Syntactic foams (glass hollow spheres embedded in an epoxy matrix) were produced on purpose to be used as test materials for the present study. Two kinds of spheres (MS1 and MS2) were adjoined to a same polymer matrix, MS1 with a volume fraction of 55 and MS2 with 30 and 55%. The samples were analysed by X-ray tomography using synchrotron radiation. The three-dimensional images were used to observe the qualitative differences between the three samples. Three-dimensional image processing was then carried out to quantify the differences. The images were used to retrieve the fraction of the different phases which was in fairly good agreement with the expected values. The external and internal diameter of the spheres and their thickness were also measured. The MS1 spheres are smaller, thicker and their size distribution is less homogeneous compared to the MS2. The size distribution of the spheres before blowing was retrieved and evidenced to be similar for the two kinds of spheres. The thickness depends only weakly on the diameter of the spheres.
Syntactic foams consisting in glass hollow microspheres embedded in a polymeric matrix are being more and more extensively used for the thermal insulation of offshore pipelines and bundles which convey oil and gas resources from the extraction sites located in deep water (Franklin & Wright 1999; Van Belle 2002; Watkins & Hershey 2004). The thermal insulation of these conveyors is crucial to maintain a low viscosity of the fluid to be transported. Polymer syntactic foams can provide substantial heat loss resistance while withstanding the hydrostatic pressure induced by the water (300 bar at 3000 m of depth). The thermal resistance is brought by the cellular and porous character of the material as well as the low conductivity of the polymer itself. The mechanical resistance attributed to the closed-cell nature of the cellular microstructure is governed by the ratio between glass thickness and diameter. Therefore, optimized microsphere geometry fit-for-thermal insulation purpose in deep water needs a compromise between mechanical and thermal performance (Fine et al. 2003).
It is largely admitted that for a complete understanding of their thermal and mechanical behaviour, a clear relation has to be established between the structure and the properties of the cellular materials. The understanding of this relation allows much better modelling methods to be proposed. These methods can then be used to optimize the microstructure in relation with the targeted thermal and mechanical properties. In the case of cellular materials, the structure should be studied at two different scales: the microstructure of the constitutive material itself and also the so called ‘cellular’ microstructure (Maire et al. 2003a,b). The microstructure governs the properties of the solid part of the material, but the most important feature has been evidenced to be the cellular microstructure. This term designates the mutual arrangement of the solid and gaseous phases in the cellular material. It can be characterized by the volume fraction of void, but also by much more complex microstructural parameters such as the cell size, the wall or beam thickness and length, etc.
X-ray tomography has appeared recently to be a very powerful tool allowing to characterize the microstructure and also the deformation modes of cellular materials (Bart-Smith et al. 1998; Degisher et al. 2000; Elmoutaouakkil et al. 2000; Benouali & Froyen 2001; Coléou et al. 2001; Müller et al. 2001; Nuzzo et al. 2001; Elmoutaouakkail et al. 2002; Elliott et al. 2002; Olurin et al. 2002; Maire et al. 2003a,b; Salvo et al. 2004). It allows the pertinent parameters of the cellular microstructure to be characterized very precisely (Maire et al. 2003b; Salvo et al. 2004). The tomography technique allows for instance to capture architectural differences between materials exhibiting identical relative densities. The knowledge of the actual structure and arrangement of the solid phase in three dimensions has straightforwardly suggested to use this new kind of information as an input for finite element models which describe better the peculiarities of the behaviour of these materials (Ulrich et al. 1998; Roberts & Garboczi 2000; Maire et al. 2003a; Youssef et al. 2005).
This paper deals with the three-dimensional characterization of model epoxy-glass syntactic foams by X-ray microtomography. For a better control of the microstructure, the foams have been fabricated on purpose for this study. The images obtained are used to assess the characteristics of the cellular microstructure in the case of two different kinds of glass spheres. One kind of spheres was incorporated at two volume fraction levels. The microstructure is analysed in terms of the local fraction of the three components (air, glass and polymer) and of the size and thickness of the hollow spheres.
2. Materials and experimental techniques
The polymer consisted in a mixture of a difunctional epoxy resin (Diglycidyl ether of bisphenol A, DGEBA) and a diamine hardener (4,4′-methylenebis(3-chloro-2,6-diethylaniline, MCDEA) at stoichiometric ratio (a/e=1; Ellis 1993; Pascault et al. 2002). It leads to a network with high glass transition temperature (Tg of 175 °C) after extensive cure (Girard-Reydet et al. 1995; Bonnet et al. 2000; Fine et al. 2003). Two kinds of hollow spheres were used as fillers hereafter referred as MS1 and MS2, respectively. They exhibit almost similar geometries but differing glass nature. However, the hollow spheres are fabricated in both cases from initially plain glass spheres. A population of plain spheres including foaming agent is blown through a flame in which the diameter of the glass increases. The spheres are then quickly cooled down in order to fix their dimensions. Table 1 summarizes the information given by the technical data sheets of these products. Note that the methods used to measure the mean external diameter is different for the two providers. The MS1 spheres is expected to have a density slightly superior and their glass thickness should be higher compared to the MS2 spheres and/or their diameter is smaller.
With these two kinds of spheres, two model foams were produced with a targeted volume fraction of spheres of 55%. These will be referred in the paper as samples MS1-55 and MS2-55 depending on the nature of the spheres. A third sample was also produced with 30% of MS2 and will be referred as MS2-30 in the rest of the paper.
Diepoxy and diamine monomers were heated to 90 °C for 20 min and mixed in a reactor vessel while gently stirring before filler material was added at a volume fraction of 30 or 55%. Mixing time of 20 min under vacuum allowed to reach an homogeneous mixture free of bubbles. The liquid mixture was then cast in large moulds of designed thickness (30 mm), cured according to table 2 and followed by a quick cooling to room temperature. The glass transition (Tg) was systematically checked by differential scanning calorimetry (on a DSC Q100 device from Waters), taken at the onset during ramp of 10 °C min−1.
The Tg of the foams reaches the same value as the polymer (175 °C), assessing that the network had reached a maximum cure extent (Girard-Reydet et al. 1995; Bonnet et al. 2000). The density of the pure polymer material was 1.2 g cm−3. Thermogravimetric analysis (TGA) was performed (with a TG 209 device from Netzsch) on the materials to check their actual mass fraction of spheres. The experimental conditions for the heating ramp for these measurements were: 10 °C min−1 from 30 to 700 °C. Table 3 summarizes the results obtained. The density measured using the standard pycnometrical technique is also indicated.
The pycnometrical density of syntactic foam materials was very close to the value calculated from a simple mixture law, suggesting that there is no significant porosity in the matrix of the samples.
Parallelepipedic samples of 1×1×10 mm3 were cut for X-ray tomography scanning.
(b) X-ray tomography
The general principle of the tomography technique has been described in a previous paper (Maire et al. 2001). The experimental implementation requires an X-ray source, a rotation stage and a radioscopic detector. A complete analysis is made by acquiring a large number (here 1200) of X-ray absorption radiographs of the same sample under different viewing angles (one orientation for each radiograph). A final computed reconstruction step is required to produce a three-dimensional map of the local absorption coefficients in the material which gives indirectly a picture of the structure at the scale of the resolution of the set-up used. The reconstruction was performed thanks to the high speed tomography (HST) program developed at the European synchrotron radiation facility (ESRF) by Andy Hammersly (http://www.esrf.fr/computing/scientific/HST/HST_REF/hst.html). The images were obtained using a synchrotron radiation tomograph located at the ID19 beam line of the ESRF in Grenoble (France). In this set-up the source is 100 μm small but located 150 m from the sample. The 6 MeV electrons produce hard X-rays in a wiggler. These X-rays were monochromated at 9.7 keV with a multilayer monochromater. The absorption images were collected using a fast read out 2048×2048 CCD camera.
The resolution is defined in the present work as the lateral size of a voxel in the final image. A value of 0.7 μm was reached thanks to the fluorescent screen and optic set-up used for the detector. This allowed the low thickness of hollow spheres to be imaged with a sufficient separation. Due to the extremely high-lateral coherence of the X-rays available at the ID19 synchrotron beam line, diffraction patterns form between two rays propagating on each side of an interface between two phases of different refractive index in the material (Buffière et al. 1999). These over imposed interferences spread over a lateral distance, which is not negligible compared to the thickness of some of the hollow spheres. As a consequence, in the regions surrounding these air/glass and polymer/glass interfaces, the contrast was a bit complicated by the presence of these interferences. This limited the resolution with which the thickness could be determined. This will be discussed in details later in the paper. The obtained three-dimensional images were then processed and analysed using appropriate softwares.
3. Image processing results
(a) Qualitative images
Figure 1 shows the structure of the data in three dimensions. This figure shows the boundary of the bloc investigated. It also shows three orthogonal extracted grey level slices and how they intersect in the reconstructed bloc. Figure 2 shows the same bloc after thresholding of the images to visualize the glass phase only. These qualitative images show the power of the technique for the complete investigation of the arrangement of the three phases in space. Figures 3a–c show three of the extracted tomographic orthogonal slices (one for each of the samples). These grey level images are comparable to a light microscope visualization of the microstructure. Note, however, that these are obtained non-destructively and that the reconstructed three-dimensional image consists in a pile up of several thousands of these contiguous slices. Some noticeable differences between the three samples can be observed. As expected, there is clearly less spheres in the MS2-30 specimen. Disregarding their volume fraction, the spheres seem quite identical in the MS2-30 and MS2-55 samples. The MS1-55 sample is very different from the MS2-55 one. At first sight the average of the size distribution is smaller in the MS1-55 sample but the width of the distribution seems to be larger. All these observations will be comforted by the quantitative measurement performed according to the procedure described in the following section. The matrix seems to be free of pores intersecting the chosen slices. It has been carefully checked that no pores were detected in the matrix in any of the three specimen scanned. This is consistent with what was deduced from the pycnometry measurement and validates the fabrication procedure of the model materials. Note that the fabrication process of the hollow spheres results in the presence of imperfect objects: a large majority of the spheres are hollow but there is also a small fraction of imperfect objects in the population.
(b) Image processing procedure
Given the experimental conditions during the acquisition of the images, the size of the total reconstructed data (typically 1400×1400×2000 voxels for each sample) precludes the analysis at once of the entire block representing one sample. The recorded images were then first cut into smaller sub-volumes. In order to keep the data representative and after several convergence tests, a size of 500×500×350 cubic voxels was chosen. Several of these little sub-volumes were cut from the MS2-55 sample to check the representativeness of the selected size.
In reality, three phases coexist in the material: air, glass and polymer. The present work aims at characterizing the mutual arrangement of these three different phases. The grey level three-dimensional images have firstly to be transformed into ternary images containing only three values of grey level depending on the phase to which each voxel belongs. This first transformation is commonly named ‘segmentation’ of the image. In order to ease the segmentation procedure, the grey level images were pre-filtered using a non linear diffusion filter (Chen & Vemuri 2000). The result of this smoothing filter is shown in figure 4 which shows the same type of slices as those shown in figure 1. The images were thresholded for a value of the grey level permitting to obtain the glass phase. The matrix was then selected by a ‘region growing procedure’ during which a seed was chosen manually inside the matrix. The software agglomerated to the original seed all the voxels having a grey level similar to this of the seed. The criterion for the agglomeration was that the difference between the levels had to be smaller than a tailored limit. The remaining voxels were then assumed to belong to the air phase. Figure 5a–c shows three extracted tomographic slices after segmentation (one for each of the samples). The processed three-dimensional images were then used in the way described in the following section to quantify the microstructure.
(c) Quantification of the microstructure
(i) Volume fraction of the three phases
Once the images were segmented into three grey levels, it was first possible to perform global measurements. The volume fraction of each phase could be measured by simply counting the respective number of voxels of each colour. In the present study, instead of calculating the different ratios over the entire volume in the block, those in the different orthogonal z slices of each bloc were rather calculated as sketched in figure 6. This allowed to quantify simply the fluctuation of the repartition of each phase along one direction in the material. The result could then be given as an average and a standard deviation of the value of the volume fraction of the phase over the slices at different z values in the sub-volume. It was verified that the result on the average value do not depend on the direction in which the orthogonal slices were cut (i.e. perpendicular to x, y or z) although the standard deviation slightly depended on this direction. The results for the three different materials is given in table 4. The measurements were performed on the air and ‘air+glass’ phases. The volume fraction of polymer and air were calculated from these two measured values.
In the case of the MS2-55 material, eight sub-volumes have been used for the measurement in order to demonstrate the relatively good homogeneity of the material and the representativeness of the size of the blocs (3003 voxels). The standard deviation of the measurement on these eight sub-volumes being very low (see table 4), it has then been decided to work on two sub-volumes only for the other materials. Table 4 shows that the targeted values during the fabrication have been more or less reached (30 and 55% of the air+glass phase). We measure a higher content in the 55% targeted materials and a smaller content in the 30% material. It is also very clear that these tomographic results disagree with the ATG measurement of the phase content. The glass fraction is overestimated and the polymer fraction is underestimated by the image processing measurement. For this measurement we believe that ATG measurements are better. It has been mentioned above that the phase contrast present in the three-dimensional images at the interface between the three different phases biases the exact determination of the thickness which, in any case, can not be achieved with a resolution better than 1 voxel. Given the average fraction of spheres (30–55%) and their average diameter (35–40 μm) a slight mistake of 1 voxel (0.7 μm) in the measurement of the thickness of the glass shell can modify the volume fraction of approximately 5 and 3% (in the case of respectively the 55% material and the 30% material). Given this limitation, the global measurements presented in this section are in reasonable agreement with the targeted values (and values measured by ATG presented in table 3) but due to the image processing chain of measurement (filtering, segmentation, threshold) one should keep in mind that the thickness of the shell is certainly overestimated mainly towards the exterior of the spheres.
(ii) Measurement on individual objects
In order to perform measurements on each individual sphere, the segmented volume was labelled. In this procedure the air phase in each sphere was numerically recognized as a cluster of connected voxels forming an independent object. Each detected object was affected a different label. The separation of the air phase in three-dimensional was quite straightforward because the air voxels located inside each glass core were unambiguously separated from their neighbours by the glass shell. A dedicated computer three-dimensional image analysis routine implemented as a plugin1 in the ImageJ freeware (http://rsb.info.nih.gov/ij/) was then used to calculate the morphology (volume V, surface S, aspect ratio, centroids, etc.) of each object. The objects being nearly spherical, the two following parameters were calculated to quantify this morphology: the equivalent diameter Deq and the sphericity s. Deq is the diameter of the sphere having the same volume V as the objectwhere s was calculated as a combination of the actual volume and surface of each object as suggested in (Buffière et al. 2001)V and S being the volume and the surface of the object, respectively.
The measurement was performed on objects larger than 100 voxels. This implies that fragments of spheres were excluded from the analysis. The volume fraction of these excluded objects remained very low (0.01% of the total air content).
In the rest of the paper, the objects touching the border of the investigated sub-volume were systematically excluded from the measurement because their morphology is likely to be modified by the presence of the border.
Table 5 shows the results of the measurement of these parameters (air volume, internal diameter and sphericity) for the three considered materials.
The spheres were also treated as plain objects by performing a labelling on the air+glass phase. This allowed to perform the same analysis as the one described above to retrieve the external diameter of the spheres. Note, however, that in this case, the number of contacts between the different spheres being very important, a simple threshold method was not sufficient to separate the different objects. It was necessary to apply a separation method based on mathematical morphology. This method is implemented in the Aphelion software through the tool ‘ClusterSplitConvex’. It consists in a combination of different morphological operations on the images: threshold, distance map calculation, filtering and threshold of the distance map. The results of this numerical separation is shown as an example in figure 7 in the case of one single slice extracted from one of the MS2-55 treated blocs. Once the plain spheres were separated, it was possible to calculate their external diameter. The results of this measurement is also presented in table 5. From the difference between the mean of the internal and external diameter, the mean thickness of the glass could be retrieved. This calculation (measured here by the method called ‘diam average’, see later) is also given in table 5.
The following conclusions can be drawn from table 5. The MS1-55 material contains much more objects than the two others. The MS2-30 foam contains half less objects than the MS2-55. In the three materials, the objects are measured to be very spherical (s=0.95). For a same kind of sphere (compare MS2-55 and MS2-30), the average volume, equivalent diameters and thickness of the shell are quite similar. The distribution in the volume of the spheres is huge in the three cases as underlined by the value of the standard deviation (the complete shape of the distribution of the diameters will be presented later in the paper). The width of the distribution (again measured to be very wide especially in the case of the MS1-55 material) is consistent with the observations made in figures 3 and 7. The external diameter distribution of the spheres before incorporation was also obtained using a standard method. This method consists in laser granulometry measurements (on Mastersizer 2000 from Malvern) in aqueous media. Particles pass in front of an optical device measuring the diffraction and diffusion of the laser beam. 50% of the volume of spheres have a diameter under 37 μm for the MS1 spheres and under 46 μm for the MS2 spheres. The informations from the providers, given in table 1, are contradictory but the methods used by the two providers were not the same. In conclusion, with the image analysis used here, the external mean diameter of the MS2 spheres appears to be slightly larger than the MS1 one and it confirms that the MS1 spheres are smaller than the MS2 sphere, generating a slightly higher density (0.38 g cm−3 against 0.35 g cm−3).
The actual dimensions given by tomography in both cases are higher than indicated by the standard method. Indeed, there is a small amount of broken spheres. They are considered as full size sphere by tomography. However, the standard method gives for the fragment the diameter of an equivalent sphere with the same volume than the fragment. The measured diameter by the standard method is thus smaller than the diameter of the initial sphere, given by tomography.
(iii) Thickness/diameter ratio
The image processing software used for quantifying the morphology of the internal cavities also provides the information of the location of the centroid of the detected object in the sub-volume. This information was used to relate the thickness of each object to its external diameter. This was performed by associating the results of the measurement made on the air objects and on the air+glass objects of a same sub-volume. The match between the two triplets of centroids was used to decide of the correspondence between the two kinds of objects. This filtering procedure has the drawback to reject some of the objects for which it is impossible to find a correspondence. This procedure has been applied for the more spherical objects, for which it is straightforward to define a thickness (measured here by method called ‘diam objects’, see later). The knowledge of the internal and external diameter of a same object allowed to measure its thickness in a slightly different way compared to the one previously used in the preceding section. This thickness is plotted as a function of the external radius of the corresponding object in figure 8 for the MS2-55 and MS1-55 materials. Although a certain degree of scatter exists in the measurement (especially in the case of the MS1 spheres with some objects presenting higher thickness at low diameter) there seem to be a correlation between the thickness of each sphere and its size. It is observed indeed that the thickness increases very slightly with the mean diameter of the sphere. Note, however, that the slope of this increase is very small.
(iv) Granulometry by mathematical morphology
When the phase to characterize is continuous all through the sample, the above local measurements based on the definition of different objects can no longer be performed because the phase consists in only one object. This is for example the case for the polymer phase in the investigated materials. It would be interesting, however, to measure the thickness of the polymer in the foam and its distribution. It is possible to perform such a measurement by applying the granulometry by mathematical morphology method presented in (Elmoutaouakkail et al. 2002). This method provides a tool to measure the three-dimensional granulometry of a phase in an image. It consists in performing sequential closing using an isotropic structural element of increasing size. It is well known in mathematical morphology that a closing using an element of size c eliminates the features having a thickness of less than 2×c in the three-dimensional image. By counting the number of voxels eliminated by such an operation, it is then possible to measure the amount of phase exhibiting this particular (2×c) thickness. Applying this method sequentially for increasing values of c allows then to measure the volume frequency distribution of the thickness of the considered phase in the material. This granulometry has been measured in the three materials under study. The result of these measurement is shown in figure 9a–c for the glass, the polymer and the air+glass phase, respectively.
The granulometry on the glass phase (figure 9a) has been intentionally presented with a log scale in the frequency axis to highlight the differences between the three materials. It shows again the very small thickness (measured here by method called ‘granulo’, see later) of the hollow spheres used. 90% of the air phase has a thickness smaller than 5 μm. The MS1 spheres are slightly different in thickness distribution than the two MS2 materials. The granulometry of the polymer phase is shown in figure 9b which illustrates that the two materials reinforced with 55% of spheres have a remarkably similar distribution while the material reinforced with 30% of spheres exhibits larger regions of polymer. Note that this characteristic distribution cannot be obtained using another method. Figure 9c only compares the granulometry measured for the glass+air phase on the two 55% materials. This distribution in size could also have been retrieved from the measurement on the individual objects. In the present case, the objects being relatively isotropic, the two different ways of extracting the distribution (mathematical morphology and from the measurement on individual objects) are likely to give nearly identical results so only the granulometry technique has been used for this part of the study. Together with the tomography granulometries, the figure 9c also shows the one determined using a standard method on the spheres before incorporation (presented earlier in the paper).
The distribution of the external diameters is in good agreement in the MS1 and MS2 materials. This was already shown in the measurements on the objects in the preceding section. Tomography gives results slightly higher as explained earlier.
(a) Thickness measurement
Three different methods have been used in the present study to quantify the thickness:
difference between the average external and internal equivalent diameter of the objects; in this case, the objects are all assumed to be perfect hollow spheres which is not the case in reality; this will be referred as method ‘diam average’;
difference between the external and internal equivalent diameter of some spherical objects for which a correspondence is made between the centroids of the air and air+glass objects; the drawback of this method is to reject the non perfect objects; this will be referred as method ‘diam objects’;
granulometry by mathematical morphology; this method accounts for all the spheres in the material (perfect or not); this will be referred as method ‘granulo’.
Table 6 summarizes the measurement of the thickness by these different methods for the three materials. Sample MS2-30 was not measured using method ‘diam objects’. For methods ‘diam objects’ and ‘granulo’, it is possible to measure a minimum and a maximum value of the thickness in the population of spheres.
The measurements using the different methods are complementary. The differences can be explained regarding the peculiarities of each procedure involved. The MS2-30 sample has the smallest thickness. It should be close to the one measured in sample MS2-55. The discrepancy can be possibly explained by a higher number of fragments in the 55 materials or rather by a slight difference in the threshold procedure of the three-dimensional grey level images. Methods ‘diam average’ and ‘granulo’ give rather similar results (these are two global methods) although the latter measures a slightly larger thickness. Method ‘diam objects’ gives the smallest thickness. This is natural because it only considers the spherical spheres which are also likely to be the thinnest (the imperfect spheres are rejected from the measurement). The minimum value (whatever the real thickness is) obtained using the method ‘granulo’ has to be equal to two times the resolution (2×0.7=1.4 μm). It induces a shift in the mean value towards higher value. The maximum value obtained with this method has to be related to the larger imperfect sphere present in the material. This value appears to be larger in the MS1 than in the MS2 material. The minimum value obtained using the ‘diam objects’ method can be more precise because a high number of voxels is used in the determination of the actual volume and then of the equivalent diameter of each object. The minimum thickness is then more reliable with this measurement than with the ‘granulo’ one. The value of the maximum measured with this method has to be regarded as the maximum of the thickness of the perfect spheres. Again this is slightly larger for the MS1 hollow spheres.
(b) Thickness to diameter ratio
The thickness of the hollow objects has been measured to increase only slightly with their external diameter. This rather equal value of the thickness is quite remarkable and is certainly a character, which is due to the high temperature blowing fabrication process of these hollow objects. As explained above, the thickness can be measured using different methods. None of these is perfect, but the three are complementary. It is worth noting that the tomography provides here a information which is very difficult to obtain using standard methods. In the case of scanning electron microscope (SEM), one would have to work on broken spheres for example. The scatter in the thickness to diameter ratio is higher for the MS1 spheres. This again shows that this product is less homogeneous than the other.
(c) Granulometry of the spheres before blowing
The nearly constant thickness of these hollow objects demonstrates that the size distribution of the initial plain spheres is rather scattered. If the volume of the initial plain sphere was a constant, say Vp, the relation between the thickness t and the external diameter d of the hollow sphere would be (if t is small compared to d)with a coefficient A depending on Vp. The thickness would in any case be decreasing quite strongly with d. The actual distribution of the plain spheres before blowing can be determined from the volume of glass in each object, for instance calculated using the thickness and diameter shown in figure 8. This calculated distribution is shown in figure 10. These two distributions are remarkably identical. This shows that the difference between the fabrication of the hollow sphere lies in the blowing process itself and not in the granulometry initial plain spheres used.
Model epoxy-glass syntactic foams have been produced on purpose to study the effect of the kind of hollow spheres (MS1 and MS2) and their volume fraction (30 and 55%) on the mechanical properties of these materials. The cellular architecture of three of these model syntactic foams has been imaged in the present study by high-resolution synchrotron X-ray tomography. The experiments were carried out using a 0.7 μm resolution. This allowed very fine details such as the thickness of the hollow spheres to be observed unambiguously. The selected samples were the MS1-55, MS2-55 and MS2-30.
The images obtained with the three kinds of samples were firstly analysed qualitatively. It appeared that the size distribution is less homogeneous in the MS1-55 material. A very small amount of imperfect objects and broken fragments of spheres could be observed in the microstructure whereas no pores were detected in the matrix.
The fraction of the three components (air, glass and polymer) were measured in the three materials. The determined fraction of glass is overestimated certainly because the image processing leads to a higher diameter towards the exterior of each spheres. This is evidenced by the comparison of the image and the ATG measurements. The uncertainty in this parameter is partly due to the phase contrast in the images.
The size distribution of the external and internal diameter of the spheres were measured to be more scattered in the MS1 materials than in the two MS2 ones.
The thickness of the hollow spheres was measured using three different ways of analysing the images. The MS1 spheres seem to be slightly thicker than the MS2 ones. Tomography is indeed one of the only methods capable to allow such a direct measurement especially after the incorporation of the spheres in the final product.
The thickness depends only slightly on the external diameter of the sphere. This main finding indicates that the initial size of the plain spheres before blowing is distributed. This initial size distribution has been retrieved from our measurements.
The authors would like to thank the Institut Français du Pétrole and the Association Nationale de la Recherche Technique for financial support. Eric Dedreux and Pierre-Philippe Broizat have been participating to the experiments at the ESRF and have analysed the images obtained during a training period in order to obtain their engineering degree. Elodie Boller was local contact for the ESRF experiment. The authors wish to acknowledge them all for their help.
One contribution of 18 to a Discussion Meeting Issue ‘Engineered foams and porous materials’.
↵The implementation was performed by Luc Salvo from the GPM2 laboratory in Grenoble.
- © 2005 The Royal Society