Download Author template for journal articles

Microfibrillated cellulose foams obtained by a
straightforward freeze-thawing-drying procedure
Supplementary Materials
Sébastien Josset, Lynn Hansen, Paola Orsolini, Michele Griffa, Olga Kuzior, Bernhard
Weisse, Tanja Zimmermann, Thomas Geiger
Sébastien Josset, Lynn Hansen, Paola Orsolini, Tanja Zimmermann, Thomas Geiger
Applied Wood Materials, Swiss Federal Laboratories for Materials Science and Technology
(Empa), Duebendorf, Switzerland
email: [email protected], +41587654723
Michele Griffa
Center for X-Ray Analytics and Concrete/Construction Chemistry Laboratory, Swiss Federal
Laboratories for Materials Science and Technology (Empa), Duebendorf, Switzerland
Olga Kuzior
Center for X-Ray Analytics, Swiss Federal Laboratories for Materials Science and
Technology (Empa), Duebendorf, Switzerland
Bernhard Weisse
Mechanical Systems Engineering, Swiss Federal Laboratories for Materials Science and
Technology (Empa), Duebendorf, Switzerland
Tomographic data analysis
The conversion of the X-ray tomogram of the scanned layer of each foam sample into two
distinct 3D images, each labeling each voxel as belonging to either a material phase (“white”
voxel) or not (“black” voxel), is called binary image segmentation (also known as image
binarization). It was performed by the “Threshold” command of ImageJ. Such binarization
consists of selecting a voxel value as a threshold and of classifying the voxels with values
above the threshold as belonging to one material phase and those with values below the
threshold to the second one, the two material phases being in this case the pore space and the
cell wall of the foam. Given the large difference in X-ray attenuation coefficient of the cell
walls compared with air, it was possible to automatically determining the threshold value for
distinguishing between the two phases. The first 3D binary image, identifying the voxels with
values above the threshold, was used as the 3D mask classifying the foam cell wall voxels. Its
Page 1 of 5
complementary one (voxels with values below the threshold) was used as the 3D mask
identifying the air voxels.
Setting the threshold limit is crucial, since the whole computation is performed based on the
binarization obtained through this step: voxel with values inferior to the threshold limit set by
the operator will be assigned to „air“, whereas the other will be identified as the cellulosic
matrix. A too low threshold limit is beneficial to the determination of the walls but generates
„noise“ in the pores. On the contrary, a too high limit produces less noise but lacks in the
correct rendering of the walls.
Figure 1S is a slice of the stack obtained with the foam F9urea. The outputs obtained after
setting a threshold value of 75, 80, and 85 (gray scale values) are depicted in the Figure 2S
(A1, B1, and C1). In the range 75-85, the walls are well determined and the noise produced is
lower at higher threshold levels. After removing small isolated aggregates, the outputs at the
three threshold values present only minor differences (A2, B2, and C2), so that the postprocessing is not sensitive to the chosen threshold limit.
The commonly used approach for the analysis of the pore size distribution of a porous/cellular
material is to consider each pore/cell as a separate object and to compute the pore/cell size
considering the set of pores/cells as a statistical ensemble. As definition of pore/cell “size” the
diameter of a sphere with volume equal to the volume of the pore/cell is commonly used.
Such approach and definition provide meaningful results only when (1) the pore space of the
cellular material is really made of distinct and separated regions, i.e., when the material is a
closed cell one with little to no amount of interconnections between the cells, and (2) the cells
are very close to spherical regions. Both conditions are rarely met by real world foams and
absolutely not satisfied by our foams, characterized by a large degree of volume
interconnectivity between the cells.
The continuous size distribution analysis proposed by Torquato (Torquato 2002) is based
upon a different approach: the entire pore space is considered as a large hole characterized by
a cumulative distribution of sizes. According to this approach, each “pore”, as a separated
region, or set of interconnected pores does not have a unique size, rather a “spectrum” of local
sizes, where the adjective “local” means that for each point inside the pore space a value of its
side at that point can be calculated, making the pore size a function of space rather than just a
number associated to distinct pore and separated pore regions.
We adopted the algorithm of Münch & Holzer (2008) for actually performing a continuous
pore size distribution analysis. Such algorithm first calculates the 3D Euclidean distance
transform of the 3D mask of the pore space. Then, the transform is used to calculate how
Page 2 of 5
much of the pore space volume can be covered by growing, at any position, a sphere with a
given critical diameter Dc, inscribed into the pore space itself. The calculation is performed
for a finite number of Dc values, allowing building up a complementary cumulative
distribution function (cCDF) of Dc, the latter acting as a definition of “size” of the pore space.
Since the calculation of Dc is performed voxel-by-voxel for the pore space, a spatial map of
Dc values can be obtained for the segmented pore space, as presented in Figs. 8(a), 8(c) and
8(e), where the values of Dc are mapped to a color scale.
Figure 1S. Slice of the image stack of the F9urea foam.
The gray scale indicates the value assigned to each voxel.
Page 3 of 5
A1
A2
B1
B2
C1
C2
Figure2S. A1, B1, and C1: slices of the binarized output after setting the thresholding
respectively to 75, 80 and 85. A2, B2, and C2: output after removal of isolated elements
respectively smaller than 15 (A1), 10 (B1), and 5 (C1) voxels.
Page 4 of 5
Münch B, Holzer L (2008) Contradicting Geometrical Concepts in Pore Size Analysis
Attained with Electron Microscopy and Mercury Intrusion Journal of the American
Ceramic Society 91:4059-4067 doi:10.1111/j.1551-2916.2008.02736.x
Torquato S (2002) Sections 2.6 and 12.5.4. In: Random Heterogeneous Materials Microstructure and Macroscopic Properties. Springer New York
Page 5 of 5