The real densities of the CNF–CoFe2O4 composite papers were 0.7983 g/cm3 (x = 5), 1.1967 g/cm3 (x = 20), and 1.5058 g/cm3 (x = 35). Assuming that all water was evaporated from the dried CNF–CoFe2O4 composite paper and taking the theoretical densities of CoFe2O4 and cellulose (5.29 [40] and 1.50 g/cm3, respectively), the volume fractions of the CoFe2O4 particles dosed at x = 5, 20, and 35 were calculated as 10.9, 21.0, and 27.5 vol.%, respectively, in the final CNF–CoFe2O4 composite paper (see Table 1). The average thicknesses of the CNF–CoFe2O4 composite paper containing 10.9, 21.0, and 27.5 vol.% CoFe2O4 were 0.25, 0.49, and 0.92 mm, respectively. The real density of the CoFe2O4 sintered plate was 4.298 g/cm3. The relative density of the CoFe2O4 sintered plate was calculated as 81.2% of the theoretical density of 5.29 g/cm3.
Table 1
Parametric values of the CNF–CoFe2O4 composite papers
CoFe2O4 content

10.9 vol.%

21.0 vol.%

27.5 vol.%

\({\text{V}}_{\text{c}\text{f}\text{o}}\)

0.109

0.210

0.275

\({V}_{\text{p}}\)

0.744

0.731

0.689

\({V}_{\text{m}}\)

0.147

0.059

0.036

Apparent\({E}_{}^{\text{*}}\)

0.523 GPa

0.269 GPa

0.195 GPa

\({d}_{33}^{\text{*}}\)

–8.95\(\times\)10−12 m/A

–66.5\(\times\)10−12 m/A

–166\(\times\)10−12 m/A

\(\text{A}\text{p}\text{p}\text{a}\text{r}\text{e}\text{n}\text{t} {\mu }_{33}^{\text{*}\text{T}}\)

0.0769\(\times\)10−6 H/m

0.127\(\times\)10−6 H/m

0.228\(\times\)10−6 H/m

Apparent\({k}_{33}^{2}\)

5.45\(\times\)10−16

9.37\(\times\)10−15

2.36\(\times\)10−14

Figure 2 shows the size distributions of the CoFe2O4 particles. The average particle size was 56 µm. The CoFe2O4 powder comprised small and large particle populations with approximate diameters of 10 and 150 µm, respectively. As shown in Fig. 3, the XRD patterns of the 10.9 vol.% CNF–CoFe2O4 composite paper matched those of the CoFe2O4 particles. Therefore, the CoFe2O4 was stable against chemical transformations during the fabrication process. Figure 4 shows the SEM images of the CNF–CoFe2O4 composite paper. Although the CoFe2O4 particles were dispersed through the CNF matrix, they were agglomerated by the hand mixing process. The size distribution peak at 150 µm in Fig. 2 was probably contributed by large agglomerates of CoFe2O4 particles. Figure 5 shows the EDX mapping of the 27.5 vol.% CNF–CoFe2O4 composite paper (the micrograph is shown in Fig. 4(c)). The EDX detected C, O, Co, and Fe on the surface of the CNF–CoFe2O4 composite paper and implied that CoFe2O4 was stable during the fabrication process, reconfirming the XRD results. Note that no characteristic intensities of the Xrays appeared in the shadow of the EDX detector because they were attenuated by the uneven surface of the CNF–CoFe2O4 composite paper surface.
Figure 6 shows the magnetic properties of the CNF–CoFe2O4 composite paper and CoFe2O4 plate. The CoFe2O4 additives magnetized the CNF paper. The maximum magnetization of the CNF–CoFe2O4 composite paper linearly increased with increasing proportion of CoFe2O4 particles. Consistent with the present results, Williams et al. [41] reported that the magnetic properties of magnetizing cellulose fibers depend on the volume percentage of the implemented magnetic filler in the fiber matter. The magnetic curve of the CNF–CoFe2O4 composite paper reached saturation more slowly than the CoFe2O4 sintered plate. In Eq. (4), the effective magnetic permittivity \({\mu }_{33}^{\text{*}\text{T}}\) of the CNF–CoFe2O4 composite paper under stressfree conditions was given by
$${\mu }_{33}^{\text{*}\text{T}}=\frac{{B}_{3}}{{H}_{3}}$$
9
.
The apparent effective magnetic permittivities \({\mu }_{33}^{\text{*}\text{T}}\) of CNF–CoFe2O4 with CoFe2O4 contents of 10.9, 21.0, and 27.5 vol.% were evaluated as 0.0769\(\times\)10−6, 0.127\(\times\)10−6, and 0.228\(\times\)10−6 H/m, respectively (see Table 1).
Figure 7 shows the magnetostrictive properties of the CNF–CoFe2O4 composite paper and CoFe2O4 plate. In the CNF–CoFe2O4 composite paper, the magnetostriction was negative and positive in the directions parallel and perpendicular to the magnetic field, respectively, as expected. The magnetostriction of the CoFe2O4 plate was − 90 ppm under a magnetic field of 217 kA/m. The maximum negative magnetostriction of the CNF–CoFe2O4 composite paper deviated from the fitting line [see Fig. 7(e)]. Note that the 10.9 and 21.0 vol.% CNF–CoFe2O4 composite papers failed to achieve magnetostrictive saturation under a magnetic field of \({H}_{3}=\pm\)733 kA/m. These results imply that the CNFs between the CoFe2O4 particles deformed with magnetostriction of the CoFe2O4 particles and facilitated linear magnetostriction of the whole CNF–CoFe2O4 composite paper. In Eq. (3), the effective piezomagnetic constant \({d}_{33}^{\text{*}}\) of the CNF–CoFe2O4 composite paper under stressfree conditions was calculated as
\({d}_{33}^{\text{*}}=\frac{{\epsilon }_{3}}{{H}_{3}}\).
.
After straightline fitting of the linear portions of the curves in Fig. 7(a)–(c), the \({d}_{33}^{\text{*}}\) values of the CNF–CoFe2O4 composite papers containing 10.9, 21.0, and 27.5 vol.% CoFe2O4 were calculated as − 8.95\(\times\)10−12, − 66.5\(\times\)10−12, and − 166\(\times\)10−12 m/A, respectively (see Table 1). Clearly, the \({d}_{33}^{\text{*}}\) of the CNF–CoFe2O4 composite paper increased with increasing CoFe2O4 particle addition. From Eq. (3), the effective piezomagnetic constant \({d}_{31}^{\text{*}}\) of the CNF–CoFe2O4 composite paper under stressfree conditions was also obtained as
$${d}_{31}^{\text{*}}=\frac{{\epsilon }_{1}}{{H}_{3}}$$
11
.
Similarly, the \({d}_{31}^{\text{*}}\) values of the CNF–CoFe2O4 composite paper containing 10.9, 21.0, and 27.5 vol.% CoFe2O4 were calculated as 0.391\(\times\)10−12, 18.8\(\times\)10−12, and 27.1\(\times\)10−12 m/A, respectively.
Figure 8(a) shows the stress–elongation curves of the CNF–CoFe2O4 composite papers. Here, the elongation was estimated from the displacement of a universal testing machine crosshead. Between 0 and 0.2% elongation, the slopes of the stress–elongation curves of the 10.9, 21.0, and 27.5 vol.% CNF–CoFe2O4 composite papers were determined as 0.523, 0.269, and 0.195 GPa, respectively (see Table 1). These values were taken as the apparent effective Young's moduli. Panels (b) and (c) of Fig. (8) plot the ultimate tensile strengths (UTSs) and fracture elongations versus CNF volume fraction in the CNF–CoFe2O4 composite papers. The CNF volume fractions in the 10.9, 21.0, and 27.5 vol.% composite papers were 14.7, 5.9, and 3.6 vol.%, respectively. The UTS of the CNF–Fe2O4 composite paper was increased by the connection between the CoFe2O4 particles via the CNFs. On the downside, the CoFe2O4 additives decreased the UTS. As strength and toughness are usually considered to be inversely proportional, the CNF–CoFe2O4 composite paper probably has good toughness, and further experiments will reveal its durability as a vibrationenergy harvesting device. The apparent \({k}_{33}^{2}\) values of the 10.9, 21.0, and 27.5 vol.% CNF–CoFe2O4 composite paper were 5.45\(\times\)10−16, 9.37\(\times\)10−15, and 2.36\(\times\)10−14, respectively (see Table 1). The improved magnetomechanical coupling factor after adding CoFe2O4 implies that the CNF–CoFe2O4 composite paper is a promising candidate for energy harvesting applications.