function of the local particle concentration, it is possible to apply the proposed continuous properties finite element model. The material properties used in the modelling i.e. the thermal conductivity ú

Figure 1 -

 1 Figure 1 -On the right: sketch of the freezing device. A flux of cold nitrogen is pumped at constant rate on a ring in contact with a copper finger, in contact with the colloidal suspension. A heating element controlled by a PID controller is used for regulating the temperature at the base of the suspension. A double shield provides thermal isolation from the ambient. On the left: the geometry (cylindrical symmetry) and boundary conditions of the finite element model. The natural convection was applied to the upper boundary of the suspension and on the polypropylene mould.

Figure 2 -

 2 Figure 2 -The dimensionless compressibility factor z (upper side), the freezing temperature Tf expressed in K (lower side) as a function on the particle fraction Φ.

Figure 3 -

 3 Figure 3 -The specific heat capacity Cp and the density ρ for the liquid phase of the suspension (upper side). The Stefan and Lewis used in the Stefan problem (lower side) as a function on the particle fraction Φ.

Figure 4 -

 4 Figure 4 -The diffusivity coefficient D as a function of local temperature and particle fraction.

Figure 5 -

 5 Figure 5 -The result of the radiography of the alumina sample frozen with the temperature profile "par1". The sample measures 16 mm in height and 3 mm in mean diameter. The morphological zones are indicated in the diagram on the left. The three slices on the right indicate the results of X-ray tomography. The bottom slice shows the suspension at the upper limit of zone A (small R-crystals). The middle slice shows the suspension in the zone B: R-crystals rapidly grow and few Z-crystals nucleate close to the polypropylene mould; since the zone C is approaching, the biggest R-crystals tent to group. The upper slice shows the suspension in the zone D (steady state zone), characterized by Z-crystals.

Figure 6 -

 6 Figure 6 -The four morphological zone for the all the temperature profiles. The upper diagram shows the subdivision of each sample in the morphological zones. The lower diagram shows the results of the radiography at the end of the solidification process.

Figure 7 -

 7 Figure 7 -The upper diagram shows the temperature profiles applied at the base of the colloidal suspension (a). The lower diagram shows the particle fraction as a function of the distance from the base of the suspension, plotted for all the temperature profiles (b).

Figure 8 -

 8 Figure 8 -The correction of the error due to the shape of the solidification front.The diagram on the right shows the prediction by finite elements of the shape of the solidification front in three instants of the process. The uncertainty generated by the shape of the freezing front presents an upper and a lower limit. The error, defined as the difference between the upper and the lower limit, is plotted in the bottom diagram.

Figure 9 -

 9 Figure 9 -The comparative diagrams of the velocity of the freezing front. The experimental results (test, solid line) are compared to the results by finite elements (FE, dashed line) and analytical model (ODE, meshed pattern line). The upper diagram shows the velocities of the freezing front when a constant or linear temperature profile is applied at the base of the suspension (a). The lower diagram shows the velocities in the cases of the parabolic temperature profiles (b). The velocity was calculated by differentiating the position of the freezing front, considered as the projection of the front on the mould, and corrected according to the error estimation described by Figure 6.

  The formulation of the Stefan problem is

Table 1 -Thermal properties (FEM and analytical modeling)

 1

		L-phase	S-phase copper polypropylene
	kT [W/mK]	0.6	0.9187	403	0.12
	Cp
	[J/Kg	2434	1457	385	1925
	K]
	ρ [Kg/m³]	2426	2218	8930	950

Table 2 -Morphological zones

 2 Details on the analytical modelThe Stefan problem requires the estimation of the numbers of Stefan (St) and Lewis (Le). The two numbers are defined as following: T is the absolute local temperature of the suspension, and D0 is the Stokes-Einstein diffusivity, defined as follows:

	Zone	R-crystals	Z-crystals	morphological
				stability
	A	growing	growing	no
	B	stop growth growing	no
	C	no	growing	no
	D	no	yes	yes

T

,

ACKNOWLEDGEMENTS

Financial support was provided by the National Research Agency (ANR), project NACRE in the non-thematic BLANC programme, reference BLAN07-2_192446.


Julie Russias

Eduardo Saiz

Sylvain Deville

Karol Gryn

G Liu

Ravi K Nalla

Antoni P Tomsia

Fabrication and in vitro characterization of threedimensional organic/inorganic scaffolds by robocasting

A key issue for the fabrication of scaffolds for tissue engineering is the development of processing techniques flexible enough to produce materials with a wide spectrum of solubility (bioresorption rates) and mechanical properties matching those of calcified tissues. These techniques must also have the capability of generating adequate porosity to further serve as a framework for cell penetration, new bone formation, and subsequent remodeling. In this study, we show how hybrid organic/inorganic scaffolds with controlled microstructures can be built using robotic assisted deposition at room temperature. Polylactide or polycaprolactone scaffolds with pore sizes ranging between 200-500 μm and hydroxyapatite contents up to 70 wt % were fabricated. Compressive tests revealed an anisotropic behavior of the scaffolds, strongly dependent on their chemical composition. The inclusion of an inorganic component increased their stiffness but they were not brittle and could be easily machined even for ceramic contents up to 70 wt %. The mechanical properties of hybrid scaffolds did not degrade significantly after 20 days in simulated body fluid. However, the stiffness of pure polylactide scaffolds increased drastically due to polymer densification. Scaffolds containing bioactive glasses were also printed. After 20 days in simulated body fluid they developed an apatite layer on their surface.

INTRODUCTION

The demand for biomaterials to assist or replace organ functions and improve quality of life is rapidly increasing. [START_REF] Service | Tissue engineers build new bone[END_REF] Traditional biomaterials for bone replacement are developed from materials designed originally for engineering applications that have serious shortcomings associated to the fact that their physical properties do not match those of the surrounding tissue and, unlike natural bone, cannot self-repair or adapt to changing physiological conditions. Thus, an ideal solution, and a scientific research challenge, is to develop bone-like biomaterials (or tissue engineering scaffolds) that will be treated by the host as normal tissue matrices and will integrate with bone tissue while they are actively resorbed or remodeled in a programmed way, with controlled osteogenic activity. This material will require an interconnected pore network with tailored surface chemistry for cell growth and penetration, and the transport of nutrients and metabolic waste. It should degrade at a controlled rate matching the tissue repair rates producing only metabolically acceptable substances and releasing drugs or stimulating the growth of new bone tissue at the fracture site by slowly releasing bone growth factors (e.g., bone morphogenic protein or transforming growth factor-β) throughout its degradation process. In addition, its mechanical properties should match those of the host tissues and the strength and stability of the material-tissue interface should be maintained while the material is resorbed or remodeled.

In recent years, there has been an increasing interest in the fabrication of porous threedimensional structures with complex functionalities not only for use in tissue engineering but also for many other applications such energy generation, structural, electronics, etc. Techniques such as solvent casting, particulate leaching, gas foaming, etc. [START_REF] Ambrosio | A novel amorphous calcium phosphate polymer ceramic for bone repair. Part 1: Synthesis and characterization[END_REF][START_REF] Mathieu | Architecture and properties of anisotropic polymer composite scaffolds for bone tissue engineering[END_REF][START_REF] Kothapalli | Biodegradable HA-PLA 3D porous scaffolds: Effect of nano-sized filler content on scaffold properties[END_REF][START_REF] Cheng | Fabrication and characterization of β-dicalcium silicate/poly(D,L-lactic acid) composite scaffolds[END_REF] have been traditionally used for synthesizing porous structures, but they suffer from numerous drawbacks including need for specialized tooling and molds, poor reproducibility, lack of proper control of porosity and interconnectivity, and, consequently, poor, unpredictable mechanical properties. This has been one of the motivations behind the development of new solid freeform fabrication techniques such as direct ink-jet printing, robotic assisted deposition or robocasting, and hot-melt printing, which usually involve "building" structures layer-by-layer by deposition of colloidal inks following a computer design; this can be achieved with great precision and reproducibility. [START_REF] Hollister | Porous scaffold design for tissue engineering[END_REF][START_REF] Roy | Performance of degradable composite bone repair products made via three-dimensional fabrication techniques[END_REF][START_REF] Xiong | Fabrication of porous scaffolds for bone tissue engineering via low-temperature deposition[END_REF][START_REF] Kalita | Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling[END_REF][START_REF] Chu | Mechanical and in vivo performance of hydroxyapatite implants with controlled architectures[END_REF][START_REF] Grida | Extrusion freeforming of ceramics through fine nozzles[END_REF] One of the techniques that is gaining popularity during the last few years is robocasting [START_REF] Cesarano | Freeforming objects with low-binder slurry[END_REF][START_REF] Smay | Colloidal inks for directed assembly of 3-D periodic structures[END_REF] where computer-controlled deposition of a thick slurry is performed to form three-dimensional structures layer-wise at room temperature. Until now, robocasting has been used to print ceramic inks where consolidation of the structures is achieved through a fluid through-gel transition during printing. [START_REF] Michna | Concentrated hydroxyapatite inks for direct-write assembly of 3-D periodic scaffolds[END_REF] One of the great challenges is to develop the right inks or suspensions to print materials with a wider range of chemistries with precision and reproducibility. In this work, we demonstrate how this technique can be used to build three-dimensional organic/inorganic hybrid structures with controlled porosity, custom compositions, and appealing mechanical properties. The inorganic component of the materials is either hydroxyapatite (HA), an osteoconductive calcium phosphate closely related to the inorganic component of bone, or a bioactive silica-based glass. Since the formulation of the first bioactive glasses by Hench, they have been extensively used in the fabrication of biomaterials and composites due to their capacity to generate hydroxyapatite and form excellent bond with osseous tissue. [START_REF] Hench | Third-generation biomedical materials[END_REF] For the organic component we have chosen either polylactide (PLA) or polycaprolactone (PCL), two biocompatible and fully resorbable polymers with different stiffness, approved by the Food and Drug Administration (FDA) for medical applications. The work describes the development of hybrid inks for the fabrication of porous scaffolds by robotic assisted deposition and analyzes the physicochemical factors that control their final properties, in particular their in vitro evolution in simulated body fluid.

MATERIALS AND METHODS

Scaffolds fabrication

The inorganic component of the hybrid inks was either commercially available HA powders (Trans-tech Adamstown, MD, USA) with a particle size between 1 and 3 μm [Fig. 1(a)], Bioglass® with the composition 45S5 developed by Hench or a high-silica bioactive glass originally developed in our laboratory for the fabrication of coatings on metallic alloys (6P53B)16 (Table I). The glass powders have a wide particle size distribution with an average of ∼13 ± 2 μm [START_REF] Lopez-Esteban | Bioactive glass coatings for orthopedic metallic implants[END_REF] [Fig. 1(b)]. Properties of the different materials used (density, Young's modulus, and compressive strength) are given in Table II. Two different polymers were used in the inks: polylactide (PLA) (molecular weight = 92.1 kg/mol, 86.4% L isomer) and polycaprolactone (PCL) (Sigma Aldrich, Saint-Louis, MO, USA, molecular weight = 80 kg/mol). To prepare the inks, 5 g of polymer (PLA or PCL) were dissolved in 15 mL of methylene chloride (J.T. Baker, Phillipsburg, NJ, USA) at room temperature for 2 h using a magnetic stirrer. The required amount of HA or glass was added to the solution, together with 5 mL of denatured ethanol (water content <0.1%) to control the viscosity of the slurry and the evaporation kinetics and homogenized in a ball mill with alumina balls for 1 h. The final quality of the ink was assessed in terms of printability-measured as the minimum tip diameter suitable to extrude the ink without clogging and stability (i.e., shape retention capacity during drying and sintering) of the assembled structures.

Porous scaffolds were printed with a robocasting machine (3D inks, Stillwater, OK, USA) whose 3-axis motion was independently controlled by a custom-designed, computer aided direct-write program (Robocad 3.0, 3D inks, Stillwater, OK, USA). The deposition process was carried out in ambient atmosphere at room temperature. The three-dimensional periodic scaffolds (∼15 × 15 mm2 in length and ∼4 mm in height corresponding to 17 layers) consisted of a linear array of parallel rods in each layer aligned such that their orientation was orthogonal to the previous layer [Fig. 2(a)]. The center-to-center rod spacing was varied between 0.5 and 1 mm in order to change the porosity of the samples. Once a layer was printed, the nozzle was raised by a fixed height, which depends on the tip diameter, and another layer was deposited. The diameter of the printing nozzles was varied from 5 to 410 μm and the printing speed between 5 and 20 mm/s. During printing, the flow rate was adjusted to the nozzle diameter and the printing speed [Eq. ( 1)] in order to print a continuous line of uniform thickness:

𝑉 = 𝜑 𝜑 2 𝑉
where V p is the speed of the piston, ϕ t is the diameter of the tip, ϕ s is the diameter of the syringe, and Vw is the printing speed. Samples were printed on glass slides and were easily removed after drying overnight at room temperature in air.

Physical, microstructural, and mechanical characterization

The average porosity was calculated using the measured diameter of the printed rods and their spacing. The microstructure and composition of the printed parts were analyzed by X-ray diffraction (D500 diffractometer, Siemens AG, Munich, Germany), optical microscopy (Axiotech microscope, Carl Zeiss AG, Oberkochen, Germany), and environmental-scanning electron microscopy (ESEM: S-4300SE/N, Hitachi, USA) with associated energy dispersive spectroscopy (EDS). To obtain a three-dimensional perspective of the structure, particularly to reveal subsurface defects, synchrotron X-ray computed tomography was performed at the Advanced Light Source (ALS, Berkeley, CA). Imaging was achieved on representative structures with 26 keV monochromatic X-rays and a 6 μm voxel size (resolution). The tomography data were reconstructed into three-dimensional images by a Fourier-filtered back-projection algorithm as described in detail elsewhere. [START_REF] Kinney | X-Ray tomographic microscopy (XTM) using synchrotron radiation[END_REF] The Vickers micro hardness of the printed lines was measured by placing at least five indentations on 6 μm polished surfaces with a load of 30 g. Compression tests of strength, in the direction parallel and perpendicular to the printing plane, were carried out on a ELF® 3200 series voice-coil mechanical testing machine (EnduraTEC Inc., Minnetonka, MN) with a crosshead speed of 0.2 mm/min on pieces (4 × 3 × 3 mm3) cut with a blade from the printed scaffolds. At least four tests were performed for each composition and each direction.

The in vitro response of the scaffolds was studied by immersing the samples in 30 mL of simulated body fluid (Table III) at 37°C for 20 days. The solution was prepared by dissolving reagent-grade chemicals of NaCl, NaHCO3, KCl, K2HPO4, MgCl2.6H2O, CaCl2, and (CH2OH)3CNH2 into distilled water and buffered with HCl to pH 7.25 at 37°C. 23 The evolution of the pH in the solution was measured with a pH meter (model 3000, VWR Scientific). After 20 days of immersion, the samples were washed with large amounts of distilled water and air dried prior to microstructural and mechanical characterization.

Table III Thermal properties of PLA (in as received conditions, after 20 days at 37°C in air and after 20 days at 37°C in SBF) were determined using a differential scanning calorimeter (DSC). The measurements were run under Neon/Helium 50/50 volume mixture gas at a heating rate of 100°C/min using a Perkin Elmer Diamond DSC calibrated with indium. The typical sample weight was 1 mg. There was no thermal treatment of the samples before the first heating scan in order to preserve their history. The reported glass transition temperatures (Tg) were taken as the mid-point of the step transition based on first heating scans from 25 to 150°C.

RESULTS AND DISCUSSION

Physical and microstructural characterization of the printed samples

The process used in the preparation of the inks is based on the dissolution of the polymers in methylene chloride, like the standard procedure used for the preparation of biodegradable polymer and HA/polymer microspheres for drug delivery and composite fabrication. [START_REF] Odonnell | Preparation of microspheres by the solvent evaporation technique[END_REF][START_REF] Russias | Microspheres as building blocks for hydroxyapatite/polylactide biodegradable composites[END_REF] The two key differences are that no polyvinyl alcohol or any other difficult to eliminate and potentially toxic surfactants are used and that small quantities of a second organic phase (ethanol) are added in order to tailor the ink viscosity and drying rates to the printing conditions. During printing, solvent evaporation creates a solid skin on the extruded line immediately after it exits the tip [Fig. 2(b)]. This skin confers some degree of rigidity to the printed line and allows the fabrication of stable three-dimensional structures [Figs. 2(c,d)]. Consolidation of the lines is achieved by matching the printing speeds to the drying kinetics of the ink. For very slow printing speeds (typically less than 5 mm/s), the paste will dry up in the printing nozzle, thus clogging it; if the printing speed is too fast (faster than 20 mm/s), the line diameter is not homogeneous and the lines can be discontinuous.

The printing behavior of the inks also depends on their inorganic content. High particle loads can result in large viscosities and poor printability. However, by adjusting the amount of ethanol (the amount of ethanol vs. inorganics, i.e., ceramic powders, is ∼40 wt %) it is possible to prepare hybrid scaffolds with inorganic contents as large as 70 wt %, very close to the mineral content of cortical bone. This is very important since the ceramic content influences the stiffness, a key mechanical parameter that should be matched with the host tissue. Typical required Young's modulus (E) varies between 0.4 and 350 MPa for soft tissue and cartilage and up to 10-1500 MPa for hard tissue.6 Particular attention should be paid to the control of the evaporation of the organic component during ink preparation. Because of the use of methylene chloride as a solvent, drying is quite rapid and the ink properties need to be maintained in the range adequate for printing by hermetically sealing the containers. However, because the main mechanism of consolidation is drying, control of the rheological properties does not need to be as strict as for ceramic inks. [START_REF] Smay | Colloidal inks for directed assembly of 3-D periodic structures[END_REF] Furthermore, during robocasting of ceramic parts different strategies (such as printing in oil baths) are used to avoid drying and the associated dimensional changes and stresses during printing. [START_REF] Miranda | Sintering and robocasting of β-tricalcium phosphate scaffolds for orthopedic applications[END_REF] In the process described in this work, the viscoplastic behavior of the parts allows them to sustain the stresses generated during simultaneous printing and drying. This viscoplastic nature permits further stretching of the printed line to form thin polymer and polymer/ceramic fibers and ribbons (down to 1 μm in diameter). Figure 3 shows very thin polymer and hybrid threads fabricated in this manner. It can be clearly observed that the minimum achievable diameter of the thread is controlled by the size of ceramic particles. Biodegradable fibers can be used in drug delivery applications or in the fabrication of meshes for implants and scaffolds. It was not possible to successfully prepare an ink containing the Bioglass composition developed by Hench. This is attributed to the highly hygroscopic nature of this glass (related to its high bioactivity) that promotes fast reactions with small amounts of water in the environment or in the ink. This fact also hampers the use of Bioglass in the preparation of suspensions to coat metallic alloys by enameling [START_REF] Pazo | Silicate glass coatings on Ti-based implants[END_REF] and motivated the development of a family of high-silica bioactive glasses like 6P53B that are much less hygroscopic and more amenable to the preparation of suspensions. Although several techniques have been proposed to prepare Bioglass/polymer foams and porous materials [START_REF] Rezwan | Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering[END_REF][START_REF] Kazarian | Characterisation of bioactive and resorbable polylactide/Bioglass(R)) composites by FTIR spectroscopic imaging[END_REF][START_REF] Chen | Poly(D,L-lactic acid) coated 45S5 bioglass (R)-based scaffolds: Processing and characterization[END_REF] by using the 6P53B composition, it was possible to prepare hybrid inks optimized for rapid prototyping.

Partial wetting of the ink on the printed material increases the contact area and provides better bonding between lines [Fig. 4(a)], enhancing the stability of the structure.

In the hybrid scaffolds the ceramic phase is homogeneously distributed in the polymer [Fig. 4(b)] and there are no visible surface defects or microporosity. By changing the center-to-center rod spacing (0.5 and 1 mm), samples with 2 different porosities are The final line thickness depends on several factors: nozzle diameter, printing speed, printing height [ΔZ in Fig. 2(b)], and drying shrinkage (typically ∼25% in volume).

After leaving the nozzle, the ink was observed to swell, with the degree of swelling depending on the printing speed (flow rate) and the nozzle diameter. As shown in Figure 5, for a 410-μm tip, the swelling and the printing speed influence are minimal and the drying shrinkage is important since the final average line diameter is around 200 μm. For a very thin capillary of 5 μm, there is a significant swelling that can be controlled by increasing the printing speed and the diameter of the printed lines can be reduced from 400 to 100 μm, without affecting the pore size, by changing the printing speed from 5 to 20 mm/s. In a further step, the scaffolds can be infiltrated to make dense samples with controlled composition and phase distributions. By using phases with different degradation rates porosity can be created "in situ" providing interesting possibilities for the control of the bioresoption and the mechanical behavior in vivo. For example, we have been able to successfully infiltrate a PLA/HA (70 wt % of HA) scaffold with a PCL/HA slurry (70 wt % of HA, with a slurry prepared exactly in the same conditions than the inks for printing) under vacuum (150 mbar) without leaving residual porosity (Fig. 6). The systematic analysis of the microstructure and properties of these materials will be the subject of a future work.

In vitro behavior in simulated body fluid

In vitro tests in cell-free solutions with ionic concentrations similar to those of body fluids allows analysis of the chemical and microstructural evolution of the materials under conditions that simulate their biological interactions with the body and provide fundamental data to predict and understand their in vivo behavior and long term stability. [START_REF] Kokubo | Solutions able to reproduce in vivo surface-structure change in bioactive glass-ceramic A-W[END_REF] After 20 days in simulated body fluid microporosity develops on the surface of pure PLA scaffolds (pore size from 0.5 to 1 μm) (Fig. 7). To analyze the possible changes in the polymer structure induced by the in vitro treatment at 37°C, DSC analysis of the "as received" PLA and after 20 days at 37°C in air and in SBF are performed (Fig. 8). The DSC analysis confirms that, as expected, the as received PLA is amorphous since it contains 14% of D isomer. However, its glass transition temperature increases from 33.0°C for the as received materials to 49.1°C after 20 days at 37°C or to 60.8°C after 20 days at 37°C in SBF. These results indicate that the structure of the polymer is changing during the in vitro tests: the polymer chains are organizing and the polymer is getting denser. This temperature and humidity are two factors responsible for the densification of the PLA. No diffusion of SBF ions into the polymer is observed by EDS analyses. The volume change associated with the densification might be responsible for the formation of the micropores. The addition of HA to the PLA reduces significantly the shrinkage of the material and micron size pores do not form on HA/PLA scaffolds even after 20 days in SBF. Degradation of the PCL-based scaffolds (with or without hydroxyapatite) results in the formation of a network of polymer fibers between the printed lines (Fig. 9) while their surface becomes rougher. The formation of acidic products during the hydrolytic degradation of resorbable polymer materials has been reported to cause adverse body reactions and additions of various calcium phosphates to the polymer have been proposed as a mean to buffer the release of acidic products and avoid these reactions. [START_REF] Hutmacher | Scaffolds in tissue engineering bone and cartilage[END_REF][START_REF] Bergsma | Late degradation tissue-response to poly(lactide) bone plates and screws[END_REF][START_REF] Vandergiessen | Marked inflammatory sequelae to implantation of biodegradable and nonbiodegradable polymers in porcine coronary arteries[END_REF][START_REF] Trantolo | Buffered biodegradable internal fixation devices[END_REF] Figure 10 shows the pH evolution of the simulated body fluid solution in which the PLA-based samples were immersed. The behavior is similar for PCL based scaffolds. The pH remains stable, around 7.25, for pure polymer and HA/polymer composites. The presence of glass particles has two effects: the pH of the solution increases to reach 7.8 after 20 days of immersion for scaffolds containing 6P53B glass and apatite crystals precipitate on the scaffold surface (Fig. 11). This is due to a rapid ion exchange of Na+ from the glass with H+ and H3O+ followed by a polycondensation reaction of surface silanols to create a highsurface area silica gel. This gel can provide a large number of sites for heterogeneous nucleation and crystallization of a biologically reactive hydroxy-carbonate apatite (HCA) layer equivalent to the inorganic mineral phase of bone. [START_REF] Hench | Third-generation biomedical materials[END_REF] The ion exchange from the bioactive glass can buffer the acidic products resulting from polymer degradation and promote apatite precipitation. It has been proposed that this growing apatite layer favors the bonding to bone of bioactive glasses and has a significant impact on the activity of osteogenic cells.

Mechanical characterization

Microhardness

As expected from the intrinsic properties of the polymers (Table II) the printed lines of the PLA-based scaffolds are much harder than the equivalent PCL composites (Fig. 12). The hardness of the glass is 6.2 GPa. [START_REF] Lopez-Esteban | Bioactive glass coatings for orthopedic metallic implants[END_REF] There is a wide spread in the hardness data reported for sintered HA but it seems to range between 3.5 and 6.5 GPa for a fully dense ceramic. [START_REF] Hoepfner | The influence of the microstructure on the hardness of sintered hydroxyapatite[END_REF][START_REF] Kumar | Modulus and hardness evaluations of sintered bioceramic powders and functionally graded bioactive composites by nano-indentation technique[END_REF][START_REF] Thangamani | The effect of powder processing on densification, microstructure and mechanical properties of hydroxyapatite[END_REF] The addition of glass increases the hardness but there is a larger dispersion in the measurements probably due to the larger grain size and the larger dispersion of the grain size distribution. After immersion in simulated body fluid the hardness of pure PLA and PLA/HA materials increase slightly. This might be due to the observed densification of the polylactide during the in vitro tests.

Figure 12: Micro hardness of the printed lines samples in as received conditions and after 20 days in a SBF. Organic/inorganic samples have 70 wt % of inorganic phase.

Compression strengths

Compression tests are performed in two directions (Fig. 13), perpendicular (direction 1) and parallel (direction 2) to the printing plane. During the tests, the scaffolds do not fail in a brittle manner and show an elasto-plastic response with large plastic "yielding". The insets on Figure 13 show SEM pictures of the samples in both directions after compression. Only PLA/HA samples tested in the direction 2 show a maximum in the stress vs. strain curve at around 7-10 MPa. This is probably due to the fact that they are harder and stiffer and the printed lines buckle instead of being continuously deformed like in the other scaffolds (Fig. 13). The lines do not debond during testing in any direction, indicating excellent adhesion between the printed rods. The stress-strain curves for samples with the same composition and microsctructure are very similar (Fig. 13), allowing the comparison of the mechanical response of different materials. Considering the samples' geometry and due to their large deformation, it is difficult to calculate an absolute value of the Young's modulus from the compression tests. However, the slope of the compression curves (calculated using a linear fit of the data up to the elastic limit) can provide several trends.

1. The porosity (in the range used in this work, between 55 and 75 vol %) does not affect significantly the mechanical response of the samples. 2. The mechanical response of the scaffolds is clearly anisotropic (Fig. 13).

3. The mechanical properties can be easily adjusted by controlling the composition of the material: type of polymer and inorganic content. Addition of up to 70 wt % of hydroxyapatite increases the stiffness up to two orders of magnitude [Fig. 14(a)] and PLA-based scaffolds are much stiffer than those containing PCL [Fig. 14(b)]. For an HA/polymer scaffolds with a porosity of 55% (pore size ∼200 × 200 μm2) and an HA content of 70 wt %, the values of the slopes in the direction perpendicular to the printing plane varies between 84 ± 9 MPa for a PLA-based materials and 24 ± 5 MPa for PCL-based materials. In the parallel direction, the slopes vary between 150 ± 40 and 110 ± 20 MPa for PLA and PCL-based scaffolds, respectively. This is expected since the elastic modulus of dense PLA and PCL are respectively 2.7 and 0.4 GPa (Table II). 4. After twenty days in SBF, pure PLA scaffolds become much stiffer and the slope of the strain-stress curve up to the elastic limit increases from 3 ± 2 to 76 ± 19 MPa [Fig. 15(a)]. Like the parallel increase in microhardness, this is related to the observed densification of the polymer as a result of the in vitro treatment.

The PLA scaffolds also become stiffer after 20 days in air at 37°C. The slope's average value of their strain-stress curve up to the elastic limit is 35 ± 6 MPa.

As it is confirmed by the DSC analysis, the long treatment at 37°C promotes densification and this process is enhanced in SBF (Fig. 8). The moisture plasticizes the polymer chains favoring their rearrangement and enhancing densification. This result suggests that thermal treatments can be used to further manipulate the mechanical response of the material.

SUMMARY

This work demonstrates how robotic assisted deposition can be successfully used for the fabrication of porous hybrid organic/inorganic materials of various chemical compositions with well controlled architecture and porosity. The technique is versatile enough to allow the combination of a wide range of materials, including bioactive glasses whose addition can be used to buffer the possible formation of acidic degradation product coming from the hydrolytic degradation of the polymer and to promote apatite formation. In addition, by selecting the adequate organic component and manipulating the organic/inorganic ratio of the scaffolds, we can control their stiffness and fabricate materials much more rigid than porous polymers while avoiding the brittleness of ceramic parts. Moreover, multi-component materials can be fabricated through the simultaneous use of multiple nozzles and because the processing is performed at room temperature, in situ seeding with cells and addition of drugs or growth factors to the organic component is easily achievable. These characteristics suggest that robotic assisted deposition can be a fast and economical alternative for the fabrication of "on demand" scaffolds for biomedical applications.

Figure 1 :

 1 Figure 1: Scanning electron micrograph of (a) hydroxyapatite powders and (b) 6P53B glass powders used in this work.

Figure 2 :

 2 Figure 2: (a) Schematic representation of the robocasting process. The syringe displacement and the liquid flow through the nozzle are controlled by the computer. (b) During the printing, the inks swell after leaving the capillaries and the evaporation of the solvent creates a solid skin favoring the consolidation of the printed line. (c) Low magnification picture showing one of the scaffolds fabricates in this study (HA/PLA, 70 wt % HA scaffold with 17 layers). (d) Three-dimensional reconstructed image of a HA/PLA (70 wt % HA) grid obtained by synchrotron X-ray computed tomography. It can be observed that the material does not exhibit large defects

27

 27

Figure 3 :

 3 Figure 3: (a) Pure PLA flexible ribbon and (b) thin HA/PLA (30/70 wt %) thread extruded after printing. Hydroxyapatite grains are embedded in the polymer fiber and determine its minimum diameter.

  processed. A center-to-center rod spacing of 0.5 mm corresponds to a porosity of 55% and a pore size of about 200 µm [Fig.4(c)], while a center-to-center rod spacing of 1 mm gives a porosity of 75% and a pore size of about 500 µm [Fig.4(d)].

Figure 4 :

 4 Figure 4: Scanning electron micrographs showing different aspects of the microstructure. All the scaffolds showed in this picture have been printed using a nozzle with an internal diameter of 410 μm. (a) Three-dimensional reconstructed image of the junction between HA/PLA (70 wt % HA) printed lines obtained by synchrotron X-ray computed tomography. It can be observed that the ink wets partially the printed lines providing additional support and leading to good bonding between lines (white circles). (b) Close up of an HA/PLA (70 wt % HA) printed line showing the homogeneous distribution of the HA particles (white) in the polymer. (c) HA/PCL (70 wt % HA) scaffold (center-to-center rod spacing ∼0.5 mm, corresponding to a porosity of ∼55%); the pore size and thickness of the printed lines is very homogeneous. (d) 6P53B glass/PLA (70 wt % 6P53B glass) scaffold (center-to-center rod spacing ∼1 mm, corresponding to a porosity of ∼75%).

Figure 5 :

 5 Figure 5: Evolution of the final line diameter versus the printing speed for the printing of a pure PLA ink through nozzles with two internal diameters. The insert shows a scanning electron micrograph of a PLA grid printed with a 5-μm tip at a printing speed of 15 mm/s.

Figure 6 :

 6 Figure 6: Scanning electron micrograph of a PLA/HA (70 wt % HA) scaffold cross section infiltrated with PCL/HA (70 wt % HA). No residual porosity can be observed after the infiltration process.

Figure 7 :

 7 Figure 7: (a) Scanning electron micrographs of a PLA scaffold after 20 days in SBF. Note the presence of micron size pores homogeneously dispersed on the polymer surface. (b) The inset shows these pores at a larger magnification.

Figure 8 :

 8 Figure 8: Evolution of the glass transition temperature and stiffness up to the elastic limit for PLA scaffolds in an as received condition, after 20 days at 37°C in air and after 20 days at 37°C in simulated body fluid.

Figure 9 :

 9 Figure 9: Scanning electron micrograph of a PCL/HA (70 wt % HA) scaffold after 20 days in SBF. Polymer filaments are bridging the lines. The degradation of the scaffold surface is clearly visible.

35

 35

Figure 10 :

 10 Figure 10: pH evolution of the solution during 20 days of immersion in SBF for PLA, PLA/HA, and PLA/6P53B glass materials. Note the increase in pH for the 6P53B glass/PLA scaffold.

Figure 11 :

 11 Figure 11: Scanning electron micrographs of the 6P53B glass/PLA scaffold after 20 days of immersion in SBF. (a) Apatite crystals have precipitated on the scaffold surface. (b) The apatite layers consist of small nano-crystals (inferior to 50 nm) that cover progressively the scaffold.

Figure 13 :

 13 Figure 13: Strain-stress curves obtained from compression tests made on different grids of HA/PLA (70 wt % HA) samples with 55% of porosity in the two directions (a) perpendicular (direction 1) and (b) parallel (direction 2) to the printing plane. The insets show some SEM images of the samples after compression tests in direction 1 and 2. The stress-strain curves in each direction are very similar. The samples do not fail in a brittle manner and the behavior is anisotropic. Buckling of the printed lines of the PLA/HA scaffolds can be clearly observed in the inset [Fig. 13(b)].

5 .

 5 The compressive behavior of the PLA or PCL-based hybrid scaffolds containing 70 wt % of hydroxyapatite do not change significantly after 20 days in simulated body fluid. The elastic modulus of HA is 10-100 times larger than the one of the polymer (TableII) and the main contribution to the Young's modulus of the composites comes from the inorganic phase that does not undergo any visible degradation during in vitro testing in SBF. However, the bioactive glasses react with simulated body fluid and there is an appreciable decrease of the stiffness in the scaffolds containing 6P53B after 20 days in SBF [Fig.15(b)].

Figure 14 :

 14 Figure 14: (a) Influence of the ceramic content on the compressive behavior of the scaffolds. The strain-stress curves are obtained from compression tests made on PLA and HA/PLA samples in two directions. Addition of hydroxyapatite increases significantly the stiffness of the material. (b) Influence of the organic phase. Samples containing PLA are stiffer.

Figure 15 :

 15 Figure 15: (a) Strain-stress curves obtained from compression tests made on pure PLA samples in the direction 1. The sample has become stiffer after in vitro testing in SBF. (b) Strain-stress curves obtained from compression tests made on 6P53B glass/PLA (70 wt % 6P53B glass) samples in the direction 1.Before immersion, 6P53B glass/PLA composites have a slope's average value of their strain-stress curve up to the elastic limit of 105 ± 18 MPa. This value is comparable with the one of the as received HA/PLA in direction 1. After 20 days in a physiological environment, the slope's average value of the composites with bioactive glass decreases to 62 ± 10 MPa (∼40% reduction) due to a partial dissolution of the glass in the solution before the formation of apatite crystals at the surface of the scaffold.

Table I .

 I 6P53B and Bioglass Compositions in Weight and mol %. Values in parentheses are in mol %.

	SiO2	Na2O	K2O	CaO	MgO	P2O5
	6P53B 52.Bioglass 45 (46.1) 24.5 (24.3) 0.0 (0.0)	24.5 (26.9) 0.0 (0.0)	6.0 (2.6)
	Table II. Density, Young's Modulus, and Compressive Strength of the Raw Materials
	Density (g/cm 3 )	Young Modulus (GPa)	Compressive Strength (MPa)
	PLA	1.24	2.7 17		40-120 (pellet) 18
	PCL	1.14	0.4 17		-
	Sintered	3.16	35-120 19		120-900 19
	dense HA
	Bioglass®	2.7	35		∼500 18
	6P53 B	2.7 16	70 20		∼70 21

7 (51.9) 10.3 (9.8) 2.8 (1.8) 18.0 (19.0) 10.2 (15.0) 6.0 (2.5)

  . Ion Concentrations of the SBF used in this Work and of Human Plasma

	Ion Concentration (mM)
		Na + K +	Ca 2+ Mg 2+ Cl -HCO3 -	HPO4 2-	SO4 2-
	SBF	142.0 5.0	2.5	1.5	147.8 4.2	1.0	0.5
	Human plasma	142.0 5.0	2.5	1.5	103.0 27.0	1.0	0.5

Acknowledgements

We acknowledge the support of the dedicated tomography beamline (BL 8.3.2) at the Advanced Light Source (ALS).


Jérémy Dhainaut

Giulia Piana

Sylvain Deville

Christian Guizard

Michaela Klotz

Freezing-induced ordering of block copolymer micelles

We demonstrate here the ordering of block copolymer micelles by ice templating, below 0 °C. We used this for the preparation of silica monoliths that present an ice-templated macroporosity, combined with a 2D hexagonal mesostructure templated by the addition of P123. We propose a mechanism triggered by the progressive freezing-induced concentration.

Monoliths that combine hierarchical porosities in the range of mesopores and macropores have attracted widespread interest in catalysis and separation processes. Surfactant self-assembly can be combined with various macropore forming methods such as foaming, 1,2 spinodal decomposition, 3 or hard templating by colloidal crystals. 4 However, the macropores formed by these routes are tortuous. Conversely, ice templating is a processing route that yields straight macropores. Ice templating takes advantage of ice crystal growth to template macropores in the range of micrometers to tens of micrometers. 5 Under unidirectional solidification conditions, the ice crystals grow preferentially along the temperature gradient direction. As the solubility limit of almost any compound in ice is extremely low, any species present in the initial suspension will be rejected and progressively concentrated by the growing ice crystals. Sublimation of the ice crystals, followed by thermal treatment, leads to centimeter-sized monoliths with directional macropores.

Extensive research on silica thin film formation by evaporation induced self-assembly (EISA) showed that well-ordered mesoporous materials can only be obtained by controlling the hydrolysis and condensation of silicon alkoxide. 6,7 Building upon this experience, we want to trigger such concentration induced self-assembly by removing the solvent by freezing instead of evaporation. Similar sol-gel parameters (pH, ageing temperature, time, etc.) may then be relevant for structural control by ice templating. However, the process temperatures are below 0 °C, where, notwithstanding rare exceptions, 8 surfactants do not self-assemble into lyotropic liquid crystal mesophases. Pluronic 123 (P123) is a triblock copolymer composed of ethylene oxide (EO) and propylene oxide (PO) blocks with general formula (EO)20(PO)70(EO)20. The solubility of its EO and PO blocks is sensitive to temperature, and spherical micelles are only formed between 20 °C and 65 °C, even under acidic conditions. 9 Nonetheless, we demonstrate here that a favorable combination of ice templating, surfactant self-assembly, and solgel chemistry allows mesophase ordering of P123 by ice templating.

P123 was first dissolved in water at a mild temperature (<35 °C). In order to favor hydrolysis and limit condensation, the pH of the water was adjusted between 1.1 and 1.8 using hydrochloric acid. Tetraethylorthosilicate (TEOS) was then added to reach the following molar compositions: 1 SiO2 : 71-83 H2O : 0.017 P123. After ageing (<35 °C, 3 h), the as-formed ethanol was removed by rotary evaporation to increase the freezing point of the suspension. This suspension was then divided into two equivalent parts. The first one was let to evaporate at 90 °C in an oven, to trigger EISA. The second part was ice-templated, following the procedure described in S1 (ESI †), to cause freezing-induced self-assembly (FISA). Freezing of the solution occurred at -15 °C. After freeze-drying to selectively remove the ice crystals, both samples were thermally treated at 450 °C for 4 h with a heating rate of 1 °C min-1.

The mesostructure of EISA and freezing-induced self-assembled (FISA) samples were explored by TEM (Fig. 1 and Fig. S2,ESI †). 2D hexagonal structures with long-range ordering are observed in both cases. The pore-center-to-pore-center average distance was estimated to be 10.9 nm. Small angle X-ray diffraction patterns (Fig. 2 and Fig. S3, ESI †) of both samples exhibit three reflections that can be indexed according to the p6mm symmetry, the 2D hexagonal structure. The inter-reticular distances of reflections in both patterns are comparable. The most intense peak, at 2θ = 0.96°, can be indexed to the (10) plane, while reflections at 1.67° and 1.93° correspond, respectively, to the ( 11) and (20) planes of the planar p6mm space group. The corresponding cell parameter is 10.6 nm, a value consistent with the pore-center-to-pore-center distance estimated by TEM. These results clearly show that FISA, under the conditions reported here, results in organized mesoporosity. The diffracted intensities measured are a combination of the form factor and the structure factor. In the case of P123, both responses are in the same scattering region. This impacts the total intensity and can modify relative intensities between the diffracted peaks.10 TEM analysis of both samples indicates similar quality of ordering for EISA and FISA. The macroscopic pore structure obtained by FISA is shown in Fig. 3A. The arrow indicates the freezing direction. In comparison with macropores typically obtained for ice templated suspensions,11 the macropore structure has an open, foam-like morphology. A closer view of the fracture surface (Fig. 3B) reveals a 1.3 μm thick secondary pore structure, perpendicular to the macropore. TEM observations (Fig. S4,ESI †) confirmed the bundle-like organization in this region. Ordered mesopores obtained from P123 templating are oriented parallel to these bundles. This orientation is lost halfway through the inorganic wall. The interface between oriented and disordered pores is clearly visible. In the inner region, TEM observations (Fig. S5, ESI †) reveal a more random orientation of the mesopore domains. During ice templating, water transforms into ice crystals, which results in the segregation of any components, i.e. silica oligomers and tri block copolymer micelles, initially incorporated into the solution. This concentration effect is significant, as concentration will increase until a maximum value is reached. 12 HCl will also be rejected and locally shift the pH. Based on the fraction of ice crystals, and assuming that all species are rejected from the growing crystals, we can estimate the pH to decrease from 1.3 to 1. Therefore we propose, from the aforementioned experimental results, a mechanism in which the silica oligomers and the micelles are rejected by the ice crystals and rearrange themselves to form an ordered mesoporous structure. The micelles serve as sacrificial templates for mesopores whereas ice crystals are responsible for creating macroporous skeleton walls at the upper level. Interestingly, the SiO2/surfactant ratio (0.017) at which ordering occurs upon freezing is identical to the usual SiO2/surfactant ratio for the synthesis of SBA-15. 13 Thus, in comparison with EISA, [START_REF] Brinker | (ESI) available: Detailed synthesis protocol, small angle X-ray diffraction patterns, TEM images and mercury porosimetry[END_REF] we can also speculate that the extraction of the solvent by freezing induces block copolymer concentration, leading to an ordered mesostructure. However, at this stage, there is no experimental evidence of this mechanism and of whether the micelles may pre-exist in the initial solution or can be formed upon freezing. More experimental data are needed to identify the formation mechanism, which could be self-assembly, crystallisation, or precipitation. Due to the dynamic nature of the process, there is interplay between the thermodynamic and kinetic conditions, the question of whether the thermodynamic equilibrium is achieved or not is thus still open. The local conditions at the freezing front eventually change due to concentration by solvent extraction. Moreover they are probably different from the batch solution as for example the latent heat released by the solidification of water will impact the local temperature. Considering the experimental data of the present work, it can be only argued that the increase of the concentration triggers ordering of the micelles, which results in an ordered mesoporous structure.

The technique described here for the preparation of macroporous silica monoliths with organized mesoporous walls is reproducible (Tables S1 andS2, ESI †) and could potentially be suitable for the fabrication of other multi-scaled porous inorganic materials. These results are of interest at several levels. From a materials science point of view, the complex hierarchical porous materials exhibit a unique combination of very high pore volume, well-calibrated mesopores, and oriented macropores. Such structures may be of interest for applications where diffusion kinetics are critical, such as adsorbents, catalysts, and catalyst carriers, especially in liquid media. Because FISA occurs in the bulk, centimetre-sized or even larger monoliths can be processed. The principles of FISA described here are generic and may be extended to other self-assembly systems, inorganic matters, and solvents, relying on concentration gradients to trigger their organization.

Figure 1 :

 1 Figure 1: Comparative TEM images of (a) EISA and (b) FISA-templated mesoporous silica.

Figure 2 :

 2 Figure 2: Comparative small angle X-ray diffraction patterns of EISA and FISA-templated mesoporous silica.

Figure 3 :

 3 Figure 3: SEM images of FISA-templated mesoporous silica. Scale bars: 100 μm (A) and 500 nm (B).

Figure 4 :

 4 Figure 4: Nitrogen adsorption-desorption isotherm of FISA-templated mesoporous silica. The inset represents the BJH mesopore size distribution.

Acknowledgements

Financial support from Saint-Gobain is gratefully acknowledged. A. Addad is acknowledged for help with TEM imaging. The TEM facility in Lille (France) is supported by the Conseil Regional du Nord-Pas de Calais, and the European Regional Development Fund (ERDF).