Preparation of cellular alumina ceramics via biological foaming with yeast and its microstructural characterization via stereological relations

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ScienceDirect Journal of the European Ceramic Society 35 (2015) 187–196

Preparation of cellular alumina ceramics via biological foaming with yeast and its microstructural characterization via stereological relations T. Uhlíˇrová, E. Gregorová, W. Pabst ∗ , V. Neˇcina Department of Glass and Ceramics, Institute of Chemical Technology, Prague, Technická 5, 166 28 Prague 6, Czech Republic Received 23 May 2014; received in revised form 5 August 2014; accepted 12 August 2014 Available online 30 August 2014

Abstract The preparation of highly porous (cellular) alumina ceramics via biological foaming with yeast is described and its microstructure is characterized via image analysis using stereological relations. The ceramics prepared usually have total porosities in the range 78–84% and the porosities related to large pores (volume fraction of foam bubbles) are usually in the range 58–75%. The mean chord length and Jeffries size, i.e. pore size measures related to the interface density and the mean curvature integral density, respectively, are rather close to each other (usually 0.8–1.4 and 0.8–1.2 mm) with a ratio close to unity (0.9–1.4), and the mean surface-to-surface distance gives a realistic picture of the average wall thickness (usually 0.46–0.69 mm). Using a special processing variant (excess ethanol addition) it is possible to obtain microstructures with lower porosity (total porosity 68–70%, foam bubble volume fractions 50–56%) and smaller pore size (approx. 0.5 mm). © 2014 Elsevier Ltd. All rights reserved. Keywords: Biological foaming with yeast; Shaping; Microstructure-final; Porosity; Alumina

1. Introduction Porous and cellular ceramics (ceramic foams) are known to have a wide range of applications, ranging from light-weight materials and thermal insulation, where the volume fraction of pores (porosity) is the key characteristic, to filters and catalyst support media in which pore size, shape and surface are the most important microstructural parameters.1,2 The properties of these materials are determined by the solid phase, which ensures e.g. their high-temperature behavior and corrosion resistance, as well as the microstructure, which is responsible for most structural and functional properties and features of behavior.3–6 On the other hand, the microstructure of porous ceramics is a result of processing and can be controlled by choosing appropriate processing methods,7–9 e.g. using pore formers,10–12 possibly in connection with swelling of the latter,13–16 or direct foaming methods,17–20 and optimized processing conditions.21 In

∗

Corresponding author. Tel.: +420 220 444 136; fax: +420 220 444 350. E-mail addresses: [email protected] (T. Uhlíˇrová), [email protected] (E. Gregorová), [email protected] (W. Pabst), [email protected] (V. Neˇcina). http://dx.doi.org/10.1016/j.jeurceramsoc.2014.08.020 0955-2219/© 2014 Elsevier Ltd. All rights reserved.

particular, the shaping step is crucial for the resulting microstructure, because it determines the overall microstructural features of the ceramic, so that the high-temperature processing (drying and firing) results in strengthening and densification of the microstructure, during which possible defects (principal or accidental) cannot be eliminated any more. A famous example of such principal microstructural defects are the pore channels in the struts of ceramic foams prepared by the polymer sponge template method (replica technique), which seriously limit their mechanical properties.22,23 Therefore considerable research efforts are directed toward developing processing techniques that avoid this type of defects, while at the same time maintaining a high overall porosity. For this purpose direct foaming techniques have become popular, because they allow porosities of more than 70% to be readily attained (in contrast to the use of pore formers, even swelling ones, where porosities of more than 60–70% usually cannot be attained). A very recent development among direct foaming techniques is biological foaming with yeast. This method has been tested for preparing porous ceramic bodies in our laboratory many years ago (around 2007), but probably the first published papers in the open literature were those by Schunk et al.24 who proposed the use of yeast to prepare zeolite catalyst supports and, three years later

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(2010), by Menchavez et al.25 who used yeast to prepare porous silicate ceramic materials from red clay. At about the same time (2009/2010) Manap and Jais used yeast for preparing porous silica granules, usable e.g. as fillers, from rice husk ash.26,27 Some hints on yeast-based foaming techniques are also hidden in the patent literature, where we found two US patents,28,29 one of which concerns porous phosphate ceramic bone graft materials29 and the other mentions yeast – among many other substances – as an example of a foaming agent in a very general way,28 two older German patents30,31 and three very recent Chinese patents.32–34 However, only three of the latter concern the use of yeast as a foaming agent,30–32 mentioning building and insulating materials as well as “granular aggregates” of alumina, zirconia, mullite and metal particles as examples, while the other two33,34 use dry yeast powder as a mere pore former, obviously without exploiting its foaming capability. The same holds for several published journal papers, where dry yeast granules are used as pyrolizable pore formers.35–42 Thus it can be concluded that up to now there seems to be only one journal paper and about three or four (not very clear) patents in which the use of yeast as a foaming agent is proposed for preparing highly porous cellular ceramics (ceramic foams). In none of the works mentioned the roles of sugar and starch during processing and the microstructure of the resulting ceramic foams have been systematically analyzed. Therefore the preparation of cellular alumina ceramics by biological foaming with yeast has been the subject of a recent thesis at the ICT Prague,43 and in previous work the influence of the type and amount of sugar and starch on the processing and the resulting ceramic have been investigated.44 Sugar is used as a fuel for the yeast cells, i.e. the fermentation process consists in reaction of sugar (in aqueous media) to ethanol and carbon dioxide, the latter being responsible for the foaming. Three types of sugar – glucose, fructose and sucrose – have been tested with the outcome that the influence of the type of sugar on the resulting ceramic is negligibly small. Therefore it was concluded that sucrose, which is the cheapest and most easily available one, is the sugar of choice for this process. On the other hand, swelling starch serves as a foam stabilizer,44 and when its swelling ability in hot water is exploited (like in starch consolidation casting12–16 ) it is ideally suited as a foam stiffener. From the starch types tested in previous work, i.e. rice, corn and potato starch,43,44 potato starch performed best, probably because of its high swelling ability. Therefore, rice and corn starch have been discarded at an early stage and have not been considered in subsequent research. The concentrations of sugar and starch have been optimized for alumina suspension, resulting in 1.5 wt.% of sucrose and 20 vol.% of potato starch (both related to alumina).43,44 Moreover, it has been found that the pH value has a decisive influence on the foaming process. While yeast cells are able to survive at pH values in the range 2–8, pH values in the range 4–6 are optimal for the fermentation process.43,44 In the present paper we give a detailed account of the microstructure of alumina foams or cellular alumina ceramics prepared under these optimized conditions. We also report on first results concerning the possibility of controlling the microstructure by adding ethanol and give an example

of how a mold with a porous interface may affect the resulting microstructure. In spite of the current interest in yeast as a foaming agent for the preparation of porous ceramics, including highly porous cellular ceramics, and despite the fact that yeast has been used for food preparation since prehistorical times e.g. for the baking of bread, and has been used in polymer technology as a foaming agent as well,45 there seems to be no work dealing with the quantitative microstructural characterization of the resulting (ceramic) materials. The present paper is meant to fill also this gap. For this purpose we apply stereology-based image analysis.46–50 After briefly summarizing the basic stereological relations, including those which are less commonly used (e.g. mean curvature integral density and Jeffries size), we give a detailed account on processing items concerning the preparation of cellular alumina ceramics and finally present the results of the microstructural characterization in the form of correlation charts and tabulated values, including statistical errors.

2. Theoretical Porous materials can be considered as a special case of heterogeneous materials, i.e. materials with internal phase boundaries. The microstructure of heterogeneous materials can generally be characterized by microstructural parameters (global descriptors), which are representative of the whole sample if the material is uniform (i.e. gradient-free). Two-dimensional (2D) sections through three-dimensional (3D) microstructures of heterogeneous materials allow the determination of metric parameters, but not topological ones.47 The number of independent metric parameters that can be determined from 2D sections is limited to three. Using the standard index notation common in stereology,47,48 these are the volume fraction φ = VV . (dimensionless, e.g. porosity), the interface density SV (units [mm−1 ], e.g. pore surface density) and the mean curvature integral density MV . ([mm−2 ], characterizing e.g. pore surfaces).47 When the microstructure is isotropic, uniform and random, estimators for these parameters can be determined from arbitrary single sections by superimposing straight lines in arbitrary directions and periodically arranged points, e.g. realized by superimposing square grids onto micrographs. Based on these basic parameters, or the quantities directly measured for estimating them, other common parameters, such as size measures (mean chord length, Jeffries size) and other measures (e.g. distance measures) can be derived.47,48 With respect to the focus of this contribution (porous materials) we confine ourselves here to two-phase microstructures.The volume fraction of the phase of interest, e.g. porosity, is determined via the Delesse-Rosiwal law46–49 Φ ≡ V V = AA = LL = PP ,

(1)

where AA , LL and PP are the area, line and point fractions, respectively. Usually, i.e. when the porosity is not too low, point fractions are used for this purpose, because point counting (e.g. using the grid points of a square grid) is the most efficient method from a statistical point of view.47,48

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The interface density is determined via the Saltykov relation46 SV = 2PL ,

(2)

where PL is the number of intersection points per unit length of the probe line (grid lines), and the mean curvature integral density via the net tangent count (yielding in general the 2D Euler characteristic47 ), which in the case of simply connected objects (not necessarily convex) can be replaced by a count of objects per unit area NA , i.e. by the relation,47 MV = 2π · NA .

(3)

¯ which is a dimensionThe mean chord length of pores L, invariant measure of the pore size, is calculated via the relation47–49 ¯ = 4φ = 4VV = 2PP , L SV SV PL

(4)

and the mean distance between pore surfaces (surface-to-surface distance), which corresponds to the wall thickness between the pores of interest, via the relation47 4(1 − φ) 4(1 − VV ) 2(1 − PP ) λ¯ = = = . SV SV PL

(5)

On the other hand, the Jeffries size of the pores, which is an inherently 2D size measure (i.e. not dimension-invariant), can be calculated via the relation  φ J= . (6) NA The Jeffries size in this sense (i.e. for a two-phase material) is not a standard concept. It is however, a natural extension of the concept of the so-called “Jeffries grain size”, its counterpart for dense single-phase polycrystalline materials,46 which is intimately related to the “ASTM grain size”.50 The physical meaning of the Jeffries size (sometimes – in the context of grains in polycrystalline microstructures – misleadingly called “mean section diameter”) is the edge length of an “average” square, the area of which equals the area of an “average” pore section (more precisely, a number-weighted arithmetic mean section area). Since the area of a circle equals the product of ¯ for monodisperse mean chord length and diameter, the ratio L/J circular sections would be 0.886.50 However, higher values of this ratio are expected50 and have been found for real microstructures with polydisperse grains, e.g. 0.935.48 It should be noted that the mean chord length is a size measure based on the interface density SV (i.e. in the case of pores the pore surface density), while the Jeffries size (of simply connected objects) is related to the mean curvature integral density MV (i.e. the density per unit volume of the surface integral of the mean curvature), which in the case of polyhedral grains or inclusions is related to the length of edge lines per unit volume. Both SV and MV are dimension-invariant, i.e. assume the same values on the plane (2D section) and in space (3D microstructure). The absolute error of all these measurements can be calculated from the standard error (=standard deviation of the

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cumulative sample mean) and the normalized deviation (tvariate) according to the so-called Student t-distribution, which determines the reliability of the result, i.e. the probability with which the true population mean is expected to lie within the confidence intervals around the (cumulative) sample mean. Thus the absolute error corresponding to 95% reliability is generally given by the relation48 Δx = t0.95 (n) · σ(x),

(7)

where σ( x ) is the standard error of the cumulative sample mean x and t0.95 (n) the t-variate for 95% reliability, with the argument n denoting the so-called “degrees of freedom”, which are related to the number of measurements in each sample, e.g. the number of grid points P used for measuring the porosity (n = P − 1) or the number of pore sections intersected by grid lines (=half the number of intersection points of grid lines with pore section outlines, i.e. n = Pintersection /2 −1), or the number N of samples (n = N − 1). Generally, after the measurements have been performed, the standard error can be calculated from the usual standard deviation σ(x) via the relation48 σ(x) σ(x) = √ , N

(8)

where N is the number of samples and σ(x) is the usual standard deviation46,48   (xi − x)2 , σ(x) = (9) N −1 where xi are the individual sample means (usually based on many single measurements in one sample). Additionally, for some of the above parameters, it is possible to estimate the standard error directly from the (cumulative) number of single measurements (if necessary even before the measurements are made, e.g. to determine in advance the necessary number of measurements to be made). In particular, the standard error of the volume fraction (porosity) determined by point counting φ = VV = PP is determined by the total number P of grid points used for this measurement, i.e.46–49   φ(1 − φ) PP (1 − PP ) σ(φ) = σ(Pp ) = = (10) P P and the standard error of the interface density SV is determined by the relation46,48,49 SV σ(SV ) = k1 · √ , Pintersection

(11)

where Pintersection is the number of intersection points of grid lines with pore section outlines and k1 is an empirical factor, whose values are reported to range from approximately 0.5–1.546 or even 2.0,49 and sometimes the value 0.65 is preferred.48 In this contribution we set k1 = 1. Similarly, the standard error of the mean curvature integral density MV can be calculated from an empirical relation of the same type, i.e. σ(MV ) = k2 · √

MV , Nsection

(12)

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where Nsection is the number of pore sections counted and k2 is an empirical constant, whose value is reported to be 1.03.48 In this contribution we set k2 = 1. Since the aforementioned size and distance measures are calculated from two measured quantities, viz. the volume fractions and either the interface density or the mean curvature integral density, the law of error propagation has to be invoked for calculating the standard errors of these quantities.48 All errors in this paper are calculated as arithmetic means of the observed errors and the expected errors where available, corresponding to 95% confidence intervals. Relative errors are calculated by dividing the absolute errors by the corresponding mean values. 3. Experimental 3.1. Raw materials The following raw materials have been used for the preparation of the highly porous cellular ceramics (alumina foams): submicron alumina powder with median particle size 0.7 ␮m (CT 3000 SG, Almatis GmbH, Germany), alkali-free polyelectrolyte dispersant (Dolapix CE64, Zschimmer & Schwartz GmbH, Germany), potato starch with median granule size approx. 47 ␮m (Solamyl, Natura a.s., Czech Republic), sucrose (white sugar Bíl´y cukr Krystal, Tereos TTD a.s., Czech Republic), distilled water, ethanol, dry bakers’ yeast (Saccharomyces cerevisiae, Labeta a.s., Czech Republic), citric acid (Lach-Ner s.r.o., Czech Republic).

(glazed tiles), except for one sample type that was prepared in a mold attached to a porous support (unglazed wall tile). The inner surfaces of the polyethylene molds had previously been coated with alkali-free grease (Apiezon, M & I Materials, UK) in order to minimize adhesion to the walls and to facilitate subsequent demolding. After 5 min soaking at room temperature (for reactivation of the initially dry yeast), the mold was placed in a laboratory drier at 80 ◦ C for 8 h, where foaming occurred, until the water content decreased below a critical level and drying set in. During heating, the starch begins to swell and gelatinize, thus stabilizing the foam. In the sample type prepared with the polyethylene cylinder on a porous support (unglazed tile), additionally, dewatering via the semi-permeable interface interfered with the foaming step. Yeast cells need a sufficient amount of water to induce foaming, and where this water is lacking, as in the regions close to the porous interface (due to capillary suction of the porous support), foaming does not occur or is at least significantly suppressed. After 8 h the foams were ready for demolding and the temperature was increased to 105 ◦ C for 2 h, during which the samples were dried to constant mass. Subsequently the as-dried samples were fired in an electric furnace at 1570 ◦ C using a standard firing schedule (heating rate 2 ◦ C/min, 2 h dwell at maximum temperature, free cooling in the furnace). After firing and cooling the samples (cylinders with diameter approx. 35–40 mm) were cut into slices of thickness 2–5 mm using a diamond saw, see Fig. 1. These slices were used for the microscopic investigation. 3.3. Microscopic image analysis

3.2. Processing and sample preparation Aqueous alumina suspensions with varying composition – alumina contents of 70, 73 or 75 wt.% – were prepared by mixing distilled water with alumina powder, dispersant (1 wt.% related to alumina), sucrose (1.5 wt.% related to alumina) and 20 vol.% of starch (related to alumina, assuming densities of 1.5 g/cm3 and 4.0 g/cm3 for starch and alumina, respectively). The ethanol content varied between 2.5 and 10 wt.% (related to water). After homogenization of the suspension (2.5 h in polyethylene bottles with alumina balls on a shaker with 300 rpm) the pH was set to 5.5 using citric acid, yeast was added (7.4 wt.%) and the mixed suspension was vigorously agitated using a household mixer for 2 min (it should be emphasized, that this mixing step introduces a small amount of air bubbles as in any other ceramic suspension, but does not yet induce foaming – starch starts to act as a foam stabilizer only when swelling, i.e. at higher temperature, and other foam stabilizers are not present at this stage). Eight different sample types have been prepared, see Table 1. Sample types 1 through 6 were prepared exactly as described, while for samples of type 7 and 8 yeast was first mixed with an aqueous solution of citric acid and then mixed with the suspension, either after 5 min dwell at room temperature (type 7) or immediately (type 8) after mixing. The ceramic suspensions were then cast into molds consisting of cylindrical polyethylene tubes (with an internal diameter of approx. 45 mm) attached in a water-tight fashion using a plastic mass (Hobby mass, Koh-inoor Hardtmuth a.s., Czech Republic) to a non-porous supports

Micrographs of the planar sections were taken using an optical microscope (Inspector Tristo 160 Digital, Müller, Germany)

Fig. 1. Horizontal cross section through a typical sample of cellular alumina ceramics prepared by yeast-mediated biological foaming (alumina foam after firing at 1570 ◦ C).

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Table 1 Processing details and characteristics of the six sample types prepared in this work. Sample type number

Alumina content in the suspension [wt.%]

1 2 3 4 5 6 7 8

70 75 73 70 70 70 70 70

Ethanol content (related to water) [wt.%] − 5 5 5 10 2.5 − −

equipped with a digital camera (DCM-130, Müller, Germany) and evaluated using a commercial image analysis software package (Lucia G, Laboratory Imaging, Czech Republic). Image preprocessing (e.g. binarization procedures) was not used in order not to introduce additional bias into the results. The evaluation was done manually on 8 or 16 micrographs for each sample using superimposed square grids with 63 or 25 grid points, respectively (i.e. the total number of grid points was 504 or 400, respectively). The number of grid points falling onto pore sections of one sample (i.e. of one planar section covered by 8 or 16 micrographs) was 250–337 or 262–301, the total number of intersection points of grid lines with pore section outlines 517–1021 or 660–810 and the total number of pores in the measurement frames (excluding two border lines and three corners) was 182–996 or 562–1021, respectively. Two to five samples (slices, i.e. planar sections) were investigated for each sample type. 4. Results and discussion 4.1. Sample type characterization Table 1 summarizes the crucial processing details and lists the characteristics of the six sample types prepared in this work. The total porosity was calculated from the bulk density (determined as the mass-to-volume ratio) and the theoretical density of alumina (corundum, i.e. ␣-Al2 O3 ), which is 4.0 g/cm3 . Most sample types exhibit total porosities in the range 78–84%, except for samples of type 5, which exhibit porosities of only 68–70%, evidently due to the presence of a high amount of ethanol in the suspension which inhibits the fermentation process. Samples of type 1, which have been prepared in the mold with porous interface (porous support), exhibit a strong microstructural gradient, in particular significantly lower porosity in the contact region with the porous support, see Fig. 2. This can be explained by the rapid dewatering via the porous (semipermeable) interface: due to the lack of water in this region the viability of the yeast cells is seriously limited. On the other hand, porous supports (or even molds) could be deliberately used to prepare porous microstructures with gradients, exhibiting e.g. a bone-like structure with a dense shell (corresponding to cortical bone) and a porous core (corresponding to trabecular or cancellous bone). In samples of type 7 and 8 yeast was first mixed with an aqueous solution of citric acid and then mixed with the suspension, either immediately (type 8) or after 5 min dwell at

Porous support

Total porosity [%]

Yes No No No No No No No

83.9 78.0 78.8–79.8 80.9–84.4 67.9–69.5 81.3–83.4 78.3–79.4 78.9–80.2

room temperature (type 7). It is evident that there is no significant difference between these two types and the other types except for the samples prepared with 10% of ethanol. It can be concluded that biological foaming with yeast is a quite robust process that leads to reproducible microstructures. On the other hand, ethanol – which is a natural product of the fermentation reaction and (being toxic to yeast cells) normally leads to a selfregulation of the fermentation process – can be used to limit the fermentation process artificially and thus to control the porosity of the resulting ceramic foam. 4.2. Microstructure of cellular ceramics (alumina foam) Fig. 3a–h shows typical microstructures of the cellular ceramics prepared (alumina foam after firing). It can be seen that an essential feature of this microstructure are large (mm-sized) pores which are the result of the foam bubbles resulting from the carbon dioxide evolution during the fermentation process mediated by the yeast cells. Apart from these large pores there are small pores with a size much more than one order of magnitude smaller (below 50 ␮m) that are the relics of starch burnout (starch acts as a foam stabilizer and stiffener during this process43,44 ) and which are not visible at this magnification. A small amount

Fig. 2. Comparison of contact regions with the semi-permeable interface (vertical sections through bottom parts of samples); left – contact region to porous support (gradient microstructure), right – contact region to non-porous support (uniform microstructure).

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Fig. 3. Microstructure of cellular ceramics (alumina foams after firing) prepared via biological foaming with yeast from suspensions (sample types: a – type 1, b – type 2, c – type 3, d – type 4, e – type 5, f – type 6, g – type 7, h – type 8).

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4.3. Global metric descriptors determined via stereology-based image analysis Table 2 lists the microstructural characteristics (global metric descriptors) measured via stereology-based image analysis based on optical micrographs for alumina foams (cellular ceramics) prepared via biological foaming with yeast. For the different sample types the ranges of mean values calculated from individual slices (8–16 for each slice) are given. The relative errors listed are averaged values from all sample types. Microscopic image analysis (MIA) has been used to measure the porosity that is exclusively due to the large bubbles evolving during the fermentation process of the yeast (CO2 release). This porosity is usually in the range 58–75% (with an absolute error of 3–5%), i.e. 10–20% lower than the total porosity determined from the geometrical bulk density (mass-to-volume ratio) and the true (theoretical) density, see Figs. 4 and 5. The difference is mainly caused by the pores that remain as a result of starch burnout. For samples of type 5 the porosity determined by MIA is correspondingly lower (50–56%). Also the interface density and the mean curvature integral density is significantly different between samples of type 5 (4.1–4.6 mm−1 and 15.3–16.3 mm−2 , respectively) and the other sample types (2.1–3.1 mm−1 and 3.0–7.7 mm−2 , respectively). Therefore, it is not very surprising that also the size measures related to the latter two quantities are different. The mean chord length (related to the interface densities) of pores for samples of type 5 is around 0.49 mm, compared to 0.8–1.4 mm for the other types, and – similarly – the Jeffries pore size (related to the mean curvature integral density) for samples of type 5 is around 0.46 mm, compared to 0.7–1.2 mm for the other types. We note in passing that in the present case these two different ¯ is size measures yield quite similar pore sizes, i.e. the ratio L/J relatively close to unity (0.9–1.4).

1 0.9

Porosity from MIA [1]

0.8 Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8 Reference line

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Porosity from bulk density [1]

Fig. 4. Correlation between the porosity measured via microscopic image analysis (MIA) to the total porosity determined from the bulk density and the true (theoretical) density.

The mean distance, more precisely the interface–interface distance between the pore surfaces is a measure of the wall thickness which may be compared with the wall thickness measured via tomographic techniques. For the alumina foams prepared here it is usually in the range 0.47–0.69 mm, only for samples of type 5 it is slightly smaller (0.39–0.47 mm), which seems surprising at first sight but is caused by the fact that for this sample type the pores are significantly smaller. The relative errors of all the parameters determined are below 12%. Averaged values of the relative errors are 6.6, 8.3, 9.0, 9.5, 5.3, 7.5 and 11.8% for the porosity, interface density, mean curvature integral density, ¯ Jeffries size J„ the ratio L/J ¯ and the mean mean chord length L, distance, respectively. Figs. 6 and 7 show the interface densities and the mean curvature integral densities in dependence of the total porosity determined from the bulk density (mass-to-volume ratio). It is evident that both parameters are strongly correlated with porosity and exhibit a steep decrease with increasing porosity, i.e. both SV and MV are higher for lower porosity. All sample types are rather similar, except for type 5 (prepared with 0.9

0.8

Porosity from MIA [1]

of (nanosized) interstitial pores between the ceramic grains may be present as well, but with respect to the high sintering temperature these pores will of course not contribute any significant porosity. Nevertheless, in principle this microstructure is hierarchical, and if desired, partial sintering at a lower temperature might be used to increase the interstitial porosity (as long as the pores are open, porosity and pore size in this range are best characterized via mercury porosimetry). The pore shape of the large pores resulting from the foam bubbles is not always isometric. We attribute these deviations from isometric or spherical shape to the fact that in the wet foam large pores have a lower internal gas pressure than smaller pores (simply because of the interplay of geometry and surface tension) and therefore are more prone to steric interactions with neighboring pores (excluded volume effects). In particular, when extremely large pores occur, these are often oblate and oriented due to gravitation effects. However, the smaller the pores are, the more they approach spherical shape and/or random orientation, so that the microstructure appears to be isotropic and in many cases (but not always) uniform throughout the macroscopic sample, see Fig. 3a–h.

193

Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8 Reference line

0.7

0.6

0.5

0.4 0.6

0.7

0.8

0.9

Porosity from bulk density [1]

Fig. 5. Correlation between the porosity measured via microscopic image analysis (MIA) to the total porosity determined from the bulk density and the true (theoretical) density (zoomed detail).

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Table 2 Microstructural characteristics (global metric descriptors) of cellular ceramics prepared via biological foaming with yeast (alumina foams after firing); the relative errors are averaged values from all sample types. 1

2

3

4

5

6

7

8

φ = VV SV [mm−1 ] MV [mm−2 ] Mean chord length [mm] Jeffries size [mm] ¯ Ratio L/J Mean distance [mm]

0.72–0.75 2.11–2.17 3.45–3.72 1.38–1.42 1.12–1.18 1.20–1.23 0.47–0.54

0.58–0.66 2.59–3.09 4.94–6.48 0.79–1.04 0.78–0.92 1.00–1.12 0.50–0.58

0.61–0.66 2.31–2.80 2.98–4.68 0.96–1.08 0.95–1.15 0.93–1.01 0.48–0.68

0.66–0.70 2.06–2.23 4.61–4.93 1.23–1.38 0.94–1.00 1.30–1.43 0.58–0.69

0.50–0.56 4.12–4.56 15.3–16.3 0.46–0.51 0.45–0.47 1.02–1.10 0.39–0.47

0.66–0.71 2.10–2.53 4.11–5.82 1.13–1.33 0.89–1.02 1.14–1.30 0.46–0.63

0.59–0.62 2.89–3.13 6.99–7.66 0.76–0.84 0.70–0.74 1.09–1.14 0.50–0.56

0.61–0.68 2.43–3.05 6.27–7.38 0.80–1.13 0.72–0.83 1.11–1.36 0.52–0.57

6

2

5.4

1.8

4.8

1.6

4.2

Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8

3.6 3 2.4 1.8 1.2

Mean chord length [mm]

Interface density [mm^-1]

Sample type

0.6

Relative error [%] 6.6 8.3 9.0 9.5 5.3 7.5 11.8

1.4

Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8

1.2 1 0.8 0.6 0.4 0.2

0

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

Porosity from bulk density [1]

0.3

0.4

0.5

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Fig. 8. Correlation between the mean chord length of pores and the total porosity (determined from bulk density and theoretical density).

a large amount of ethanol). As expected, the absolute values of these parameters are orders of magnitude smaller than the values determined e.g. for porous ceramics prepared by traditional slip casting of starch-containing alumina suspensions into plaster molds.51 The interface densities determined in this case are 39.5–191.5 mm−1 and 16.3–65.5 mm−1 , for alumina ceramics prepared with 5–40 vol.% of corn and potato starch, respectively. Similarly, the mean curvature integral densities are 860–4460 mm−2 and 5610–35,720 mm−2 , respectively.51

Figs. 8 and 9 show the mean chord length and the Jeffries size in dependence of the total porosity. Since these quantities are inversely related to the interface densities and mean curvature integral densities, it is not surprising that they exhibit a steep increase with increasing porosity. Obviously the pore size obtained by biological foaming with yeast is much larger than that resulting from the burnout of starch when the latter is used as a pore former.12–14,51,52 The mean chord length of the pores is orders of magnitude larger than that resulting from starch burnout, which has been determined as 8.3–9.7 and

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Fig. 6. Correlation between the interface density (pore surface density) and the total porosity (determined from bulk density and theoretical density).

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Fig. 7. Correlation between the mean curvature integral density and the total porosity (determined from bulk density and theoretical density).

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Fig. 9. Correlation between the Jeffries size of pores and the total porosity (determined from bulk density and theoretical density).

T. Uhlíˇrová et al. / Journal of the European Ceramic Society 35 (2015) 187–196 2 1.8

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1.6 Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8 Reference line

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increasing porosity, viz. from 94–226 ␮m to 11–34 ␮m as the porosity increases from approx. 7 to approx. 43%, respectively. It has to be emphasized that in the present investigation only the large pores resulting from the fermentation process (CO2 release) have been considered, and neither those resulting from starch burnout in the walls, nor the pore throats between the latter. The pore structure on this level is relatively well known from previous investigations.19,51,52 5. Summary

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Fig. 10. Correlation between the Jeffries size and the mean chord length of pores.

24.5–26.8 ␮m for nominal starch contents of 5–40 vol.% of corn and potato starch, respectively.51 Note that in both cases the mean chord length is significantly smaller than the Feret diameters of the pores, which in the case of starch as a pore former corresponds to approx. 14 and 47 ␮m for corn and potato starch, respectively. As can be seen from Fig. 10, the mean chord length and the Jeffries size are relatively close (ratio 0.9–1.4). That means, both size measures – that derived from the interface density and that derived from the means curvature density – provide a consistent picture of the pore size and its correlation with porosity. On the other hand, Fig. 11 shows that the mean distance between pore surfaces, which corresponds to the average wall thickness, seems not to be very much affected by changes in porosity. It has to be taken into account, however, that the overall range of porosities obtained here by biological foaming with yeast is not very large (68–84%). In previous work, where porous alumina has been prepared by traditional slip casting with starch as a pore former and the porosities obtained, albeit lower, are in a wider range (approx. 7–43%), the mean distance between pore clearly decreases with

Mean distance (interf.-interf.) [mm]

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Fig. 11. Correlation between the mean distance between pores (interface–interface, i.e. surface-to-surface) and the porosity (determined from bulk density and theoretical density).

Highly porous cellular ceramics (alumina foams) have been prepared by biological foaming with yeast and subsequent drying (80–105 ◦ C) and firing (1570 ◦ C), and the microstructure of the prepared ceramics has been characterized by image analysis using stereological relations. It has been shown that the ceramics prepared usually have total porosities in the range 78–84% and that the porosities made up by large pores (volume fraction of foam bubbles) are usually in the range 58–75%. Further it has been shown that the mean chord length and the Jeffries size, i.e. pore size measures related to the interface density and the mean curvature integral density, are relatively close to each other (usually 0.8–1.4 and 0.8–1.2 mm) with a ratio close to unity (0.9–1.4) and that the mean surface-tosurface distance gives a realistic picture of the average wall thickness (usually 0.46–0.69 mm). Using a special processing variant (excess ethanol addition) it is possible to obtain microstructures with lower porosity (total porosity 68–70%, foam bubble volume fractions 50–56%), smaller pore size (approx. 0.5 mm) and slightly thinner walls. Absolute errors have been calculated using normalized deviations corresponding to 95% reliability in the Student distribution and the standard errors for the quantities in question (both observed and estimated). It has been found that even in the worst case (mean pore distance) relative errors are below 12% when the number of measurements is of order 400–1000. Acknowledgement This work is supported by the Czech Science Foundation ˇ within the project (Grant Agency of the Czech Republic GACR) “Porous ceramics with tailored elasticity and thermal conductivˇ ity” (P108/12/1170) and by specific university research (MSMT No. 20/2014). References 1. Scheffler M, Colombo P, editors. Cellular ceramics – structure, manufacturing, properties and applications. Weinheim: Wiley-VCH; 2005. 2. Öchsner A, Murch GE, Lemos MJS, editors. Cellular and porous materials – thermal properties simulation and prediction. Weinheim: Wiley-VCH; 2008. 3. Gibson LJ, Ashby MF. Cellular solids – structure and properties. 2nd ed. Cambridge: Cambridge University Press; 1997. 4. Rice RW. Porosity of ceramics. New York: Marcel Dekker; 1998. 5. Pabst W, Gregorová E, Malangré D, Hostaˇsa J. Elastic properties and damping behavior of alumina–zirconia composites at room temperature. Ceram Int 2012;38:5931–9.

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