Microstructure and properties of LZSA glass-ceramic foams

Materials Science and Engineering A 476 (2008) 89–97

Microstructure and properties of LZSA glass-ceramic foams E. de Sousa a , C.R. Rambo a,b,∗ , D. Hotza a,b , A.P. Novaes de Oliveira a,c , T. Fey d , P. Greil d a

Graduate Program on Materials Science and Engineering—PGMAT, Federal University of Santa Catarina—UFSC, P.O. Box 476, 88040-900 Florian´opolis, SC, Brazil b Department of Chemical Engineering—EQA, Federal University of Santa Catarina—UFSC, P.O. Box 476, 88040-900 Florian´ opolis, SC, Brazil c Department of Mechanical Engineering—EMC, Federal University of Santa Catarina—UFSC, P.O. Box 476, 88040-900 Florian´ opolis, SC, Brazil d Department of Materials Science, Glass and Ceramics, University of Erlangen-Nuremberg, Martensstrasse 5, D-91058 Erlangen, Germany Received 15 February 2007; received in revised form 16 April 2007; accepted 29 May 2007

Abstract Commercial polyurethane foams with a monomodal pore size distribution were used to produce LZSA glass-ceramic foams by the polymeric sponge method. A suspension containing LZSA glass powder, bentonite and sodium silicate was prepared in isopropanol to impregnate the polymeric foams by dip coating. The sintering conditions were varied in the range of 700–850 ◦ C for 30–180 min. The cellular microstructure of glass-ceramic foams was characterized by scanning electron microscopy (SEM) and micro-computer X-ray tomography (␮CT). Optimum physical, mechanical and fluidynamic properties of the LZSA glass-ceramic foams were obtained at 750 ◦ C for 60 min. Main crystalline phases detected were ␤-spodumene and zirconium silicate. The compressive strength of the foams (0.1–10 MPa) is strongly dependent on their overall porosity and their behaviour could be explained using the Gibson-Ashby model. The Darcyan permeability of LZSA foams was found to be in the range of 0.1–4 × 10−9 m2 , which is in the order of magnitude of cellular supports for aerosol filters, and, therefore, suitable for several other technological applications. © 2007 Elsevier B.V. All rights reserved. Keywords: Cellular materials; Glass-ceramic foams; Polymeric sponge method; Mechanical properties; Permeability

1. Introduction The interest in ceramic foams has increased along with new processes and applications. Several synthesis routes are available to produce this class of materials such as bubbles generation in slurries or in a green body during a specific thermal treatment, control of sintering conditions in order to achieve a partial densification, reaction sintering, sol–gel methods, direct foaming, pyrolysis of organic additives and polymeric sponge method [1–3]. The choice of a processing technique depends on the desired structure, e.g. open or closed cells, pore size and pore geometry. The polymeric sponge method (PSM), also known as replica method, offers a simple, inexpensive and versatile way for producing ceramic foams. This method consists of dipping the ∗ Corresponding author at: Department of Chemical Engineering—EQA, Federal University of Santa Catarina—UFSC, P.O. Box 476, 88040-900 Florian´opolis, SC, Brazil. Tel.: +55 48 3721 9448; fax: +55 48 3721 9687. E-mail address: [email protected] (C.R. Rambo).

0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.05.098

polymeric sponge into a slurry containing ceramic particles and appropriate additives (binders, dispersants, etc.) followed by drying and heating to burn out the organic part, leading to an open-cell ceramic skeleton [4]. The most common applications for open-cell ceramics are catalyst supports and molten metal, hot gas and diesel exhaust filters [5]. In filtration applications, the main criteria to evaluate the ceramic filters are permeability, efficiency for removing impurities and mechanical strength [6]. Ideally, the ceramic filter should be able to remove the maximum of impurities with minimum resistance to the flow of fluids [6]. This characteristic can be obtained by increasing the volume and/or increasing size of pores. However, these two options usually compromise the mechanical strength of the structure. Therefore, the optimization of the relationship permeability/mechanical strength depends on the ideal combination of pore size and porosity [7]. Additionally, in gas filtration, the fractional collection efficiency is also sensitive to the nominal pore count and tortuosity of the structural layer (ceramic foam support) [8,9]. Commercial ceramic foam filters with porosities between 70% and 90% exhibit Dar-

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cian permeability typically in the range of 10−10 to 10−8 m2 and compressive strength varying from 0.5 to 2 MPa [10]. Among a wide range of ceramics that can be used for filtration purposes, zirconia, silicon carbide and alumina are the most usual [11]. However, only few works dealt with the production of glass-ceramic foams. Glass-ceramics belonging to the Li2 O–ZrO2 –SiO2 –Al2 O3 (LZSA) system have been selected due their good chemical and thermal shock resistances [12] and a very low thermal expansion coefficient (4–6 × 10−6 ◦ C−1 ) [13]. These intrinsic properties of LZSA glass-ceramics make them suitable for applications where very low shrinkage at high temperatures is required (usually up to 700 ◦ C). Although PSM is a simple method, several processing parameters are important to produce a foam that exhibits the desired performance such as polymeric template, ceramic slurry (solid weight fraction, dispersion medium and additives), impregnation method and thermal treatment (drying, burning out the organic components and sintering the ceramic part). In former works, the rheological behaviour of LZSA parent glass powder suspensions in aqueous media was evaluated [14,15]. The suspensions were characterized by shear thinning behaviour and critical solid fraction of 50 vol.% or 72.45 wt.%, according to the Dougherty-Krieger model. For suspensions containing 60 wt.% solids, sodium silicate caused an increase in suspension viscosity and a thixotropic behaviour, which may be adequate for the polymeric sponge method. For an optimized impregnation by the PSM, the slurry must be fluid enough to enter, fill and uniformly coat the sponge network, and subsequently recover enough viscosity under static conditions to remain in the sponge [5,11]. This work evaluates the influence of sintering conditions on physical, mechanical and fluidynamic properties of the LZSA glass-ceramic foams prepared by the polymeric sponge method. 2. Experimental procedure The LZSA glass-ceramic was prepared from Li2 CO3 , ZrSiO4 , SiO2 and spodumene (Li2 O–ZrO2 –SiO2 –Al2 O3 ) as raw materials. Details of the preparation and characterization are described in a previous publication [16]. The slurry was prepared with isopropanol, containing 60 wt.% LZSA parent glass powder (Colorminas, 3.22 ␮m mean particle size, 4.95 m2 /g specific surface area and 2.63 g/cm3 density), 5 wt.% bentonite (Colorminas, 4.47 ␮m mean particle size, 29.45 m2 /g specific surface area and 2.49 g/cm3 density), used as a binder and 1 wt.% sodium silicate (Merck, Natronwasserglas 105621, 7.5–8.5% Na2 O, 25.5–28.5% SiO2 ) used as dispersant. Isopropanol was first mixed with sodium silicate in a plastic bottle with alumina balls as grinding media for 12 h. Subsequently, the glass powder was added to the solution and then milled for another 12 h. Finally, bentonite was added and the slurry was milled for another 12 h. Commercial polyurethane foams with a monomodal pore size distribution (55 ± 5 pores per inch) and porosity of 95 ± 1% were used as templates. The polymeric foams were cut in pieces of approximately 25 mm × 30 mm × 20 mm and immersed in the LZSA glass-ceramic slurry. The impregnated foams were

slightly compressed to remove the excess of slurry and dried at room temperature for 24 h. After drying, the samples were submitted to the heat treatment, which was performed in an electrical furnace in air. The samples were first heated up to 450 ◦ C at 1 ◦ C/min with 1 h soaking time to burn out the polymer chains without collapsing the deposited ceramic powder. Afterwards, the samples were sintered at different sintering temperatures (700, 750, 800 and 850 ◦ C) and soaking times (30, 60, 120 and 180 min) with a heating rate of 5 ◦ C/min. The cooling rate to room temperature was set to 10 ◦ C/min. The strut density (ρs ) was determined by He-pycnometer (AccuPyc 1330, Micromeritics, Norcross, GA) using powdered pieces of the samples. The pore volume (total porosity), ε, of a set of six samples of each batch was estimated from the relation between the strut density and the geometrical density, according to the expression: ε = (1 − ρG /ρs ), where ρG is the overall density of the LZSA foams (the mass of a sample divided by the geometrical measured volume). X-ray diffraction (XRD, Diffrac 500, Siemens AG, Mannheim, Germany) with Cu K␣ radiation was used to identify the phases of the LZSA glass-ceramic foams. The morphology and microstructure of LZSA glass-ceramic foam was analyzed by scanning electron microscopy (SEM, Philips, Model XL-30, Eindhoven, The Netherlands). The cell size and the strut thickness distribution were calculated using an X-ray microtomograph (␮CT40, Scanco Medical AG, Bassersdorf, Switzerland). The X-ray tube was equipped with a tungsten target and operated at 50 kV and 80 ␮A at a wavelength of 0.024 nm. The specimens were scanned in x, y and z directions with an isotropic resolution of 37 ␮m3 . A CCD line array was used to detect the transmitted intensity through the sample. Xray source and detector were covered with slit collimators. The object was rotated through 360◦ with one step per degree and the raw data were recorded as sinugrams. A detailed description of foam structure characterization by ␮CT was reported by Zeschky et al. [17]. The compression strength of a set of 12 samples with nominal dimensions of 25 mm × 30 mm × 20 mm was determined at room temperature using a universal testing device (Instron, Model 4202, Instron Corp., Canton, MA). The speed of the crosshead was set constant to 1 mm/min. The gas permeability of 5-mm thick cylindrical samples (with radius r = 5 mm) was measured using a gas flowmeter. The slices were sealed in an Al crucible that allows only one directional gas flow along the axis of the specimen. The air volumetric flow through the sample, q = V/t, was adjusted by a digital flow controller (Bronkhorst MFC-F201-AC-AAB33-V, Bronkhorst Hi-Tec, AK Ruurlo, The Netherlands), giving air velocities (vS ) up to 5 m/s. The pressure drop (P) through the sample was measured with a differential gas pressure sensor (Bronkhorst DP-P506-AAB-33-V, Bronkhorst Hi-Tec, AK Ruurlo, The Netherlands). Sets of 200 P × vS pairs were recorded. 3. Results and discussion Fig. 1 shows the influence of sintering temperature on the porosity of LZSA glass-ceramic foams. A wide range of poros-

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Fig. 1. Mean total porosity of LZSA glass-ceramic foams versus sintering temperature for different soak times. The lines are only guides for the eyes.

ity was reached, 62–88%. The porosity of the samples decreased with the increase of sintering temperature up to 750 ◦ C. After 750 ◦ C, the porosity increased slightly, except for samples sintering for 30 min soaking time, where the porosity decreased up to 800 ◦ C. The strut density of LZSA glass-ceramic foams sintered at different temperatures is shown in Fig. 2. The strut density decreases with the increase of sintering temperature. The accentuated decrease of the density at sintering temperatures above 750 ◦ C is related to the crystallization process. The XRD patterns of the samples sintered at 700–850 ◦ C for 60 min are shown in Fig. 3. The reflections associated with the sintered samples were assigned to the crystalline phases of zirconium silicate (ZrSiO4 , JCPDS file 72–0402, 4.6–4.8 g/cm3 ), zirconium oxide (ZrO2 , JCPDS file 78–0047, 5.70 g/cm3 ), lithium metasilicate (Li2 SiO3 , JCPDS file 29–0828, 2.52 g/cm3 ) and ␤-spodumene (LiAlSi3 O8 , JCPDS file 35–0794, 3.0–3.2 g/cm3 ). At 700 ◦ C, reflections assigned to the crystalline phases of ␤-spodumene, zirconium silicate and zirconium oxide were detected. On increasing sintering temperature, an increase in the intensity of the peaks related to ␤-spodumene can be observed. New peaks related to the

Fig. 2. Strut density of LZSA glass-ceramic foams versus sintering temperature for different soak times. The lines are only guides for the eyes.

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Fig. 3. XRD patterns of LZSA powdered foams, sintered for 60 min at 700, 750, 800, 850 ◦ C. M = lithium metasilicate (Li2 SiO3 ), Z = zirconium silicate (ZrSiO4 ), ZO = zirconium oxide (ZrO2 ) and S = ␤-spodumene (LiAlSi3 O8 ).

crystalline phase of zirconium silicate appeared at 750 ◦ C. At 800 ◦ C, reflections associated to the formation of a new crystalline phase, lithium metasilicate, which is undesirable due to its high coefficient of thermal expansion (8.6–11 × 10−6 ◦ C−1 ), and the vanishing of zirconium oxide are noticed. At 850 ◦ C, the crystalline phases present at 800 ◦ C are still noticed, and the peaks also increased in intensity. Therefore, two main crystalline phases were formed by the LZSA system, ␤-spodumene and zirconium silicate, which are responsible for the low coefficient of thermal expansion and high chemical and abrasion resistance, respectively. Density of glass-ceramic materials is a function of the densities of the crystalline phases formed and of the residual glass phase [18]. As already observed in Figs. 1 and 2, for the same sintering temperature samples sintered during different time intervals exhibited the same porosity and density tendencies. The difference on density for samples sintered at 700 and 750 ◦ C is not so accentuated. This result is related to the formation of the same crystalline phases at these temperatures. However, when the sintering temperature increases to 800 ◦ C, a remarkable difference on density is noticed. This difference is assigned to the new phase formed (lithium metasilicate) and to the absence of zirconium oxide. For all sintering temperatures, except for 750 ◦ C the densification was maximum when the samples where sintered for 60 min (700 ◦ C, 2.62 g/cm3 ; 750 ◦ C, 2.56 g/cm3 ; 800 ◦ C, 2.52 g/cm3 ; 850 ◦ C, 2.52 g/cm3 ). According to the density results, 60 min was the most adequate soaking time for sintering LZSA glass-ceramic foams. The influence of sintering temperature on the microstructure of the LZSA glass-ceramic foams sintered for 60 min is shown in Fig. 4. The samples sintered at 700 and 750 ◦ C maintained the pore structure of the original polyurethane template. The pores of the LZSA foams are mostly interconnected and round-shaped. Some closed cells on the samples surface can be also observed. For these temperatures, the struts exhibited some microporosity. For samples sintered at 800 and 850 ◦ C, the original pore morphology was not maintained and most of the pores were clogged, leading to a denser strut network. Therefore, a suit-

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Fig. 4. (a–h) SEM micrographs of LZSA glass-ceramic foams sintered for 60 min at different temperatures.

able sintering temperature for the LZSA glass-ceramic foams is 750 ◦ C. Fig. 5 shows the changes on the microstructure of the LZSA glass-ceramic foams sintered at 750 ◦ C for different soaking

times. The samples sintered at 750 ◦ C for 30, 60 and 120 min maintained the pore structure of the original polyurethane template. Again, the pores are mostly interconnected and roundshaped. Some closed cells on the samples surface can be also

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Fig. 5. (a–h) SEM micrographs of LZSA glass-ceramic foams sintered at 750 ◦ C for different soak times.

observed. Only samples sintered for 180 min did not reproduce the pore structure of the original polyurethane template. These results are in agreement with the porosity results shown in Fig. 1.

Fig. 6 shows ␮CT images of the LZSA glass-ceramic foams sintered at 700 and 850 ◦ C for 60 min. The 3D-reconstructed images display the main structural difference between the two samples, showing that the cellular morphology of the foam sin-

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Fig. 6. ␮CT 3D-images of glass-ceramic foams sintered for 60 min at: (a) 700 ◦ C and (b) 850 ◦ C.

tered at 700 ◦ C is more evident than on the foam sintered at 850 ◦ C, which exhibits a denser strut network. The mean strut thickness distribution of LZSA glass-ceramic foams sintered in different sintering temperatures is shown in Fig. 7. It can be seen that the mean strut thickness increased with the increase of sintering temperature up to 800 ◦ C. Above 800 ◦ C, the mean strut thickness decreased for samples sintering during 30, 60 and 120 min. For samples sintered for 180 min, the maximum mean strut thickness is located at 750 ◦ C. Above 750 ◦ C, a decrease of the mean strut thickness is observed. However, above 800 ◦ C the mean strut thickness starts to increase again. The mean cell size distribution for LZSA glass-ceramic foams sintered at different sintering temperatures is shown in Fig. 8. The mean cell size decreased with the increase of the sintering temperature up to 800 ◦ C. After this temperature, the mean cell size increased slightly with the increase of the sintering temperature. It can be concluded from Figs. 7 and 8 that the strut thickness increases with decreasing pore size as the sintering temperature increases. Both parameters are in agreement with the microstructure results displayed in Fig. 4, which endorses the use of ␮CT as a complementary tool to evaluate morphological parameters.

Fig. 7. Mean strut thickness distribution as a function of the sintering temperature of LZSA glass-ceramic foams for different soak times. The lines are only guides for the eyes.

Fig. 8. Mean cell size distribution as a function of the sintering temperature of LZSA glass-ceramic foams for different soak times. The lines are only guides for the eyes.

The typical load–displacement curve for LZSA glass-ceramic foams under compressing testing is shown in Fig. 9. Gibson and Ashby [19] developed a generic model to explain the failure mechanism in cellular solids (honeycombs and foams). In the case of brittle foams like ceramics and glasses, they collapse by brittle crushing. Three basic stages in the stress–strain curve of brittle foams are relevant. They exhibit a linear elastic deformation, characterized by a critical stress (maximum) followed

Fig. 9. Typical load–displacement curve for LZSA glass-ceramic foams.

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Fig. 10. Compressive stress–strain curves for LZSA glass-ceramic foams sintered at different temperatures and times. The lines are only guides for the eyes.

by a long collapse plateau (cells crashing at a constant stress). This plateau is truncated by a densification process, when the cell walls touch each other (stress increasing). Two main regimes can be observed: linear elastic regime, corresponding to cell edge bending or face stretching, and a stress plateau, corresponding to progressive cell collapse by brittle crushing. Densification onset occurs at 25% strain (not shown). The compressive strength curve for LZSA glass-ceramic foams sintered at different sintering temperatures is shown in Fig. 10. The compressive strength can be correlated to the sintering temperature by assuming that the strength of the porous sample is defined by the strength of the solid fraction (cell walls and struts). Hence, as the sintering temperature increases (700–750 ◦ C), as well as the sintering time, an increase of the strut thickness is expected, giving rise to a higher strength. A model that assumes the porous ceramic structure as a continuous network of material chains and interconnected openpore channels was developed, in which the following generic relation for the porosity-dependent strength was obtained [20]:  n σc ρ0 = C1 (1) σS ρS where ρ0 /ρS is the relative density (density of the porous body divided by the density of the solid part), σ 0 /σ S the relative strength (strength of the porous material divided by the strength of the solid fraction) and C1 is a constant related to the pore shape and the exponent n is a constant related to the pore geometry and distribution. For n = 1.5, Eq. (1) reduces to the Gibson-Ashby (GA) model for homogenous open cells, which is based on the catastrophic collapse of the cells at a critical stress value [19,21]. As reported by Dam et al. [22], the dependence of the cell size on the crushing behaviour of the cellular body is a result of strut cracking at the smallest cell size. For higher porosities, however, the majority of the experimental data lies lower than the predicted values. The low strength at low fractional densities is strictly related to the microstructural defects formed during the synthesis process [23] such as micropores between grains, and voids within the struts caused by oxidation of the PU template.

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Fig. 11. Compressive strength as a function of porosity of LZSA glass-ceramic foams according to Eq. (1).

Fig. 11 shows the compressive strength as a function of the relative density (ρ/ρ0 ) of LZSA glass ceramic foams. Although, a relative large scattering of the data can be seen, a noticeable decrease on the strength of the LZSA glass-ceramic foams with decreasing relative density can be observed. Fitting the experimental data using Eq. (1), with fixed n = 1.5 (GA modelsolid curve) a relatively high deviation to lower strength values from the data is observed, especially for higher relative densities (>0.2). The deviation can be attributed to microstructure defects since GA model predicts the strength for homogeneous and defect-free foams, which in turns would yield higher strength values [19]. A value of n = 3.1 was found for the LZSA glass ceramic foams, when fitted with Eq. (1) with no fixed parameters (dashed curve). C1 was found to be 0.07 for n = 1.5 (coefficient of correlation, r = 0.77) and 0.49 for n = 3.1 (r = 0.88). Similar values of n were found for cordierite open-cell foams [24]. The value of n depends on the micromechanical model used to describe the material, the proportion between open and closed cells, as well as the mechanism of load transfer among the constituents of the porous material [24]. Additionally, lower σ S values can be related to high degrees of pore disorder, which resulted in a higher value of n. Permeability is one of the most important parameter when a material is designed to serve as a filter. The permeability of a porous element under low flow velocities can be well described by Darcy’s equation for compressible fluids (Eq. (2)), which expresses a linear dependence on the superficial fluid velocity (vS ), determined by dividing the volumetric flow rate (q) by the total free-flow area (A) and explains only attrition effects on the porous media (viscous regime): P02 − P 2 μ = vs k1 2PL

(2)

where P0 and P are, respectively, the absolute fluid pressures at the entrance and at the exit of the sample, L the thickness of the porous element (parallel to the fluid flow), μ the viscosity of the air at room temperature (273 K) and pressure (1.013 × 105 Pa), and k1 is the Darcyan permeability constant.

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Fig. 12.

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Permeability curves of the foams sintered at 750 ◦ C for different times.

For higher velocities, this dependence is not linear and can be better described by Forchheimer’s equation (Eq. (3)) [25]. Here, a quadratic dependence on the fluid velocity is added to describe the contribution of kinetic effects on the pressure drop (inertial regime): P02 − P 2 ρ μ = vs + v2s 2PL k1 k2

(3)

where ρ is the density of the air and k2 is the non-Darcyan permeability constant. Both permeabilities depend exclusively on the porous structure. The effect of porosity, pore size and cross-section pore density on the permeability of ceramic filters was investigated by Salvini et al. [6] and Innocentini et al. [7]. A strong dependence on k1 was reported for pores larger than 350 ␮m (considerably increasing for larger pores), and for smaller pores (<300 ␮m), k1 tends to be less dependent on the pore size. Fig. 12 shows the permeability curves (pressure-drop versus air velocity) for the foams sintered at 750 ◦ C for different times. The resistances to flow of the samples slightly differ from different sintering times and exhibit the parabolic trend proposed by Forchheimer (Eq. (3)) rather than the linear relationship between pressure drop and fluid velocity stated by Darcy’s law (Eq. (2)). The intensity of the quadratic term clearly increases at higher velocities (>1.0 m/s), showing that the inertial term is not irrelevant in permeability analysis. The permeability constants k1 and k2 were obtained by fitting the pressure drop curves with Eq. (3). Fig. 13 shows the Darcyan permeability, k1 , as a function of the porosity of the LZSA glass-ceramic foams. The Darcyan permeability k1 exhibits a tendency to be constant with a slight positive slope with the raise of the porosity up to 85%. However, an accentuated difference was observed for k1 values for porosities higher than 85%. As reported by Salvini et al. [6], the Darcyan permeability strongly depends on the pore size and number of pores at the flow area, regardless of the overall porosity, for pore densities lower than ∼50 ppi. The image analysis of the surface of the LZSA glass-ceramic foams revealed a pore density of approximately 62 ppi for the foam sintered at 700 ◦ C (porosities higher

Fig. 13. Influence of porosity on gas Darcian permeability for LZSA glassceramic foams sintered at different temperatures and times.

than 85%), which supported the observations on the constancy of k1 for lower porosities (pore densities <45 ppi). As k1 also depends on the connection between the pores, which is defined by the pore geometry, the LZSA glass-ceramic foams exhibit high permeability, considering the anisotropy of the cells and compared to that of Al2 O3 -SiC filters at the same porosity and pore size range [6]. Additionally, careful considerations should be made if k1 is intended to be used to estimate permeability beyond the flow velocity range [7]. In order to verify the range of validity of the Darcy’s law, Innocentini and Pandolfelli [26] used the Forcheimmer’s number, Fo (Eq. (4)), according to Ruth and Ma [27] defined by:   vs k1 Fo = (4) v k2 where v is the kinematic viscosity (μ/ρ). Fo represents the relation between kinetic and viscous forces that contribute toward the pressure drop of the fluid. For very small Fo values (Fo  1), the inertial effect is negligible [26]. For filtering applications, the air velocity through the pores of the LZSA foams may vary in the range of 10−3 to 0.1 m/s, giving a Fo range of 10−4 to 10−1 , which indicates that the permeability of the foams at low superficial air velocity can be well described by the linear pressure drop region, characterized by the Darcyan permeability constant k1 . The values of k1 and k2 used for Fo calculation are shown in Table A1 (see Appendix A), as well as the fitting parameters and porosities of the samples. 4. Conclusions Cellular LZSA glass-ceramic foams with interconnected pores and high porosity (62–88%) were successfully produced using the polymeric sponge method. The main crystalline phases identified were ␤-spodumene, zirconium silicate and lithium metasilicate. The most adequate sintering condition for the LZSA glass-ceramic foams was 750 ◦ C for 60 min. At this condition, the samples maintained the pore morphology of the original polyurethane template. Above this temperature, the formation of lithium metasilicate occurred, which is undesirable for the system due to its high coefficient of thermal expansion. The

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compressive strength of the foams is strongly dependent on their overall porosity and their behaviour could be explained using the Gibson-Ashby model. The air pressure drop through the LZSA foams within the tested superficial air velocity range is described by a parabolic behaviour (Forchheimer’s equation), which is characterized by a Darcyan permeability constant (k1 ), and a non-Darcian permeability constant (k2 ), related to viscous and inertial fluid regimes, respectively. The Darcyan permeability of LZSA foams was found to be in the range of 0.1–4 × 10−9 m2 , which is in the order of magnitude of gas filter supports, and, therefore, also suitable for several technological applications.

and k2 , calculated by fitting Eq. (3) to the experimental data (ordered by crescent porosity), with the respective Fo-range, calculated for the velocity range of 10−2 to 4.5 m/s. References [1] [2] [3] [4] [5] [6]

Acknowledgements The authors thank Prof. Murilo D.M. Innocentini for helpful discussions. The authors also thank CAPES/Brazil, CNPq/Brazil and the Government of Bavaria/Germany for funding this work under Grant No. 007/02. Appendix A. Appendix A

[7] [8] [9] [10] [11]

Table A1 shows the calculated permeability parameters k1

[12] [13]

Table A1 Permeability parameters and respective Fo-range Mean porosity (%)

k1 (m2 )

k2 (m)

Fo-range

R2

62.3 67.5 72.2 71.5 72.4 73.5 69.9 75.4 71.8 73.7 79.3 73.9 78.9 85.3 85.7 87.9

8 × 1010 2.6 × 10−9 4.2 × 10−10 2.7 × 10−9 9.5 × 10−10 3.7 × 10−9 2.7 × 10−10 5.5 × 10−10 2.2 × 10−10 6.7 × 10−10 2.3 × 10−9 3.9 × 10−10 9.7 × 10−10 2 × 10−9 2.2 × 10−10 1.5 × 10−10

9.7 × 10−5 8.3 × 10−5 7.7 × 10−5 9.8X10−5 7 × 10−5 9.2 × 10−5 3.8 × 10−5 1.7 × 10−4 3.9 × 10−5 2 × 10−4 8.5 × 10−5 6.5 × 10−5 6.8 × 10−5 6.7 × 10−5 3.3 × 10−5 1.6 × 10−5

5.523 × 10−4 –0.055 0.002–0.208 3.66 × 10−4 –0.037 0.002–0.184 9.079 × 10−4 –0.091 0.003–0.267 4.826 × 10−4 –0.048 2.235 × 10−4 –0.022 3.7 × 10−4 –0.037 2.202 × 10−4 –0.022 0.002–0.181 4 × 10−4 –0.040 9.633 × 10−4 –0.096 0.002–0.197 4.439 × 10−4 –0.044 6.36 × 10−4 –0.064

0.9967 0.9980 0.9981 0.9981 0.9983 0.9981 0.9994 0.9964 0.9985 0.9962 0.9981 0.9990 0.9977 0.9980 0.9994 0.9985

[14] [15]

Although, the k2 data exhibit a scattered distribution over porosity, a slight decrease in k2 (decrease of kinetic effects) can be noticed, especially for higher porosities (samples sintered at 700 ◦ C), which confirms that the viscous regime is more dominant for higher porosities, rather than the inertial regime.

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[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

J. Zeschky, J. Lo, T. H¨ofner, P. Greil, Mater. Sci. Eng. A403 (2005) 215–221. R.A. Lopes, A.M. Segad˜aes, Mater. Sci. Eng. A209 (1996) 149–155. L.M. Sheppard, Ceram. Trans. 31 (1993) 3–25. K. Schwartzwalder, A.V. Somers, Method for making porous ceramics articles, US Patent USA 3.090.094 (1963). J. Saggio-Woyansky, C.E. Scott, W.P. Minner, Am. Ceram. Soc. Bull. 71 (1992) 1674–1682. V.R. Salvini, M.D.M. Innocentini, V.C. Pandolfelli, Cerˆamica 46 (2000) 97–103. M.D.M. Innocentini, P. Sepulveda, V.R. Salvini, V.C. Pandolfelli, J.R. Coury, J. Am. Ceram. Soc. 81 (1998) 3349–3352. N.L. de Freitas, J.A.S. Goncc¸alves, M.D.M. Innocentini, J.R. Coury, J. Hazard. Mater. B136 (2006) 747–756. E.A. Moreira, J.R. Coury, Braz. J. Chem. Eng. 21 (2004) 23–33. V.R. Salvini, A.M. Pupim, M.D.M. Innocentini, V.C. Pandolfelli, Cerˆamica 47 (2001) 13–18. L. Montanaro, Y. Jorand, G. Fantozzi, A. Negro, J. Eur. Ceram. Soc. 18 (1998) 1339–1350. A.P.N. Oliveira, Ph.D. Thesis, Modena, Italy, 1997. O.R.K. Montedo, A.N. Klein, A.P.N. Oliveira, Proceedings of the 3rd International Latin-American Conference on Powder Metallurgy, Florian´opolis, Brazil, 2001. C.M. Gomes, F.N. Biscaia, J.T. Quinaud, O.R.K. Montedo, A.P.N. Oliveira, D. Hotza, Ceram. Trans. 193 (2006) 9–16. C.R. Rambo, E. Sousa, A.P.N. Oliveira, D. Hotza, P. Greil, J. Am. Ceram. Soc. 89 (2006) 3373–3378. E. Sousa, C.B. Silveira, T. Fey, P. Greil, D. Hotza, A.P.N. Oliveira, Adv. Appl. Ceram. 104 (2005) 22–29. J. Zeschky, T. H¨ofner, C. Arnold, R. Wei␤mann, D. Bahloul-Hourlier, M. Scheffler, P. Greil, Acta Mater. 53 (2005) 927–937. D.R. Lide, CRC Handbook of Chemistry and Physics, 76th ed., CRC Press, 1995. L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, second ed., Cambridge University Press, Cambridge, UK, 1997. A.S. Wagh, R.B. Poeppel, J.P. Singh, J. Mater. Sci. 26 (1991) 3862–3868. L.J. Gibson, J. Biomech. 38 (2005) 377–399. C.Q. Dam, R. Brezny, D.J. Green, J. Mater. Res. 5 (1996) 163–171. H. Hagiwara, D.J. Green, Advanced Ceramics, vol. II, Elsevier Publishers, London, 1996, pp. 105–120. F.A.C. Oliveira, S. Dias, M.F. Vaz, J.C. Fernandes, J. Eur. Ceram. Soc. 26 (2006) 179–186. M.D.M. Innocentini, V.R. Salvini, V.C. Pandolfelli, J.R. Coury, J Am. Ceram. Soc. 82 (1999) 1945–1948. M.D.M. Innocentini, V.C. Pandolfelli, J. Am. Ceram. Soc. 84 (2001) 941–944. D.W. Ruth, H. Ma, Transport Porous Med. 7 (1992) 255–269.