Cellulose (2020) 27:6961–6976
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Still, the overall pore size distribution is affected by the mean bubble size also in denser foam-formed sheets than those studied here (Al-Qararah et al. 2015b). The above bubble traces cause the material distri- bution to be heterogeneous in the micro scale so that fibres are confined in narrow gaps between bubbles. Thus, the effective local density can become quite large in these densified regions. This has an important impact on the compression properties of the materials. Besides the normal pores, almost all samples included also larger voids, which may have originated from either very big bubbles or local opening of the fibre network because of drying stresses. The other typical heterogeneity came from the denser material surfaces, which was caused by the rewetting and pressing procedure used in sample making. Table 2 shows the measured initial material density and compression stress at two deformation levels, 10% and 50%, for the various trial points without added fine components. We expect the structure to become more uniform when the compression proceeds and possible voids are closed. Therefore, it is of interest to compare the slope of the stress–strain curve at the highest studied compression level (50%) with the theoretical prediction. This comparison is also included in Table 2. Compression stress (see Fig. 6a) and especially the compression modulus (see Fig. 6b) increased when polymeric water-soluble and film-forming PVA was applied as the foaming agent instead of anionic SDS. The refining of NBSK, which caused external fibril- lation of the fibres and the generation of cellulosic fines, increased the relative material strength of the PVA foamed samples (TP5) more than the strength of the SDS foamed samples (TP2). Despite material non- uniformity (see Fig. 7b), PVA increased bonding so that both types of fibres, as well as formed cellulosic fines, contributed more actively to the strength of a highly porous fibre network. The material may have densified locally because of the large voids in the material obtained using PVA, see Fig. 7b. Subse- quently, the mean free segment length in the fibre network was shorter in the densified regions. This could make a significant contribution to strength, which behaves like the square of density in these types of materials (Ketoja et al. 2019). The effect of improved bonding was seen, especially when 20% of the refined NBSK pulp was replaced with poorly
considering the statistical distribution of the ratio of stresses measured at 50% and 10% compression levels with a theoretical prediction, r 0 : 5 ð Þ r 0 : 1 ð Þ ¼ s 0 : 1 ð Þ s 0 : 5 ð Þ 2 5 : 374 ð 3 Þ In reality, other deformation modes like the bend- ing of fibres can be significant as well (Hossain et al. 2019; Bergstro¨m et al. 2019). Moreover, especially the initial deformation behaviour can be very non-uniform (Ma¨kinen et al. 2020). However, Eqs. (1, 2) provide an interesting reference curve which helps the compar- ison of the data. In the current study, we consider the slope of the stress–strain curve at high strain levels, d r ð Þ d ¼ 2 r 0 e s ð Þ s ½ ð Þ 4 ¼ 2 r ð Þ s ð Þþ 1 ½ s ½ ð Þ 2 ð 4 Þ instead of the ratio given by Eq. (3). This slope is less sensitive to the changes at small strains, which are poorly described by the simplified model lacking the effect of fibre bending or closing up of large initial voids at small strains. At 50% compression, we obtain the prediction ¼ 0 : 5 ð Þ¼ ð 5 Þ for the slope of the stress–strain curve scaled by the stress level. We will compare this value with the corresponding experimental results in addition to plotting the complete stress–strain curves against the theoretical Eq. (1). 1 r d r d 4 s 0 : 5 ð Þþ 1 ½ s 0 : 5 ½ ð Þ 2 3 : 804
Results and discussion
Effects of fibre size distribution and the type of foaming agent
The foam-formed fibre materials differ significantly from conventional water-formed random fibre net- works. Perhaps, the most striking feature is the significant proportion of large pores, which are left as traces of air bubbles. This is seen clearly in the x-ray scans of the fibre network, viewed over a series of planar sections in the thickness direction (see Supple- mentary material). The traces are not as clear in the cross-sectional side views because of the partial collapse of the pores during the density adjustment.
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