Effective Attenuation of Electromagnetic Waves by Synergetic Effect of α-Fe2O3 and MWCNT/Graphene in LDPE-Based Composites for EMI Applications

In this study, a polymer nanocomposite is synthesized using magnetic and conducting fillers for enhanced electromagnetic interference (EMI) shielding. Alfa-ferrite (α-Fe2O3) nanoparticles with minimal multiwalled carbon nanotube (MWCNT) as low as 5 weight % in combination with variable concentrations of graphene nanoplatelets (GNP) are used as fillers in low-density polyethylene (LDPE) polymer matrix. Nanofillers and the polymer matrix are characterized by various techniques such as XRD, SEM, color mapping, EDAX, TGA, etc. The EMI shielding efficiency of the LDPE-based nanocomposites is tested using Vector Network Analyzer (VNA). The results showed that composite with LDPE:MWCNT:GNP:α-FO-50:5:40:5 displayed enhanced EMI shielding (in X-band (8.2–12.4 GHz) compared to other concentrations studied. This is due to the superior ohmic, dielectric, and magnetic losses at this particular composition and to the synergism amongst the filler. An attenuation of 99.99% was achieved for 5% α-Fe2O3. The mechanistic aspects of the shielding are discussed using permittivity, conductivity, and attenuation.


Introduction
The electromagnetic Interference (EMI) problem arises due to the uncontrollable ambient propagation of electromagnetic (EM) waves from various neighboring sources. This EM disturbance in circuits creates malfunctioning of electronic devices in the proximity. Due to the significant growth and demand for wireless communication in several fields, it is difficult to suppress the EMI problem by conventional methods, such as metallic shielding. Sometimes the failure will lead to the device's malfunction [1][2][3][4]. EMI shielding materials are available in stealth, aerospace, critical electronic equipment, sensitive measurements, etc. [5,6]. The military materials are coated on surfaces for radar absorption, a vital tool in defense for bombers, drones, and missiles. It was proved that absorption was better than scattering for shielding applications [7,8]. So, one should consider a material combination that can contribute throughout the EM spectrum, especially in the multi-GHz frequency.
To obtain a material with high EMI shielding, the primary ingredient will be the combination of electrical conductivity (σ AC ) and magnetic loss permeability (µ) [8,9]. Metals have a lot of free charge carriers in their atoms, making them good EM reflectors, so they are the primary choice of EM shielders [10]. However, they lag in chemical resistivity, ease

Synthesis of α-Fe 2 O 3
In the typical solution combustion synthesis (SCS) process, α-Fe 2 O 3 nanoparticles were synthesized using urea as fuel. First, the stoichiometric ratio of ferric nitrate (8.08 g) and urea (3 g) was dissolved with 25 mL of de-ionized (DI) water. Next, the clear solution was transferred to a pre-heated furnace at 450 • C in a 100 mL petri dish. At first, a solution containing a red-ox mixture underwent dehydration, resulting in the formation of a gel. Next, the gel ignited, and the flames spread throughout the reaction mixture. The combustion sustained for a few minutes with the evolution of a large volume of gaseous by-products. Finally, a reddish brown loose porous mass was obtained that was grained and sintered at 950 • C for 3 h to improve the crystalline nature of the product [38,39].

Synthesis of GNP
The GNP was prepared by chemical exfoliation with irradiated microwave treatment. In this process, 1 g of graphite was mixed with concentrated H 2 SO 4 with APS as an oxidizer in an ice-cold bath. After 24 h, the temperature was maintained at 40-45 • C, leading to the product's gradual decomposition and the graphitic crystals' expansion by gaseous oxygen between graphene layers. The cold expanded graphite was microwave-irradiated in an alcohol and water mixture for 10 min at 80 • C. The product was then washed and dried in a vacuum hot air oven for 1 h in N 2 heating at 300 • C [40].

Preparation of Polymer Composite
The polymer nanocomposites were melt-blended in a Brabender twin-screw extruder (Plasticorder, Western Company Keltron CMEI, MODEL-16 CME SPL). by adding calculated weight % of the polymer and nanofillers at 130 • C and 100 rpm for 20 min. The product formed was removed and compression-molded to get a square sample of 2.286 cm × 1.016 cm × 0.35 cm dimension, compressed at 110 bar in a hydraulic press with a temperature of 110 • C [41]. A polymer composite combination with various fillers is given in Table 1 [42][43][44].  Figure 1 shows the X-ray diffraction of the α-Fe 2 O 3 nanoparticles, which were calcined at 900 • C for 3 h. All the diffraction lines were obtained to match the diffraction standard card (PDF#33-0664), suggesting the formation of α-Fe 2 O 3 by the solution com- bustion method. The X-ray diffraction data obtained shows a highly intense well-resolved pattern indicating the formation of a highly crystalline product. At 2θ = 32.7 • , a highly intense diffraction peak corresponds to the (104) plane with the highest intensity. No other secondary phases are identified from the XRD data. XRD pattern matches with the standard card (PDF#65-3107) [46]. Figure S1a is the XRD pattern of chemically exfoliated graphene. In the XRD pattern, there is a peak at 26.4 • , corresponding to interplanar distances of d 002 = 3.3619 Å. These data are higher than those of typical graphite (d 002 = 3.354 Å). The chemical exfoliation and microwave irradiation will enhance the space between ab planes of graphene. The prepared material retains a high crystalline quality. The Scherrer formula determined the average crystalline size of the particles. The average crystalline size GNP was found to be 16.02 nm. The pattern matches the hexagonal wurtzite structure [47]. Figure S1b shows the XRD pattern of the chemical vapor deposition (CVD)-derived MWCNT. The diffractogram shows a peak at 2θ = 25, 44, and 55 o , which can be indexed to the planes (002), (100), and (004), respectively. These peaks resemble the graphitic phase of the literature, confirming that the MWCNT is well graphitized (Joint Committee on Powder Diffraction Standards(JCPDS) card No. 75-2078) [48]. There is no residual catalytic metal or carbon other than the graphitic phase observed with the XRD pattern of MWCNT confirming the phase purity of the material. Figure 1 shows the X-ray diffraction of the α-Fe2O3 nanoparticles, which were calcined at 900 °C for 3 h. All the diffraction lines were obtained to match the diffraction standard card (PDF#33-0664), suggesting the formation of α-Fe2O3 by the solution combustion method. The X-ray diffraction data obtained shows a highly intense well-resolved pattern indicating the formation of a highly crystalline product. At 2ϴ = 32.7°, a highly intense diffraction peak corresponds to the (104) plane with the highest intensity. No other secondary phases are identified from the XRD data. XRD pattern matches with the standard card (PDF#65-3107) [46]. Figure S1a is the XRD pattern of chemically exfoliated graphene. In the XRD pattern, there is a peak at 26.4°, corresponding to interplanar distances of d002 = 3.3619 Å. These data are higher than those of typical graphite (d002 = 3.354 Å). The chemical exfoliation and microwave irradiation will enhance the space between ab planes of graphene. The prepared material retains a high crystalline quality. The Scherrer formula determined the average crystalline size of the particles. The average crystalline size GNP was found to be 16.02 nm. The pattern matches the hexagonal wurtzite structure [47]. Figure S1b shows the XRD pattern of the chemical vapor deposition (CVD)-derived MWCNT. The diffractogram shows a peak at 2ϴ = 25, 44, and 55 ο , which can be indexed to the planes (002), (100), and (004), respectively. These peaks resemble the graphitic phase of the literature, confirming that the MWCNT is well graphitized (Joint Committee on Powder Diffraction Standards(JCPDS) card No. 75-2078) [48]. There is no residual catalytic metal or carbon other than the graphitic phase observed with the XRD pattern of MWCNT confirming the phase purity of the material.

Raman Spectroscopy
Raman spectroscopy was employed to examine the carbon derivative in this work. Figure S2a of GNP shows peaks at the D band (1350 cm −1 ), G band (1582 cm −1 ), and 2D band (2700 cm −1 ) for synthesized GNPs from the chemical exfoliation process. The band G was attributed to the E2 g phonon observed in the Brillouin zone center; meanwhile, the sharpness of the G band indicates carbon atoms bonding with sp2 hybridization to yield a dense-hexagonal structure. The band D is ascribed to breath vibration mode associated

Raman Spectroscopy
Raman spectroscopy was employed to examine the carbon derivative in this work. Figure S2a of GNP shows peaks at the D band (1350 cm −1 ), G band (1582 cm −1 ), and 2D band (2700 cm −1 ) for synthesized GNPs from the chemical exfoliation process. The band G was attributed to the E2 g phonon observed in the Brillouin zone center; meanwhile, the sharpness of the G band indicates carbon atoms bonding with sp2 hybridization to yield a dense-hexagonal structure. The band D is ascribed to breath vibration mode associated with the carbon rings of sp 2 atoms and suffers reduction from the defect-induced strong sp 2 covalent bonds aroused due to freshly formed edges and sp 3 hybridization atoms. I G /I D ratio of 2.60 was found to estimate the average size of the sp 2 domain with a high degree of disorder and fewer structural defects observed in the GNP structure. At the same time, synthesis with side groups attached with carboxylic, epoxy, and oxygen functionalization was observed. The position, shape, and full-width half maxima (FWHM) correspond to the second-ordered 2D band of GNP, indicating the graphene layers [49]. Figure S2b represents the Raman spectra of the MWCNT skeleton of the MWCNT structure revealed. The bands at positions 1581 cm −1 and 1340 cm −1 are attributed to the G and D-bands, respectively. D band shows that the sp3 hybridization occurred at carbon atoms, and G-band shows that sp 2 hybridized carbon atoms formed due to the defects in the MWCNT structure. The absence of a peak at 200 cm −1 served as evidence that our product was not SWCNT. I G /I D ratio revealed the number of structural defects, which was found to be 0.97 in our case, indicating the sample was disordered due to the distortion process in the graphene layer [50].

Scanning Electron Microscopy (SEM) and EDS
The SEM at different magnifications was done to understand the prepared fillers' structure and morphologies. Figure 2a-d, shows the SEM images of α-Fe 2 O 3 nanoparticles at different magnifications. The α-Fe 2 O 3 nanoparticle shows a highly crystalline nanoparticle with highly agglomerated structures, and the particles are in polygonal shapes, with definite particle boundaries seen. The accumulation of particles with varying sizes and shapes is typical of solution combustion-derived nanoparticles. The voids and pores on the surfaces are due to the liberation of gaseous by-products during product formation.
with the carbon rings of sp 2 atoms and suffers reduction from the defect-induced strong sp 2 covalent bonds aroused due to freshly formed edges and sp 3 hybridization atoms. IG/ID ratio of 2.60 was found to estimate the average size of the sp 2 domain with a high degree of disorder and fewer structural defects observed in the GNP structure. At the same time, synthesis with side groups attached with carboxylic, epoxy, and oxygen functionalization was observed. The position, shape, and full-width half maxima (FWHM) correspond to the second-ordered 2D band of GNP, indicating the graphene layers [49]. Figure S2b represents the Raman spectra of the MWCNT skeleton of the MWCNT structure revealed. The bands at positions 1581 cm −1 and 1340 cm −1 are attributed to the G and D-bands, respectively. D band shows that the sp3 hybridization occurred at carbon atoms, and Gband shows that sp 2 hybridized carbon atoms formed due to the defects in the MWCNT structure. The absence of a peak at 200 cm −1 served as evidence that our product was not SWCNT. IG/ID ratio revealed the number of structural defects, which was found to be 0.97 in our case, indicating the sample was disordered due to the distortion process in the graphene layer [50].

Scanning Electron Microscopy (SEM) and EDS
The SEM at different magnifications was done to understand the prepared fillers' structure and morphologies. Figure 2a-d, shows the SEM images of α-Fe2O3 nanoparticles at different magnifications. The α-Fe2O3 nanoparticle shows a highly crystalline nanoparticle with highly agglomerated structures, and the particles are in polygonal shapes, with definite particle boundaries seen. The accumulation of particles with varying sizes and shapes is typical of solution combustion-derived nanoparticles. The voids and pores on the surfaces are due to the liberation of gaseous by-products during product formation. Further, the elemental distribution can be observed from EDS. The elemental distribution was confirmed by the EDS elemental mapping technique shown in Figure 3. The image shows that the element iron and oxygen was homogeneously distributed in the α-Fe2O3 crystals, and no other impurity was observed, revealing the formed product's phase purity [51,52]. Further, the elemental distribution can be observed from EDS. The elemental distribution was confirmed by the EDS elemental mapping technique shown in Figure 3. The image shows that the element iron and oxygen was homogeneously distributed in the α-Fe 2 O 3 crystals, and no other impurity was observed, revealing the formed product's phase purity [51,52].   Figure S3a,b shows the SEM image of the GNP. The layered arrangements with nonuniform surfaces that create voids of varying sizes were observed. The twist and fold arrangements in the graphene are due to the defects aroused in structure, and disorders formed are a typical feature in our synthesis process. Figure S3c,d shows the SEM images of MWCNT created in the CVD process. The randomly oriented smooth-surfaced tube looks worm-like and tangled, with uneven distribution throughout. The MWCNT has a tube diameter of 40-50 nm. No particle-like structure indicated that other carbon forms may have formed during the reaction. The pure material shown in EDS meant no elemental catalyst or gaseous things, suggesting that the MWCNT was performed with proper washing and vacuum drying after synthesis.

Thermogravimetric Analysis (TGA)
The thermal stability of the samples for pure LDPE and α-Fe2O3: CNT: GNP: LDPE composites was tested with TGA, shown in Figure 4. The pure LDPE sample decomposes rapidly at 380 °C. Before that, weight loss of ~3 weight % was due to absorbed and coordinated water molecule elimination by evaporation, for the composite sample decomposition occurred after the ~432 °C. The decomposition of MWCNT started at 400-500 °C compared to the pure, which was at 380 °C, due to the increase in thermal stability by adding fillers. After 50% weight loss of the sample, there was not much weight loss because α-Fe2O3 remained as residual material during the thermal degradation [48].   Figure S3a,b shows the SEM image of the GNP. The layered arrangements with nonuniform surfaces that create voids of varying sizes were observed. The twist and fold arrangements in the graphene are due to the defects aroused in structure, and disorders formed are a typical feature in our synthesis process. Figure S3c,d shows the SEM images of MWCNT created in the CVD process. The randomly oriented smooth-surfaced tube looks worm-like and tangled, with uneven distribution throughout. The MWCNT has a tube diameter of 40-50 nm. No particle-like structure indicated that other carbon forms may have formed during the reaction. The pure material shown in EDS meant no elemental catalyst or gaseous things, suggesting that the MWCNT was performed with proper washing and vacuum drying after synthesis.

Thermogravimetric Analysis (TGA)
The thermal stability of the samples for pure LDPE and α-Fe 2 O 3 : CNT: GNP: LDPE composites was tested with TGA, shown in Figure 4. The pure LDPE sample decomposes rapidly at 380 • C. Before that, weight loss of~3 weight % was due to absorbed and coordinated water molecule elimination by evaporation, for the composite sample decomposition occurred after the~432 • C. The decomposition of MWCNT started at 400-500 • C compared to the pure, which was at 380 • C, due to the increase in thermal stability by adding fillers. After 50% weight loss of the sample, there was not much weight loss because α-Fe 2 O 3 remained as residual material during the thermal degradation [48].   Figure S3a,b shows the SEM image of the GNP. The layered arrangements with nonuniform surfaces that create voids of varying sizes were observed. The twist and fold arrangements in the graphene are due to the defects aroused in structure, and disorders formed are a typical feature in our synthesis process. Figure S3c,d shows the SEM images of MWCNT created in the CVD process. The randomly oriented smooth-surfaced tube looks worm-like and tangled, with uneven distribution throughout. The MWCNT has a tube diameter of 40-50 nm. No particle-like structure indicated that other carbon forms may have formed during the reaction. The pure material shown in EDS meant no elemental catalyst or gaseous things, suggesting that the MWCNT was performed with proper washing and vacuum drying after synthesis.

Thermogravimetric Analysis (TGA)
The thermal stability of the samples for pure LDPE and α-Fe2O3: CNT: GNP: LDPE composites was tested with TGA, shown in Figure 4. The pure LDPE sample decomposes rapidly at 380 °C. Before that, weight loss of ~3 weight % was due to absorbed and coordinated water molecule elimination by evaporation, for the composite sample decomposition occurred after the ~432 °C. The decomposition of MWCNT started at 400-500 °C compared to the pure, which was at 380 °C, due to the increase in thermal stability by adding fillers. After 50% weight loss of the sample, there was not much weight loss because α-Fe2O3 remained as residual material during the thermal degradation [48].   Figure 5 shows the M-H curve of α-Fe 2 O 3 nanoparticles at room temperature. The nanoparticles synthesized from the SCS process reveal a magnetic coercivity value of (H c ) of 2578 Oe, indicating that the material is sufficiently magnetic. The saturation magnetization (M s ) value was 1.898 emu/g, and the remnant magnetization (M R ) of 0.576 emu/g. The material's anisotropy constant (k) was 0.3 HAkg −1 [53]. The M R /M S ratio for α-Fe 2 O 3 nanoparticles was 0.303, indicating the material is multidomain [54].

Magnetic Studies
where, µ 0 is the permeability of free space  Figure 5 shows the M-H curve of α-Fe2O3 nanoparticles at room temperature. The nanoparticles synthesized from the SCS process reveal a magnetic coercivity value of (Hc) of 2578 Oe, indicating that the material is sufficiently magnetic. The saturation magnetization (Ms) value was 1.898 emu/g, and the remnant magnetization (MR) of 0.576 emu/g. The material's anisotropy constant (k) was 0.3 HAkg −1 [53]. The MR/MS ratio for α-Fe2O3 nanoparticles was 0.303, indicating the material is multidomain [54].

Magnetic Studies
where, μ is the permeability of free space

EMI Shielding Study of Composites
The shielding ability of reposed samples is characterized as shielding effectiveness (SE). SE is a relative value that indicates the reduction in the incident power of the EM wave at a specific frequency, illustrated by Equation (2).
P, H, and E represent the incident EM wave's power, magnetic field, and electric field. The subscripts t and i correspond to the transmitted and incident waves.
The relation between shielding effectiveness due to reflection, multiple reflection, and absorption, notations, SER, SEMR, and SEA, are used, respectively. The total shielding effectiveness (SET) is SER, SEMR, and SEA.
The multiple EM reflections will form SEMR at the shield's boundaries. This phenomenon is strongly evident in samples with enhanced electrical thickness. In the proposed work, the sample thickness was limited to 3.5 mm translation to 0.11 λ, computed at 10 GHz. This value indicates that the synthesized sample is electrically thin. This value could also be safely neglected for frequencies where SEA is greater than 10 dB. SET could be approximated by Equation (4).
The VNA's measured S-parameters would be used to compute shielding effectiveness (SET) and (SEA) by using Equations (5) and (6), respectively.

EMI Shielding Study of Composites
The shielding ability of reposed samples is characterized as shielding effectiveness (SE). SE is a relative value that indicates the reduction in the incident power of the EM wave at a specific frequency, illustrated by Equation (2).
P, H, and E represent the incident EM wave's power, magnetic field, and electric field. The subscripts t and i correspond to the transmitted and incident waves.
The relation between shielding effectiveness due to reflection, multiple reflection, and absorption, notations, SE R , SE MR , and SE A , are used, respectively. The total shielding effectiveness (SE T ) is SE R , SE MR , and SE A .
The multiple EM reflections will form SE MR at the shield's boundaries. This phenomenon is strongly evident in samples with enhanced electrical thickness. In the proposed work, the sample thickness was limited to 3.5 mm translation to 0.11 λ, computed at 10 GHz. This value indicates that the synthesized sample is electrically thin. This value could also be safely neglected for frequencies where SE A is greater than 10 dB. SE T could be approximated by Equation (4).
The VNA's measured S-parameters would be used to compute shielding effectiveness (SE T ) and (SE A ) by using Equations (5) and (6), respectively. SE T (dB) = 10 log 1 where, µ is a real part of permeability µ is an imaginary part of permeability The notations ε ∞ , ε S , ε 0 , τ and σ ac Equations (8) and (9) represent the dielectric constant for a frequency range of infinity, the static dielectric constant, the permittivity of vacuum, relaxation time, and AC conductivity, respectively. Relation between ε and ε will be represented as Equation (10).
The Attenuation constant will be given by Equation (11), The shielding mechanism is explained in this section. The localization of conducive filler along with ferrite brings synergism in the LDPE composite for better shielding effectiveness for the X-band frequency. The electrical conductivity of the nanocomposite sample is essential for microwave attenuation through absorption, which is closely linked to dielectric loss. EM waves intentionally constitute the electrical and magnetic field while designing the material. The electric and magnetic dipoles should be evenly dispersed in the matrix. The incorporation of magnetically lossy material (α-Fe 2 O 3 ) and dielectrically lossy material (MWCNT/graphene) in the LDPE are carried out in these studies. α-Fe 2 O 3 was observed with high coercivity material with the pure phase determined by XRD and EDS analysis. The SE T for many such combinations was designed in this work to understand the variable combination in achieving the synergism effect with the critical concentration of the fillers. LDPE: MWCNT: GNP: α-Fe 2 O 3 nanocomposites (α-Fe 2 O 3 content x= 0, 5, 10, 20, 30, 50, and 50 weight %) in test frequency for the thicknesses 3.5 mm of the prepared samples.
From Figure 6, the graph SE T indicates that a sample with 5 weight % of α-Fe 2 O 3 in polymer matrix yields maximum Shielding effectiveness of 40 dB at 10.3 GHz; the sample with 0% ferrite has yielded 34.7 dB at 10.4 GHz-further, the 10 weight % and 20 weight %, which was 24 dB and 23.8 dB, respectively, and with 50 weight %, the most negligible value was 11.98 dB. However, the sample without any fillers but only pure LDPE has almost no considerable shielding, i.e., 1 dB. This emphasizes that the fillers distributed within the medium, contributed to the abovementioned losses. All the proposed samples demonstrate frequency dependency of absorption. A synergism was achieved with the critical concentration of 5% α-Fe 2 O 3 , 5% MWCNT, and 40% GNP 50% LDPE combinations. The sample with 0% ferrite and the rest conducting filler will have the second-best SE values because of the absence of proper microwave-absorbing material that lacks synergism to bring effective SE like the 5% sample. The remaining samples demonstrate sub-optimal SE T -the sample with 10 and 20 weight % of α-Fe 2 O 3 also has similar shielding effectiveness of 23.8 dB at 10.3 GHz but decreases by a few dB at some frequencies, indicating that the 10 weight % sample demonstrates the superior synergy for enhanced EM shielding than the 20% sample. Furthermore, the other combinations take the positions for their shielding performances-the sample with only ferrite 50 weight % yielded an SE of at least 12 dB at 10.3 GHz [55].  Shielding effectiveness due to absorption (SEA) is sh1own in Figure 7. The sample with 5% α-Fe2O3 gives a maximum SEA of 39.19 dB at 10.3 GHz frequency. The sample with 0% ferrite had 34.3 dB at 10.3 GHz; with 10 weight % and 20 weight % of α-Fe2O3 following the same SEA path of 23.29 dB and 20 dB, respectively. The same trend was observed with the remaining samples. The sample with 50% of ferrite without any conducting filler shows the most negligible value of shielding of 11.38 dB. Demonstrating the importance of conductive filler for achieving a synergetic effect on dielectric and magnetic loss parameters with the critical concentrations of fillers is evidenced overall. It must also be observed that an optimal concentration exists for conductive and magnetic filler to achieve maximum shielding effectiveness due to absorption. This can be observed in 45% ferrite, and with only 5% of MWCNT 14.25 dB indicates that at least 5% of MWCNT can bring the improvement of 3 dB to the composites. The sample without ferrite and CNT with but 50 weight % of GNP shows SEA of 21.1 dB at 10.3 GHz frequency, which indicates that the conductive filler also has good SEA characteristics [55]. Shielding effectiveness due to absorption (SE A ) is sh1own in Figure 7. The sample with 5% α-Fe 2 O 3 gives a maximum SE A of 39.19 dB at 10.3 GHz frequency. The sample with 0% ferrite had 34.3 dB at 10.3 GHz; with 10 weight % and 20 weight % of α-Fe 2 O 3 following the same SE A path of 23.29 dB and 20 dB, respectively. The same trend was observed with the remaining samples. The sample with 50% of ferrite without any conducting filler shows the most negligible value of shielding of 11.38 dB. Demonstrating the importance of conductive filler for achieving a synergetic effect on dielectric and magnetic loss parameters with the critical concentrations of fillers is evidenced overall. It must also be observed that an optimal concentration exists for conductive and magnetic filler to achieve maximum shielding effectiveness due to absorption.  Shielding effectiveness due to absorption (SEA) is sh1own in Figure 7. The sample with 5% α-Fe2O3 gives a maximum SEA of 39.19 dB at 10.3 GHz frequency. The sample with 0% ferrite had 34.3 dB at 10.3 GHz; with 10 weight % and 20 weight % of α-Fe2O3 following the same SEA path of 23.29 dB and 20 dB, respectively. The same trend was observed with the remaining samples. The sample with 50% of ferrite without any conducting filler shows the most negligible value of shielding of 11.38 dB. Demonstrating the importance of conductive filler for achieving a synergetic effect on dielectric and magnetic loss parameters with the critical concentrations of fillers is evidenced overall. It must also be observed that an optimal concentration exists for conductive and magnetic filler to achieve maximum shielding effectiveness due to absorption. This can be observed in 45% ferrite, and with only 5% of MWCNT 14.25 dB indicates that at least 5% of MWCNT can bring the improvement of 3 dB to the composites. The sample without ferrite and CNT with but 50 weight % of GNP shows SEA of 21.1 dB at 10.3 GHz frequency, which indicates that the conductive filler also has good SEA characteristics [55]. This can be observed in 45% ferrite, and with only 5% of MWCNT 14.25 dB indicates that at least 5% of MWCNT can bring the improvement of 3 dB to the composites. The sample without ferrite and CNT with but 50 weight % of GNP shows SE A of 21.1 dB at 10.3 GHz frequency, which indicates that the conductive filler also has good SE A characteristics [55]. Figure 8 shows the SE R graphs. Here, the sample with 50 weight % of GNP sample yields a maximum SE R value of 1.13 dB at 10.3 GHz frequency, and the sample with 0 weight % ferrite demonstrates a value of 1 dB at 10.3 GHz. The sample with 5% ferrite yielded the least SE R at 0.58 dB, and pure LDPE had negligible SE R at 0.6 dB, indicating EM's transparent nature. Therefore, the shielding effectiveness due to reflection is minimal. The nanomaterial composite justifies this argument. Consequently, it could be concluded that the proposed material offers a higher SE A than the reflection. This also provides that the EM wave is dissipated as heat energy within the proposed nanocomposite material, thus, proving the applicability of the proposed material as an absorber [56].
Materials 2022, 15, x FOR PEER REVIEW 10 of 18 Figure 8 shows the SER graphs. Here, the sample with 50 weight % of GNP sample yields a maximum SER value of 1.13 dB at 10.3 GHz frequency, and the sample with 0 weight % ferrite demonstrates a value of 1 dB at 10.3 GHz. The sample with 5% ferrite yielded the least SER at 0.58 dB, and pure LDPE had negligible SER at 0.6 dB, indicating EM's transparent nature. Therefore, the shielding effectiveness due to reflection is minimal. The nanomaterial composite justifies this argument. Consequently, it could be concluded that the proposed material offers a higher SEA than the reflection. This also provides that the EM wave is dissipated as heat energy within the proposed nanocomposite material, thus, proving the applicability of the proposed material as an absorber [56]. The terms SEA, SER, and SEMR compute to the SET and SEMR can be ignored, as discussed in the previous section. Polymer nanocomposite consisting of a ferrite nanoparticle filler material with excellent EM wave absorption will contribute its maximum throughout the matrix. This feature is attributed to forming of polarons and bi-polarons, making EM wave absorption possible. The synergism of conductive filler MWCNT with GNP of varied composition works better to obtain maximum absorption, and the conductive filler brings considerable electrical conductivity. Which brings non-conductive polymer (LDPE) to semiconducting nature; hence free electrons in the matrix surface partially reflect the incoming EM wave, which is evident in Figure 8. The critical concentration was the 5% ferrite with conducting filler. This combination delivered an effective synergistic combination and multiple percolation threshold.

Permittivity and Studies
According to the high-frequency principle, the shielding efficacy of the material is governed by both complex permittivity and permeability for a given EM band. Figure  9a,d illustrate the complex permittivity and permeabilities extracted from the NRW method and are shown in the graphs with frequency parameters of different combinations of the composites [57]. The value of is proportional to the extent of polarization in the substance; it also reveals the tendency of electrical charge store density. On the other hand, (Figure 9b) indicates the dissipation of electrical energy in the sample. This directly correlates with the dielectric loss tangent (Figure 9c) concept, proven in industrial materials. The terms SE A , SE R , and SE MR compute to the SE T and SE MR can be ignored, as discussed in the previous section. Polymer nanocomposite consisting of a ferrite nanoparticle filler material with excellent EM wave absorption will contribute its maximum throughout the matrix. This feature is attributed to forming of polarons and bi-polarons, making EM wave absorption possible. The synergism of conductive filler MWCNT with GNP of varied composition works better to obtain maximum absorption, and the conductive filler brings considerable electrical conductivity. Which brings non-conductive polymer (LDPE) to semiconducting nature; hence free electrons in the matrix surface partially reflect the incoming EM wave, which is evident in Figure 8. The critical concentration was the 5% ferrite with conducting filler. This combination delivered an effective synergistic combination and multiple percolation threshold.

Permittivity ε and ε Studies
According to the high-frequency principle, the shielding efficacy of the material is governed by both complex permittivity and permeability for a given EM band. Figure 9a,d illustrate the complex permittivity and permeabilities extracted from the NRW method and are shown in the graphs with frequency parameters of different combinations of the composites [57]. The value of ε is proportional to the extent of polarization in the substance; it also reveals the tendency of electrical charge store density. On the other hand, ε (Figure 9b) indicates the dissipation of electrical energy in the sample. This directly correlates with the dielectric loss tangent (Figure 9c The reasonably elevated ε indicates the availability of polarons and bi-polarons in our prepared CNT-Graphene doped polymer composite. The graphs indicate polarization effects with the sample. With the incorporation of α-Fe2O3, it could be observed that the value of ε is influenced by the critical concentration of the fillers within the LDPE medium, as demonstrated in Figure 9a. An increase in the nanocomposite fillers offers enhanced polarizability, which, in turn, manifests as high ε . For the material under study, ε represents the interfacial polarization aroused from all the possible interfaces. The material prepared here has Graphene/MWCNT/α-Fe2O3 interface because of their high electrical conductivities observed by various material scientists. Especially in the prepared sample, which has more loading of α-Fe2O3 (x = 10 weight %), the decreased ε resembles a vast reduction of conductive Graphene filler concentration, that causes an overall depletion in the polarons availability, consequently decreasing ε . The reasonably elevated ε indicates the availability of polarons and bi-polarons in our prepared CNT-Graphene doped polymer composite. The graphs indicate polarization effects with the sample. With the incorporation of α-Fe 2 O 3 , it could be observed that the value of ε is influenced by the critical concentration of the fillers within the LDPE medium, as demonstrated in Figure 9a.
An increase in the nanocomposite fillers offers enhanced polarizability, which, in turn, manifests as high ε . For the material under study, ε represents the interfacial polarization aroused from all the possible interfaces. The material prepared here has Graphene/MWCNT/α-Fe 2 O 3 interface because of their high electrical conductivities observed by various material scientists. Especially in the prepared sample, which has more loading of α-Fe 2 O 3 (x = 10 weight %), the decreased ε resembles a vast reduction of conductive Graphene filler concentration, that causes an overall depletion in the polarons availability, consequently decreasing ε .
The critical parameter which influences the shielding is ε . There will be higher values of ε . The polymer nanocomposites across the frequency spectrum (Figure 9b) recommend extreme losses of the electrical components present in the microwave, which yields higher shielding effectiveness. Dielectric loss may be credited to two other possible effects in the sample composites, mainly the dielectric relaxation process (Figure 10b). The other one is due to AC conduction loss occurring in the system of material under study [58]. The critical parameter which influences the shielding is ε . There will be higher values of ε . The polymer nanocomposites across the frequency spectrum (Figure 9b) recommend extreme losses of the electrical components present in the microwave, which yields higher shielding effectiveness. Dielectric loss may be credited to two other possible effects in the sample composites, mainly the dielectric relaxation process (Figure 10b). The other one is due to AC conduction loss occurring in the system of material under study [58]. The plot of ε versus ε across the X-band frequency spectrum was observed to be a combination of a semicircle as witnessed in the obtained Cole-Cole plots. Figure 10a-d shows the complex graphs for ε versus ε for variable frequencies and different samples. It is the locus of the ε and ε where the frequency is swept. Each semi-circular region in Figure 10a-d could be mapped to one Debye-type relaxation process. It is observed that more than one semicircle suggests multiple relaxations related to the minute interactions within the nanocomposites.
Even though improved, higher EMI shielding for the sample with optimal concentration (5 weight %) of the α-Fe2O3 was obtained predominantly from absorption phenomena, using natural magnetic resonance at 10.3 GHz. They signified that the proposed nanocomposite could be a promising material for EM wave absorption, especially in X-band. In this optimal ratio, the factors of interfacial polarization, dielectric and magnetic loss combined affect the incoming waves. Even with dielectric and magnetic loss arising due to filler loading, the generation of interfacial polarization formed between MWCNTs, Graphene, and α-Fe2O3 nanoparticles also contributes to SEA, as we attained from the Cole-Cole plot as seen in Figure 10.
The material's superior performance was contributed by high dielectric loss generated from conducting MWCNT/GNP energy loss, which occurred by ferrimagnetic α-Fe2O3 distributed in polymer, which contributes to attenuation of waves. It is also observed that, at an increased ratio of α-Fe2O3 (i.e., 50 weight %), the material would experience several agglomerations. Hereafter, to bring shielding in the X-band frequency domain, selecting proper absorption material and electrically conducting material ratios within the medium decides effective shielding capability. Debye's relaxation theory explains the concept involved with the dielectric relaxation process and permittivity. It explains the complex per given by Equations (10) and (11). The plot of ε versus ε across the X-band frequency spectrum was observed to be a combination of a semicircle as witnessed in the obtained Cole-Cole plots. Figure 10a-d shows the complex graphs for ε versus ε for variable frequencies and different samples. It is the locus of the ε and ε where the frequency is swept. Each semi-circular region in Figure 10a-d could be mapped to one Debye-type relaxation process. It is observed that more than one semicircle suggests multiple relaxations related to the minute interactions within the nanocomposites.
Even though improved, higher EMI shielding for the sample with optimal concentration (5 weight %) of the α-Fe 2 O 3 was obtained predominantly from absorption phenomena, using natural magnetic resonance at 10.3 GHz. They signified that the proposed nanocomposite could be a promising material for EM wave absorption, especially in X-band. In this optimal ratio, the factors of interfacial polarization, dielectric and magnetic loss combined affect the incoming waves. Even with dielectric and magnetic loss arising due to filler loading, the generation of interfacial polarization formed between MWCNTs, Graphene, and α-Fe 2 O 3 nanoparticles also contributes to SE A, as we attained from the Cole-Cole plot as seen in Figure 10.
The material's superior performance was contributed by high dielectric loss generated from conducting MWCNT/GNP energy loss, which occurred by ferrimagnetic α-Fe 2 O 3 distributed in polymer, which contributes to attenuation of waves. It is also observed that, at an increased ratio of α-Fe 2 O 3 (i.e., 50 weight %), the material would experience several agglomerations. Hereafter, to bring shielding in the X-band frequency domain, selecting proper absorption material and electrically conducting material ratios within the medium decides effective shielding capability. Debye's relaxation theory explains the concept involved with the dielectric relaxation process and permittivity. It explains the complex per given by Equations (10) and (11).

Attenuation Constant (α)
To ensure the absorption capability of the nanocomposite, the attenuation constant (α) in Np·m −1 was determined from the permittivity and permeability in the overall X-band (8.2-12.4 GHz). The attenuation constant indicates the amount of shielding on absorption across the frequency of interest. The value of α is predictable using Equation (13) [59]. Figure 11 represents the attenuation constant for prepared composite material.

Attenuation Constant (α)
To ensure the absorption capability of the nanocomposite, the attenuation constant ( ) in Np•m −1 was determined from the permittivity and permeability in the overall Xband . The attenuation constant indicates the amount of shielding on absorption across the frequency of interest. The value of is predictable using Equation (13) [59]. Figure 11 represents the attenuation constant for prepared composite material.

AC Conductivity
In the conducting filler loaded in the polymer (MWCNT and Graphene), the significant dielectric loss will be the AC conduction component loss. The graphene concentration is directly proportional to the AC conductivity, which, in turn, is proportional to the dielectric loss tangent, ε′′ σ/w. ). The improvement in conductivity supports the attenuating of the incoming EM waves by the reflection and absorption process due to relatively higher dielectric loss phenomena, which improved σAC extreme EM attenuation across a broad frequency spectrum. The detected dielectric losses resemble the Ohmic losses for MWCNT-GNP since it affords electrical charge flow within the material. Utilizing the detected information in Figure 12, the σAC of 5 weight % α-Fe2O3 compound was found to be maximum compared to the rest of the samples. Other combinations, i.e., 50/5/40/0% and 50/0/50/0, show a higher density of σAC. This was observed because of the proper conducive networks formed by MWCNT and Graphene [54].

AC Conductivity
In the conducting filler loaded in the polymer (MWCNT and Graphene), the significant dielectric loss will be the AC conduction component loss. The graphene concentration is directly proportional to the AC conductivity, which, in turn, is proportional to the dielectric loss tangent, ε ≈ (σ/w.ε o ). The improvement in conductivity supports the attenuating of the incoming EM waves by the reflection and absorption process due to relatively higher dielectric loss phenomena, which improved σ AC extreme EM attenuation across a broad frequency spectrum. The detected dielectric losses resemble the Ohmic losses for MWCNT-GNP since it affords electrical charge flow within the material. Utilizing the detected information in Figure 12, the σ AC of 5 weight % α-Fe 2 O 3 compound was found to be maximum compared to the rest of the samples. Other combinations, i.e., 50/5/40/0% and 50/0/50/0, show a higher density of σ AC . This was observed because of the proper conducive networks formed by MWCNT and Graphene [54].

Attenuation Constant (α)
To ensure the absorption capability of the nanocomposite, the attenuation constant ( ) in Np•m −1 was determined from the permittivity and permeability in the overall Xband . The attenuation constant indicates the amount of shielding on absorption across the frequency of interest. The value of is predictable using Equation (13) [59]. Figure 11 represents the attenuation constant for prepared composite material.

AC Conductivity
In the conducting filler loaded in the polymer (MWCNT and Graphene), the significant dielectric loss will be the AC conduction component loss. The graphene concentration is directly proportional to the AC conductivity, which, in turn, is proportional to the dielectric loss tangent, ε′′ σ/w. ). The improvement in conductivity supports the attenuating of the incoming EM waves by the reflection and absorption process due to relatively higher dielectric loss phenomena, which improved σAC extreme EM attenuation across a broad frequency spectrum. The detected dielectric losses resemble the Ohmic losses for MWCNT-GNP since it affords electrical charge flow within the material. Utilizing the detected information in Figure 12, the σAC of 5 weight % α-Fe2O3 compound was found to be maximum compared to the rest of the samples. Other combinations, i.e., 50/5/40/0% and 50/0/50/0, show a higher density of σAC. This was observed because of the proper conducive networks formed by MWCNT and Graphene [54].

Eddy's Current/Skin Effect
For the material to be a good EMI shielder, it must possess some considerable skin depth. Skin effect is responsible for the depletion of incident waves in the GHz frequency for a ferrimagnetic nanoparticle, obtained from Equation (8), where D will be the particle size, and σ is the electric conductivity of the filler's particles like MWCNT and graphene. Plots of µ (µ ) −2 f −1 would be approximately constant value when the frequency is altered; so, the magnetic loss is not only from eddy current loss. The behavior of µ (µ ) −2 f −1 concerning frequency for all proposed nanocomposites is revealed in Figure 13. The graphs reveal no straight line indicating with confidence that magnetic losses obtained are not only from eddy currents arising in the material but also from other characteristics of the material hold, such as the natural ferrimagnetic magnetic resonance phenomenon in magnetic nanoparticles in the microwave frequency domain.

Eddy's Current/Skin Effect
For the material to be a good EMI shielder, it must possess some considerable skin depth. Skin effect is responsible for the depletion of incident waves in the GHz frequency for a ferrimagnetic nanoparticle, obtained from Equation (8), where D will be the particle size, and σ is the electric conductivity of the filler's particles like MWCNT and graphene. Plots of μ μ f would be approximately constant value when the frequency is altered; so, the magnetic loss is not only from eddy current loss. The behavior of μ μ f concerning frequency for all proposed nanocomposites is revealed in Figure 13. The graphs reveal no straight line indicating with confidence that magnetic losses obtained are not only from eddy currents arising in the material but also from other characteristics of the material hold, such as the natural ferrimagnetic magnetic resonance phenomenon in magnetic nanoparticles in the microwave frequency domain. The existence of several magnetic losses (Figure 9d-f) raised in the microwave spectrum could be attributed to the exitance of the natural resonance phenomenon contributing to absorption characteristics for the material of soft magnetic α-Fe2O3 nanoparticles since bulk α-Fe2O3 obtained a natural magnetic resonance observed at 40 GHz, because of the high magnetic anisotropy constant. This is an impactful observation for substantial absorption of this X-band. So, integration of nonmagnetic phases like MWCNT-GNP in LDPE lowers net effective surface anisotropy for polymer nanocomposite by lowering the space of the inter-particle interface since the loading of several other fillers of MWCNT-GNP with LDPE improves the value of surface anisotropy of the α-Fe2O3 nanoparticles. Further, a comparative table showing various composites using iron oxide-based fillers in a different polymer matrix is summarized in Table 2.  The existence of several magnetic losses (Figure 9d-f) raised in the microwave spectrum could be attributed to the exitance of the natural resonance phenomenon contributing to absorption characteristics for the material of soft magnetic α-Fe 2 O 3 nanoparticles since bulk α-Fe 2 O 3 obtained a natural magnetic resonance observed at 40 GHz, because of the high magnetic anisotropy constant. This is an impactful observation for substantial absorption of this X-band. So, integration of nonmagnetic phases like MWCNT-GNP in LDPE lowers net effective surface anisotropy for polymer nanocomposite by lowering the space of the inter-particle interface since the loading of several other fillers of MWCNT-GNP with LDPE improves the value of surface anisotropy of the α-Fe 2 O 3 nanoparticles. Further, a comparative table showing various composites using iron oxide-based fillers in a different polymer matrix is summarized in Table 2.

Shielding Mechanism
A diagrammatic illustration of the shielding mechanism of typical absorbers is represented in Figure 14, as evidenced in previous sections. In the case of the LDPE/MWCNT /GNP matrix, the resultant attenuation was primarily from conduction loss. Hence, as revealed from the schematic diagram, shielding will affect both MWCNT-GNP and α-Fe 2 O 3 in the absorption mechanism and reflection effect. MWCNT-GNP contributes to absorption, reflection, and scattering phenomena, and α-Fe 2 O 3 contributes to absorption, scattering, and transmission effects, while LDPE is EM transparent and has only a holding medium for all the nanomaterials in its chain and gives the desired shape.

Shielding Mechanism
A diagrammatic illustration of the shielding mechanism of typical absorbers is represented in Figure 14, as evidenced in previous sections. In the case of the LDPE/MWCNT/GNP matrix, the resultant attenuation was primarily from conduction loss. Hence, as revealed from the schematic diagram, shielding will affect both MWCNT-GNP and α-Fe2O3 in the absorption mechanism and reflection effect. MWCNT-GNP contributes to absorption, reflection, and scattering phenomena, and α-Fe2O3 contributes to absorption, scattering, and transmission effects, while LDPE is EM transparent and has only a holding medium for all the nanomaterials in its chain and gives the desired shape.

Conclusions
A novel combination using α-Fe2O3 nanoparticles and minimal MWCNT and graphene in an LDPE polymer composite matrix is successfully synthesized by the melt casting method. The influence of the concentration of α-Fe2O3 as magnetic filler and MWCNT/graphene as conducting filler on the EMI shielding behavior of LDPE polymer is studied using the VNA technique. Among the various combinations of concentrations, the one with the ratio (LDPE: MWCNT: GNP: α-FO = 50:5:40:5) is found to be the optimum mix proportion that showed enhanced EMI shielding efficiency. The higher EMI shielding behavior at this particular concentration of α-Fe2O3 and graphene is due to the synergetic effect between the magnetic and conducting fillers. At the optimum concentration, superior ohmic, dielectric, and magnetic losses are observed, resulting in synergism and showing effective shielding in X-band. An attenuation of 40 dB (99.99%) was obtained for 5% α-Fe2O3. This study opens promising avenues in the field of EMI shielding, using oxidebased materials and doped-metal oxides that may act as better EMI shielding materials.

Conclusions
A novel combination using α-Fe 2 O 3 nanoparticles and minimal MWCNT and graphene in an LDPE polymer composite matrix is successfully synthesized by the melt casting method. The influence of the concentration of α-Fe 2 O 3 as magnetic filler and MWCNT /graphene as conducting filler on the EMI shielding behavior of LDPE polymer is studied using the VNA technique. Among the various combinations of concentrations, the one with the ratio (LDPE: MWCNT: GNP: α-FO = 50:5:40:5) is found to be the optimum mix proportion that showed enhanced EMI shielding efficiency. The higher EMI shielding behavior at this particular concentration of α-Fe 2 O 3 and graphene is due to the synergetic effect between the magnetic and conducting fillers. At the optimum concentration, superior ohmic, dielectric, and magnetic losses are observed, resulting in synergism and showing effective shielding in X-band. An attenuation of 40 dB (99.99%) was obtained for 5% α-Fe 2 O 3 . This study opens promising avenues in the field of EMI shielding, using oxide-based materials and doped-metal oxides that may act as better EMI shielding materials.