Hybrid Carbonyl Iron/Iron-Oxide Microfiber Textile Membranes with Magnetically Tunable Capacitance Under Compressive Loading

1. Introduction

Flexible capacitive sensors are widely used in wearable systems, human–machine interfaces, and robotic sensing because they combine mechanical flexibility, conformability, and low-power operation [1,2,3]. In the parallel-plate description, the capacitance depends on the electrode area, the electrode spacing, and the apparent relative permittivity ${\epsilon }_{\mathrm{r}}$ of the dielectric layer. Mechanical deformation generates an electrical signal by changing one or more of these parameters [1,4]. Therefore, the structure, stiffness, and dielectric response of the dielectric layer largely determine how the sensor deforms under load, and, thus, its sensitivity and operating range [1,4,5]. This has stimulated interest in dielectrics whose response can be tuned by mechanical loading together with additional external stimuli.

Magnetically responsive composites provide one such route. In magnetoactive elastomers and magnetorheological suspensions (MRSs), magnetizable microparticles are dispersed in an electrically insulating matrix [6,7]. Under a static magnetic field, the particles become magnetized and interact through dipolar forces, promoting chain-like or columnar aggregates aligned with the field [8,9]. This restructuring modifies the internal microgeometry and the local electric-field distribution and is commonly accompanied by a pronounced change in the apparent dielectric response [6,9,10]. Carbonyl iron (CI) microparticles are among the most widely used soft-magnetic fillers in such systems [8,9,11,12].

However, the use of spherical CI microparticles alone can limit the development of lightweight soft dielectrics because their high density tends to reduce sedimentation stability [13]. One way to expand tunability is to introduce a fibrous magnetic phase that restructures the field-responsive architecture without requiring very high filler loadings. For example, replacing spherical fillers with magnetic nanofibers in elastomers promotes interconnected networks and produces strong field-responsive behavior at substantially lower filler contents [14]. More recently, magnetorheological fibrous materials have been shown to exhibit pronounced controlled bending and stiffening by a magnetic field, enabling smart-textile actuation and tunable rigidity [15]. In suspensions, fibrous additives can also reinforce the field-induced structure and improve dispersion stability [16].

Hybrid textile-like composites that combine cotton fibers, CI microparticles, and iron-oxide microfibers ($\mu$Fe) are particularly interesting in this respect. In such systems, the microfiber component can reduce effective density and act as an anti-sedimentation medium, while the dielectric response varies systematically with microfiber fraction and magnetic flux density (B) [17]. These behaviors arise due to the changes induced by the microfibers in the spacing and arrangement of CI magnetic dipoles [17]. Microfiber concentration controls both magneto-dielectric and viscoelastic characteristics, and fiber-thread scaffolds can support particle chains and improve shear or damping under field [18,19]. Such results motivate hybrid particle–fiber dielectrics in which the magnetocapacitive response can be tuned through magnetic loading and phase morphology [14,17].

Textile dielectrics are attractive for wearable capacitive devices because they can undergo large reversible thickness changes while maintaining flexibility and, in some cases, high air permeability. [20,21]. Natural fibers such as cotton and cellulose strengthen this approach by offering abundant, skin-friendly scaffolds that can be electrically functionalized. Cellulosic materials are widely used in wearable sensors [22], and cotton fabrics have been modified with conductive electrodes and dielectric additives to improve capacitive performance [23]. However, these textile sensors predominantly rely on mechanically induced capacitance changes, whereas the integration of magnetodielectric tunability into porous textile dielectrics remains comparatively underexplored.

In this work, we fabricate hybrid magneto-responsive textile membranes by impregnating woven cotton scaffolds with silicone-oil (SO)-based suspensions containing CI microparticles and $\mu$Fe. Three membranes with constant CI loading (${\Phi }_{\mathrm{CI}}=10$ vol.%) and increasing $\mu$Fe content (0, 10, and 20 vol.%) are integrated as dielectric layers in planar capacitors. Using capacitance measurements at 1 kHz under controlled B and compressive pressure p, we estimate the apparent relative permittivity ${\epsilon }_{\mathrm{r}}$ and compare trends in magnetic-field sensitivity, pressure response, and apparent field-induced stiffening.

2. Materials and Methods

A schematic overview of the fabrication route (particle/fiber preparation, suspension formulation and textile impregnation), capacitor assembly, and magnetic-field-dependent electrical measurements together with the main data-reduction steps is shown in Figure 1. Details for each step are provided in the following subsections.

2.1. Materials

• CI microparticles, purchased from Sigma-Aldrich, were used as received. According to the supplier, the CI microparticles have a mean diameter of about 5 µm (Appendix A) and a mass density ${\rho }_{\mathrm{CI}}=7.68$ g/cm³ at 24^∘C. The specific saturation magnetization is ${\sigma }_{\mathrm{CI}}=195$ A·${\mathrm{m}}^2$ / kg, at magnetic field intensities $H\gtrsim 500$ kA/m [25].
• The carrier liquid is SO, grade MS100, used as received (viscosity and density at ${24}^{\circ }$C: 100 cSt and, respectively, ${\rho }_{\mathrm{SO}}=0.98$ g/${\mathrm{cm}}^3$) [26].
• $\mu$Fe were synthesized in-house as described in Section 2.2 (see also Ref. [24]). Their average diameter is $d_{\mu \mathrm{Fe}}\simeq 0.94$ µm and mass density ${\rho }_{\mu \mathrm{Fe}}=2.875$ g/${\mathrm{cm}}^3$ at ${24}^{\circ }$C. The specific saturation magnetization is ${\sigma }_{\mu \mathrm{Fe}}=22.7$ A· ${\mathrm{m}}^2$/kg, at $H\gtrsim 500$ kA/m [24].
• Commercial cotton fabric (CF) was used as the porous textile scaffold. The fabric is a woven mesh of interwoven threads. The threads have a diameter $d_{\mathrm{t}}\approx 0.12$ mm and are composed of cotton microfibers with a diameter $d_{\mathrm{y}}\approx 5.5$ µm, leaving spaces that facilitate liquid uptake by capillarity [27].
• FR-4 laminate boards coated with copper (LAM75X100H, Electronic Light, Romania), consisting of an epoxy resin/glass-fiber reinforced substrate with a single-sided copper cladding. The laminate thickness is 0.6 mm and the board size is 100 mm × 75 mm. The nominal thickness of the copper plate is 18 µm.

2.2. Synthesis of $\mu$Fe Microfibers

$\mu$Fe were synthesized using a microwave-assisted microplasma route, following the protocol reported in [24]. Iron pentacarbonyl (Fe(CO)₅) served as the iron precursor. A polyphasic precursor mixture consisting of CI microparticles, Fe(CO)₅ and SO was homogenized in an open, heat-resistant glass beaker and exposed to microwave irradiation in a domestic microwave oven (2.45 GHz; Samsung MG23F301TAK). The microwave output power and exposure time were set to 450 W and 120 s, respectively, as in Ref. [24]. The precursor composition was identical to Ref. [24] (CI: 2 cm³, Fe(CO)₅: 1 cm³, SO: 5 cm³). After microwave treatment, a loose cotton-wool-like product composed of $\mu$Fe was obtained [24]. After completion of the irradiation step, the product was cooled to room temperature and collected mechanically from the beaker and chamber surfaces. The microfibers collected were stored in sealed glass vials at room temperature until use in hybrid suspensions (Section 2.3). These processes correspond to the first two steps (1 + 2), enclosed by the dashed line, in Figure 1.

During microwave irradiation, a luminous microplasma and intermittent micro-explosion-like events can occur in the precursor mixture, promote rapid decomposition of the iron precursor and the formation of transient metal-vapor/gas streams. In cooler regions of the vessel and chamber, these vapors can condense (“dew-point” zones), generating ultrafine iron/iron-oxide particulates that further undergo nonstationary mass transfer and aggregation into a fluffy, cotton-wool-like product. The resulting hierarchical microfiber network is therefore consistent with a vapor–condensation-assembly route occurring under microplasma-assisted microwave heating (see Ref. [24] for a detailed mechanistic discussion and characterization).

2.3. Preparation of Hybrid Suspensions

Hybrid MRSs are prepared by co-dispersing CI microparticles and $\mu$Fe in SO. The volume of the components ($V_{\mathrm{CI}}$, $V_{\mathrm{SO}}$, $V_{\mu \mathrm{Fe}}$) was set to the values specified in Table 1. For each suspension, the corresponding volume fractions are calculated as follows:

$${\Phi }_k={\displaystyle \frac{V_k}{V_{\mathrm{CI}}+V_{\mathrm{SO}}+V_{\mu \mathrm{Fe}}}},k\in \{\mathrm{CI},\mathrm{SO},\mu \mathrm{Fe}\}.$$

(1)

The suspensions were prepared following a common protocol:

Step 1: 

The volumes of CI microparticles, SO, and $\mu$Fe microfibers were measured according to Table 1.

Step 2: 

The measured quantities are introduced into 20 mL Berzelius glass beakers (one beaker per composition).

Step 3: 

Each mixture is homogenized mechanically under heating (warm mixing) for approximately 300 s at about 150^∘C.

Step 4: 

After the heating stage, thermal treatment is stopped, while mechanical homogenization is continued until the mixture temperature reached ambient temperature. At the end of this step, the MRSs were obtained (step (3) in Figure 1) with the volume fractions listed in Table 1.

During preparation, the temperature was monitored using an infrared thermometer (IRT-350 type, Conrad Electronic SE, Germany). The prepared suspensions were used for textile impregnation immediately after preparation.

2.4. Fabrication of Hybrid Cotton Membranes

Hybrid CI/$\mu$Fe cotton membranes were manufactured by impregnating CF with freshly prepared hybrid MRS₁–MRS₃. Square CF specimens with a side length of 30 mm were cut from the same fabric roll. For each composition, a CF sample was placed in a 20 mL Berzelius glass beaker and impregnated with the corresponding suspension by adding an equal amount of aliquot (sufficient to fully wet/submerge the textile) and allowing capillarity uptake.

To promote infiltration into the textile network and improve the uniformity of the dispersion, each beaker containing the CF sample and suspension was subjected to a short warm treatment (approximately 300 s) while mechanically agitated. The beakers were then allowed to cool to ambient temperature. The impregnated samples were left to equilibrate at room temperature for 24 h. After this period, the resulting membranes were removed and placed above a Petri dish (or on an inert support) to allow removal of visible excess liquid by gravitational draining.

The membranes were labeled according to the suspension used for impregnation: hM₁ (from MRS₁), hM₂ (from MRS₂) and hM₃ (from MRS₃). The CI loading was kept constant in the MRSs at ${\Phi }_{\mathrm{CI}}=20$ vol.% (Table 1). After impregnation, the volume fractions of the membrane change because the cotton scaffold contributes an additional volume. Consequently, the volume fraction of CI in the membranes is ${\Phi }_{\mathrm{CI}}=10$ vol.% for all samples (Table 2). The membrane thickness measured after draining was approximately the same for all three compositions, namely $d\approx 0.42$ mm. The membranes were stored in sealed containers at room temperature until the capacitor assembly (Section 2.5).

Hybrid membranes (hM_i, $i=1,2,3$) obtained by cotton impregnation (Figure 2) have the compositions summarized in Table 2. This corresponds to step (4) in Figure 1. For each membrane, the volumes of the components (CI, SO, CF scaffold and $\mu$Fe) and the corresponding volume fractions are reported.

2.5. Planar Capacitor Assembly

Hybrid membranes hM_i (i=1,2,3) were used as dielectric layers in parallel capacitors PC_i (i = 1,2,3) manufactured from single-sided copper-clad FR-4 boards. The copper cladding served as the electrode material. For each capacitor, two identical electrodes were prepared and arranged face-to-face, with the membrane placed between them. The electrode overlap area A was defined by the geometry of the copper pad (Figure 3a) and was kept constant for all measurements. Here, it corresponded to a square region of $30\mathrm{mm}\times 30\mathrm{mm}$. Then, each membrane was centered on the lower electrode so that the overlap area was fully covered by the membrane. The upper electrode was then aligned to ensure a reproducible overlap area and to minimize lateral misalignment. This corresponds to step (5) in Figure 1.

The capacitor stack (FR-4/copper electrode–membrane–copper electrode/FR-4) was laterally aligned and enclosed using an insulating adhesive tape (3M) to ensure reproducible positioning and mechanical integrity (Figure 3a). The tape helped maintain the alignment of the stack and provided a mild mechanical restraint. The electrical connection to the copper electrodes was made using insulated leads attached to the electrodes (Figure 3b).

The total thickness of the capacitor (including the supports and FR-4 tape) was approximately 6 mm; however, in the capacitance analysis the effective separation of the electrode was taken as the membrane thickness d measured by micrometer. Representative photos of the assembled device are shown in Figure 3(c).

2.6. Magnetic-Field Setup and Electrical Measurements

Capacitance measurements were performed with the planar capacitor (Section 2.5) placed in the air gap between the N and S poles of a custom-built electromagnet (EM). This corresponds to step (6) in Figure 1. EM consists of a coil (Figure 4, position 1) wound on a ferromagnetic yoke (Figure 4, position 2). The pole gap was set at 6 mm. The coil was powered in direct-current source (DCS) mode by a regulated power supply (RXN-3020D, Rexton Electronics Co. Ltd., China), allowing continuous tuning of B up to $\approx 150$ mT.

The B in the sample region was monitored using a gaussmeter (Dexing Magnet, China) equipped with a Hall probe (Figure 4, Hs). During measurements, the Hall probe was positioned beneath the capacitor stack, aligned with the center of the electrode overlap area, to provide a reproducible reading of the local magnetic field experienced by the sample.

Capacitance was measured using an inductance-capacitance-resistance (LCR) bridge (CHY-41R, Taiwan–China) connected to the capacitor electrodes (Figure 4, Br). This corresponds to step (7) in Figure 1. Measurements were performed at a fixed frequency of 1 kHz in a parallel equivalent-circuit configuration appropriate for a planar capacitor.

In addition to the magnetic field, a controlled normal load could be applied to the capacitor stack along the direction of the magnetic field (Figure 4). A vertical hole drilled through the yoke allows a loading rod to pass. Masses (m) are placed on the loading platform to generate a compressive force $F=mg$, corresponding to $p=F/A$, where A is the area of overlap of the electrode (Section 2.5). For each membrane, the capacitor was mounted in the EM gap using identical positioning and tapping conditions. The magnetic field was set by adjusting the DCS current supplied to the coil, and the corresponding value B was read from the gaussmeter.

From the measured field and load-dependent capacitance, we subsequently determined ${\epsilon }_{\mathrm{r}}$ of the membranes, the magnetic stress (${\tau }_{\mathrm{zz}}$), the apparent strain ($e_{\mathrm{zz}}$), and the apparent modulus-like parameter (E) as described in Section 2.7. This corresponds to step (8) in Figure 1.

2.7. Data reduction and extracted quantities

For each membrane (hM_i, $i=1,2,3$), the equivalent capacitance $C(B,p)$ of the planar capacitor (Section 2.5) was measured at $f=1$ kHz (Section 2.6) as a function of B and p.

To quantify the magnetic-field-induced capacitance change, we define the magnetocapacitance as

$$\mathrm{MC}(B,p)={\displaystyle \frac{C(B,p)-C(0,p)}{C(0,p)}}\times 100\%.$$

(2)

Here, $C(B,p)$ is the capacitance measured at B and p, while $C(0,p)$ is the corresponding zero-field capacitance measured at the same p.

To quantify pressure-sensing performance, we define the average normalized pressure sensitivity as

$$S_p\left(B\right)={\displaystyle \frac{\left[C(B,p_{max})-C(B,0)\right]/C(B,0)}{p_{max}}},$$

(3)

where $C(B,0)$ is the capacitance at $p=0$ kPa, $C(B,p_{max})$ is the capacitance at maximum applied pressure $p_{max}$, and $S_p\left(B\right)$ represents the average normalized pressure sensitivity over $0\le p\le p_{max}$.

The quantities directly measured are the capacitances at the device-level $C(B,p)$ of the assembled capacitor structures. The dielectric and mechanical-response quantities introduced in the following are model-derived effective or apparent parameters. Although the primary observables are $C(B,p)$ of the assembled capacitor, the quantities reported below are attributed to the hybrid membrane within a simplified description of effective-medium. In this framework, the field- and load-dependent response is assumed to be dominated by the dielectric layer, while the electrodes and supports are treated as geometrically and electrically invariant. Consequently, ${\epsilon }_{\mathrm{r}}$ is used here as an apparent relative permittivity, $e_{\mathrm{zz}}$ as a capacitance-derived proxy, and E as an apparent modulus-like parameter derived within the adopted magnetic-stress model.

Using the parallel-plate capacitor relation, ${\epsilon }_{\mathrm{r}}$ of membrane i ($i=1,2,3$) at a given B was calculated using the zero-field thickness as

$${\epsilon }_{\mathrm{r}}\left(B\right)={\displaystyle \frac{C(B,0)d}{{\epsilon }_{0}A}},$$

(4)

where ${\epsilon }_0$ is the vacuum permittivity, A is the electrode overlap area, and d is the membrane thickness. For the present capacitors, $A\equiv L^2$, $L=30$ mm (see Figure 3) and $d=0.42$ mm. Unless stated otherwise, ${\epsilon }_{\mathrm{r}}\left(B\right)$ is evaluated at $p=0$. Because the membrane thickness may change under magnetic field and the dielectric layer is structurally heterogeneous, ${\epsilon }_{\mathrm{r}}\left(B\right)$ obtained in this way is an apparent effective quantity.

Because the measured capacitance increases under a magnetic field, the field-induced deformation is assumed to be predominantly compressive. To obtain a comparative measure of deformation from capacitance data, we estimate [28]

$$e_{\mathrm{zz}}={\displaystyle \frac{C(0,p)}{C(B,p)}}-1,$$

(5)

where $C(0,p)$ and $C(B,p)$ are the capacitances measured at the same p in the absence and presence of a magnetic field, respectively.

Following the dipolar interaction approximation adopted in [29], the magnetic interaction force acting on the membrane can be approximated as

$$F_m\approx -9{\Phi }_{\mathrm{CI}}{L}^2{B}^2/\left(2{\mu }_0\right),$$

(6)

from which we obtain:

$${\tau }_{\mathrm{zz}}=F_m/L^2\approx -9{\Phi }_{\mathrm{CI}}{B}^2/\left(2{\mu }_0\right).$$

(7)

In the following mechanical analysis, ${\Phi }_{\mathrm{CI}}$ refers to the volume fraction of CI microparticles in the final membrane (Table 2), not in the precursor suspension (Table 1). Therefore, for the membranes investigated here, ${\Phi }_{\mathrm{CI}}=10$ vol.% and ${\mu }_0=4\pi \times {10}^{-7}$ H/m, so Equation (7) becomes:

$${\tau }_{\mathrm{zz}}\left(\mathrm{Pa}\right)\approx -0.358B^2\left(\mathrm{mT}\right).$$

(8)

The negative sign indicates that the membranes undergo compression in the applied magnetic field.

An apparent modulus-like parameter of each membrane can then estimated from the ratio between${\tau }_{\mathrm{zz}}$ and field-induced strain:

$$E={\displaystyle \frac{{\tau }_{zz}}{e_{\mathrm{zz}}}}.$$

(9)

Because ${\tau }_{\mathrm{zz}}$ is estimated from a simplified dipolar magnetic-stress model and $e_{\mathrm{zz}}$ is indirectly inferred from capacitance, E should be interpreted here as an apparent comparative stiffness indicator.

3. Results

3.1. Morphology, Composition, and Magnetic Properties of $\mu$Fe

The morphology, composition, phase constitution, and magnetic properties of the $\mu$Fe used here were previously established in [24]; only a brief summary is given because these characteristics define the secondary magnetic filler in the hybrid CI/$\mu$Fe membranes. Scanning electron microscopy (SEM) observations showed that the microwave-synthesized microfibers form a complex hierarchical spiderweb-like network of interconnected filaments, with diameters in the range of approximately 0.25–2.20 µm and an average diameter of about 0.94 µm [24]. Energy-dispersive X-ray spectroscopy (EDX) analysis confirmed that the microfibers contain Fe and O, while X-ray diffraction (XRD) measurements revealed a mixed-phase iron-oxide composition consisting of $\alpha$-Fe₂O₃, $\gamma$-Fe₂O₃, and Fe₃O₄ [24].

Room-temperature magnetic measurements further showed that the microfibers are magnetically active, with a specific saturation magnetization of ${\sigma }_{\mu \mathrm{Fe}}\approx 22.7$ A·m ²/ kg, a remanent magnetization of approximately 2.86 A·m²/kg, and a coercive field of approximately 12.3 kA/m [24]. These values are substantially lower than those of CI microparticles (see Appendix A), which is consistent with the mixed-phase oxidized nature of the microfibers. At the same time, the hierarchical morphology and mixed iron-oxide composition of the $\mu$Fe provide structural and magnetic features that are complementary, rather than redundant, to those of CI. Therefore, when incorporated together with CI in cotton-based membranes, $\mu$Fe are expected to act as a secondary magnetic filler that modifies the packing of particles, constrains the field-induced rearrangement and thereby helps tune the dielectric and apparent mechanical response of the hybrid CI/$\mu$ Fe textile membranes investigated here.

3.2. Membrane Morphology and Structure

To study the morphology and structure, a SEM Inspect S PANalytical model from FEI Company (Eindhoven, The Netherlands) was used in low-vacuum mode and high voltage of 30.00 kV, coupled with EDX analysis detector with energies generated up to about 12 keV. Representative SEM images and EDX spectra of the pure cotton fabric and of a hybrid CI/$\mu$ Fe membrane fabricated are shown in Figure 5. The pristine cotton fabric exhibits the expected interconnected fibrous architecture, with individual microfibers forming an open scaffold that contains voids suitable for suspension uptake during membrane fabrication. This morphology is consistent with the role of the textile as a flexible porous support for the magnetic filler dispersed in silicone oil.

After impregnation, the membrane preserves the overall fibrous texture of the cotton scaffold, but the SEM image reveals additional solid-phase features associated with the incorporated magnetic filler. Compared to pristine fabric, the membrane appears denser and less open, indicating that the CI microparticles and $\mu$Fe are distributed within and around the cotton-fiber network. The corresponding EDX spectrum further confirms the presence of Fe-containing inorganic material in the membrane, demonstrating successful incorporation of the magnetic phase into the textile structure. In general, the SEM/EDX observations show that the hybrid membranes retain the flexible fibrous framework related to the cotton substrate.

3.3. Capacitance

The performance of membrane-based capacitors fabricated as flexible capacitive elements was first assessed by direct electrical measurements under magnetic and mechanical stimuli. For this purpose, the capacitance of the three planar capacitors PC₁-PC₃ was recorded as a function of B at $p=0$ kPa (Figure 6a), as a function of p at $B=0$ mT (Figure 6b), and during magnetic field cycling to examine hysteresis effects (Figure A2 in Appendix B).

The capacitance of all three planar capacitors increased monotonically with B in the investigated range $0\text{–}150$ mT. In zero field, the capacitance values were 0.259 nF, 0.182 nF, and 0.145 nF for PC₁, PC₂, and PC₃, respectively, and this ordering was preserved throughout the magnetic-field range. The increase was weak at low magnetic flux densities and became much more pronounced above about 60–80 mT, indicating a strongly nonlinear magnetic response. At $B=150$ mT, the capacitance reached 9.255 nF for PC₁, 5.222 nF for PC₂, and 2.261 nF for PC₃, corresponding to increases of approximately 35.7, 28.7, and 15.6 times relative to their zero-field values.

A monotonic increase in capacitance was also observed with p. In the investigated interval $0\text{–}10$ kPa, the capacitance is quasi-linear for all three capacitors. It increased from 0.259 to 0.301 nF for PC₁, from 0.182 to 0.227 nF for PC₂, and from 0.145 to 0.176 nF for PC₃. These changes correspond to relative increases of approximately 16.2%, 24.7%, and 21.4%, respectively. Although PC₁ retained the highest absolute capacitance throughout the pressure range, PC₂ displayed the largest absolute and relative pressure-induced increase. The data show that the three capacitor structures are sensitive to both magnetic field and compressive-pressure stimuli, with a much stronger absolute response to the magnetic field than to mechanical loading in the tested ranges.

For a compact comparison of the sensing characteristics, the main metrics extracted from $C\left(B\right)$ and $C\left(p\right)$ are summarized in Table 3.

3.4. Magnetic-Field Dependences of Apparent Relative Permittivity and Apparent Strain

The capacitance data were further used to evaluate ${\epsilon }_{\mathrm{r}}$, and the capacitance-derived proxy $e_{\mathrm{zz}}$, as functions of B. The corresponding results were calculated using Equations (4) and (5) and are presented in Figure 7. ${\epsilon }_{\mathrm{r}}$ increases monotonically with the B for all three membranes, while the $e_{\mathrm{zz}}$ component becomes progressively more negative. In both cases, the magnitude of the response decreases in the order hM₁> hM₂> hM₃. For low magnetic fields, the variations of ${\epsilon }_{\mathrm{r}}$ and $e_{\mathrm{zz}}$ are relatively weak, whereas much stronger changes occur in the intermediate and high-field range, followed by a tendency toward saturation at the highest values of B. At $B=150$ mT, ${\epsilon }_{\mathrm{r}}$ reaches approximately 488.8, 275.0, and 118.5 for hM₁, hM₂, and hM₃, respectively, while $e_{\mathrm{zz}}\approx -0.972$, $-0.965$, and $-0.936$.

3.5. Magnetic Stress and Apparent Modulus-like Response

${\tau }_{zz}$ calculated from Equation (8) and the corresponding apparent modulus-like parameter E (kPa) are shown in Figure 8. As expected from Equation (8), the normal ${\tau }_{\mathrm{zz}}$ is compressive and becomes increasingly negative with increasing B, changing from ${\tau }_{zz}=0$ at $B=0$ to ${\tau }_{zz}\approx -8.06$ kPa at $B=150$ mT. The magnitude of ${\tau }_{zz}$ increases nonlinearly throughout the investigated field range, reflecting its approximately quadratic dependence on B.

The apparent modulus-like parameter exhibits a membrane-dependent behavior at low and intermediate magnetic fields, followed by a clear increase at higher fields for all three membranes. At $B=10$ mT, the apparent modulus values are approximately 1.38, 2.23, and 5.29 for hM₁, hM₂, and hM₃, respectively, indicating that hM₃ is the most rigid membrane in the low-field range. For hM₁, E gradually increases from approximately 1.38 at 10 mT to 8.29 at 150 mT. For hM₂, E increases from about 2.23 at 10 mT to 8.35 at 150 mT, with a weak minimum around 50–60 mT. For hM₃, the modulus is initially the highest, decreases from about 5.32 at 20 mT to about 3.54 at 70 mT, and then increases again to about 8.61 at 150 mT. At the highest applied field, the apparent modulus values are close for all three membranes, ordering hM ₃> hM₂> hM₁.

For a compact sensor-oriented comparison, the selected dielectric and apparent mechanical metrics derived from the membranes hM₁, hM₂, and hM₃ are summarized in Table 4. The values show that hM₁ has the highest ${\epsilon }_{\mathrm{r}}$ and magnetocapacitance, while hM₃ exhibits the lowest dielectric response and the highest apparent modulus-like parameter in the intermediate magnetic field. $e_{\mathrm{zz}}$ at $B=150$ mT remains strongly negative for all three membranes, while the apparent stiffening ratio decreases from hM₁ to hM₃.

4. Discussion

4.1. Origin of the Magnetic-Field-Induced Dielectric Response

Both C and ${\epsilon }_{\mathrm{r}}$ increase monotonically with B for all membranes (Figure 6a and Figure 7a). In the present planar-capacitor configuration, this behavior is consistent with the magnetic-field-induced restructuring of the CI-rich phase and the resulting change in the electrical response of the heterogeneous dielectric layer [29,30]. Under an applied magnetic field, the CI microparticles become magnetized and tend to interact along the field direction, which is expected to promote the development of field-induced structures within the cotton scaffold impregnated with SO [30,31,32].

The response is distinctly nonlinear. At low field the capacitance changes only slightly and then rises much more rapidly in the intermediate range, before approaching saturation at the highest fields. This progression is consistent with the field-induced structuring within the membrane [30]. At low B, only limited rearrangement is expected, while at higher B the magnetic interactions become strong enough to induce a much larger change in the internal configuration of the membrane. The smaller incremental variation observed at the highest fields suggests that the system approaches a near-saturated state, so that further increases in B produce only modest dielectric changes.

The simultaneous evolution of ${\epsilon }_r$ and $e_{zz}$ further indicates that the dielectric response is coupled to the apparent compressive deformation. As the magnetic field increases, ${\epsilon }_r$ increases, while $e_{zz}$ becomes increasingly negative. This indicates that the dielectric enhancement is linked both to changes in the polarization pathways and to field-induced changes in the internal geometry of the composite layer.

4.2. Effect of $\mu$Fe Loading on Magnetocapacitance and Apparent Deformation

As the fraction of $\mu$Fe increases, the zero-field capacitance decreases, the magnetic-field-induced capacitance change decreases, and ${\epsilon }_{\mathrm{r}}$ in a given field is reduced (Figure 6a and Figure 7a). The same trend is observed for the magnitude of $e_{\mathrm{zz}}$: at $B=150$ mT, the absolute value of $e_{zz}$ is highest for hM₁ and lowest for hM₃ (Figure 7b). Therefore, increasing the $\mu$Fe content reduces both the magnetocapacitance and the magnitude of the apparent deformation derived from the capacitance.

A simple way to interpret these results is to treat the CI-rich phase in the porous textile as a chain-like structure embedded in an oxide-/polymer-/oil-rich dielectric background. In such a microstructural view, the device-level capacitance reflects the combined contribution of many local CI–dielectric–CI interfaces arranged in series/parallel within the electrode overlap area. Increasing the fraction of $\mu$Fe introduces an additional fibrous network rich in iron-oxides that (i) changes the packing and connectivity of the CI-rich domains and (ii) increases the fraction of low/weakly polarizable regions participating in the effective dielectric pathway. Both effects act to lower the zero-field capacitance and to limit the field-induced reconfiguration of the CI-rich phase, thereby reducing the overall magnetocapacitive response. The added fibrous phase can mechanically constrain the rearrangement of the CI-rich domains, consistent with the observed increase in apparent low-field stiffness at higher $\mu$Fe loading.

This behavior is consistent with the different roles played by the two magnetic components. CI remains the dominant magnetically active phase in the membranes because its saturation magnetization is much higher than that of the $\mu$Fe (Section 2.1; Ref. [24]). In contrast, $\mu$Fe, due to their lower magnetization and fibrillar morphology, appear to act mainly as a secondary structural component that modifies the internal spatial arrangement of the composite. A higher $\mu$Fe loading would then be expected to modify or hinder the field-induced chain-like structure of the CI-rich phase and thereby alter the field-responsive performance, while also improving dispersion stability through steric/structural effects [33]. The SEM observations are qualitatively consistent with this view. After impregnation, the cotton scaffold retains its fibrous character, but the membrane becomes denser and contains Fe-rich solid material distributed throughout the textile network (Figure 5).

4.3. Apparent Mechanical Response and Field-Induced Stiffening

The apparent modulus-like parameter E derived increases overall with B for all three membranes, although the detailed behavior in the low and intermediate fields depends on the composition (Figure 8b). In particular, hM₃ exhibits the highest apparent modulus at low B, whereas hM₁ is the softest. At higher fields, the modulus values of the three membranes become closer and all samples show a pronounced stiffening tendency.

A useful interpretation is that, at low to intermediate B, the magnetic attraction between CI-derived dipoles is partially balanced by the elastic constraint of the cotton-fiber scaffold (and, at higher $\mu$Fe loading, by the additional fibrous oxide network). In this regime, the membrane can exhibit a weak plateau or non-monotonic evolution of the apparent modulus because further dipole approach and chain compaction are mechanically constrained. At higher fields, dipolar interactions become strong enough to overcome these constraints, enabling denser field-aligned structures and producing the observed high-field stiffening. This means that the magnetic field affects not only the dielectric response but also the apparent resistance of the membranes to further compression. This behavior is consistent with bulk magneto-mechanical, magnetic-field-induced stiffening, which increases resistance to deformation as magnetic interactions grow [34]. The higher initial modulus of hM₃ further suggests that increasing $\mu$Fe loading stiffens the membrane even before strong field-induced structuring is established.

At the same time, the non-monotonic behavior observed for hM₂ and especially for hM₃ in the low-to-intermediate field range indicates that the apparent mechanical response is more complex than a simple monotonic stiffening law. This feature may reflect competition among magnetic interactions, the pre-existing constraints imposed by the cotton scaffold, and the additional constraint introduced by the $\mu$Fe phase.

4.4. Validity and Limitations

${\epsilon }_{\mathrm{r}}$ is an apparent quantity obtained for a heterogeneous dielectric layer composed of cotton fibers, silicone oil, CI microparticles, and $\mu$Fe microfibers [35]. Therefore, it represents an effective device-level response rather than the intrinsic permittivity of a uniform material. $e_{\mathrm{zz}}$ is inferred from the capacitance variation under the assumption that the main geometric change occurs along the thickness direction and that the electrode area remains unchanged. In addition, ${\tau }_{\mathrm{zz}}$ is estimated from a simplified dipolar model that does not explicitly account for the detailed morphology of the textile scaffold or the $\mu$Fe network. Consequently, the E obtained from Equation (9) describes the relative evolution of the membrane response under a magnetic field within the framework used here.

4.5. Implications for Flexible Capacitive Elements

From an application perspective, the membrane response can be tuned through composition. The preferred composition depends on whether magnetic sensitivity or mechanical constraint is the main requirement. The membrane without added $\mu$Fe, hM₁, exhibits the largest magnetic-field-induced capacitance change, the highest ${\epsilon }_{\mathrm{r}}$ and the largest magnetocapacitance. This makes it the most favorable composition when a strong magnetic-field-dependent electrical response is the main objective.

Increasing the loading of $\mu$Fe reduces the magnetocapacitive response but increases the apparent stiffness of the membrane, particularly in the low-field range. In this sense, hM₃ is less dielectrically responsive but exhibits a more mechanically constrained apparent response under the magnetic field. The intermediate composition hM₂ provides a compromise between these two tendencies. Thus, the three investigated membranes define a practical trade-off: a lower $\mu$Fe loading favors a stronger dielectric response, whereas a higher $\mu$ Fe loading favors higher apparent rigidity and lower magnetic-field-induced reconfiguration.

The pressure-response data (Figure 6b) further indicate that the electrical behavior is not governed by stimulation of the magnetic-field alone. Although all three capacitors show a measurable increase in capacitance under compressive loading, the composition dependence differs from that observed under a magnetic field: PC₂ provides the highest average pressure sensitivity in the investigated range, while PC₁ provides the strongest magnetic field-induced capacitance change. This suggests that the mechanisms controlling pressure-induced and magnetic-field-induced capacitance variations are related but not identical, and that the membrane composition can be selected according to the dominant external stimulus. In this sense, the present hybrid membranes are best viewed as composition-tunable dielectric layers for flexible capacitor-based elements with coupled magnetic-field- and pressure-dependent response.

5. Conclusions

Flexible hybrid CI/$\mu$Fe cotton membranes were prepared by impregnating a woven cotton scaffold with SO-based suspensions containing CI microparticles and $\mu$Fe. The resulting membranes were then used as dielectric layers in planar capacitors. The capacitor structures responded to both the magnetic field and compressive pressure (Figure 6). Over the investigated range of 0–150 mT, the capacitance increased monotonically for all three compositions, with the strongest magnetic-field-induced response observed for PC₁ and the weakest for PC₃. Under compressive loading in the range of 0–10 kPa, the capacitance also increased for all samples, while PC₂ showed the highest average pressure sensitivity in the tested interval.

Within the simplified analysis adopted here, the capacitance data were also used to estimate several apparent dielectric and mechanical-response parameters, including apparent relative permittivity, a capacitance-derived strain proxy, magnetic stress, and an apparent modulus-like parameter. The apparent relative permittivity increased strongly with B while the capacitance-derived strain became increasingly negative. The same analysis indicated an overall increase in the apparent stiffness parameter with magnetic field. Therefore, the data indicate that increasing the $\mu$Fe content suppresses the magnetically induced capacitance change and reduces the magnitude of the apparent deformation, while shifting the response toward higher apparent stiffness, especially at low magnetic field.

In general, hybrid CI/$\mu$Fe textile membranes behave as composition-tunable dielectric layers in flexible capacitor structures that respond to both magnetic field and compressive loading. The lower $\mu$Fe loading favors a stronger magnetic-field-induced capacitance change, whereas the higher $\mu$Fe loading is associated with a more mechanically constrained apparent response. This behavior makes such soft magnetic textile composites promising candidates for multifunctional capacitor-based sensing elements. Further work should address frequency dependence, cycling stability, reversibility, and direct mechanical validation of the capacitance-derived apparent quantities.