Enhancing Interface Connectivity for Multifunctional Magnetic Carbon Aerogels: An In Situ Growth Strategy of Metal‐Organic Frameworks on Cellulose Nanofibrils

Abstract Improving interface connectivity of magnetic nanoparticles in carbon aerogels is crucial, yet challenging for assembling lightweight, elastic, high‐performance, and multifunctional carbon architectures. Here, an in situ growth strategy to achieve high dispersion of metal–organic frameworks (MOFs)‐anchored cellulose nanofibrils to enhance the interface connection quality is proposed. Followed by a facile freeze‐casting and carbonization treatment, sustainable biomimetic porous carbon aerogels with highly dispersed and closely connected MOF‐derived magnetic nano‐capsules are fabricated. Thanks to the tight interface bonding of nano‐capsule microstructure, these aerogels showcase remarkable mechanical robustness and flexibility, tunable electrical conductivity and magnetization intensity, and excellent electromagnetic wave absorption performance. Achieving a reflection loss of −70.8 dB and a broadened effective absorption bandwidth of 6.0 GHz at a filling fraction of merely 2.2 wt.%, leading to a specific reflection loss of −1450 dB mm−1, surpassing all carbon‐based aerogel absorbers so far reported. Meanwhile, the aerogel manifests high magnetic sensing sensibility and excellent thermal insulation. This work provides an extendable in situ growth strategy for synthesizing MOF‐modified cellulose nanofibril structures, thereby promoting the development of high‐value‐added multifunctional magnetic carbon aerogels for applications in electromagnetic compatibility and protection, thermal management, diversified sensing, Internet of Things devices, and aerospace.


(China).
Characterization: The stability of different dispersions were measured by a Zeta potential analyzer (Malvern Zetasizer Nano ZS90).The micro-morphology characterization was carried by the field-emission scanning electron microscopy (Hitachi Model SU-70 and JSM-7610F).
The micro-structures and element distributions were characterized by a high-resolution transmission electron microscopy (FEI Talos F200x) equipped with an energy disperse spectroscopy.The crystalline structure was characterized by powder X-ray diffraction (DMAX-2500PC).The surface electronic properties were obtained through X-ray photoelectron spectroscopy (Thermo ESCALAB 250XI).The Fourier transform infrared spectra were recorded by an infrared spectrometer (Thermo Scientific Nicolet iS20).The N2 absorptiondesorption isotherm was obtained by a chemisorption analyzer (Micromeritics ASAP 2460).
The Raman spectra were recorded by a Raman spectrometer (Horiba LabRAM HR).The hysteresis loops were recorded by a vibrating sample magnetometer (LakeShore7404).The conductivity/resistivity was measured in a four-probe method by the Tonghui test system (TH26011CS).The stress-strain curves were obtained through a universal testing machine (IS-200N).The infrared thermal images were shot by an infrared induction camera (Fotric223s).
The electromagnetic parameters in the frequency range of 2-18 GHz were measured by a vector network analyzer (VNA, Agilent PNA N5244A) in the coaxial method.
To measure the electromagnetic parameters, the aerogels were integrally immersed in liquid paraffin by vacuum, subsequently solidified by cooling and cut into annulus (Фin, 3.04 mm; Фout, 7.00 mm).Considering the common filler is paraffin, resins, or rubbers with an average density of approximately 1 g/cm 3 , the filling rate in this study is calculated by "ρ (aerogel) / (ρ (aerogel) + 1 g/cm 3 )".Thus, the filling rate of the CoFe/carbon aerogels in this study is as low as ~2-3 wt%.

Section S2: Maxwell-Garnett theories
According to the Maxwell-Garnett theory, the effective permittivity (εeff) of a material consisting of two different components can be expressed by the followed equations:

Eq. S1
where ε1 and ε2 are the permittivity of host and guest components, respectively, ρ is the volume fraction of the guest.In this work, the host and guest components represent the tight CoFe/carbon and the air, permittivity.Thus, the ε2 is equal to 1.

Eq. S2
Therefore, the porous structures can reduce the effective permittivity.

Section S3: Electromagnetic wave absorption performance calculation
The reflection loss (RL) in this study is calculated by electromagnetic parameters, and based on the metallic backing model and transmission line theories.The calculation equations are shown as follows: Eq. S3

Eq. S4
where Zin and Z0 are on behalf of the input impedance and the free space impedance, respectively; εr and μr refer to the complex permittivity and permeability; c is the light speed in vacuum; j is the imaginary unit; and d is the absorber matching thickness.
Section S4: Quarter-wavelength matching model In the quarter-wavelength matching model, the theoretic matching thickness (tT) can be calculated by the followed equation:

Eq. S5
where λ is the wavelength of electromagnetic waves; c is the velocity of light in vacuum; fM is the matching frequency; εr and μr refer to the complex permittivity and permeability, respectively.
In this work, it can be observed (Figure S16) that the tM points were highly in tune with the tT curves, indicating that the electromagnetic absorption performances obeyed the quarterwavelength matching model.

Section S5: RCS simulation by Altair FEKO and CST Microwave studio
Model construction and excitation configuration: The width of the perfect electric conductor (PEC) plate was 150.0 × 150.0 mm, and the thickness was 5.0 mm.The thickness of covered carbon aerogel layer or CoFe/carbon aerogel layer is set as the Table S4.The position configuration of far fields was "calculate fields in plane wave incident direction".The plane waves of 6 GHz, 10 GHz, and 15 GHz (midpoint of C, X, and Ku band) single frequency were chosen as the excitation source, and the detail electromagnetic parameters are provided in Table S5.For the setting of vertical polarization waves, the incident azimuth angles were restricted within the condition of "−60° ≤ φ ≤ 60°; θ = 90°".The polarization angles were 0° for the vertical polarization, and 90° for the horizontal polarization.And the polarization mode was linear.The 3D presentation of RCS values for 22.9 wt% CoFe/carbon aerogel was obtained by CST Microwave studio, in which the parameter settings are similar to that of Altair FEKO.

Section S6: Debye relaxation theory
The polarization for a dielectric material usually refers to the charge migration or dipole orientation along the electric field.In an alternating electromagnetic field, if the charge migration or dipole orientation cannot keep up with the changing frequency of electromagnetic field, a hysteresis effect will occur, which is called electron or dipole polarization-relaxation.
With polarization and conductivity both being considered, the permittivity should be expressed as followed equations.
Eq. S6 Eq. S7 where εs and ε∞ refer to the permittivity at electrostatic field and high-frequency limit, ε0 means the permittivity of free space; ω, τ and σ are the angular frequency, polarization-relaxation time and conductivity, respectively; εp" and εc" represent the polarization loss and conductive loss, respectively.
Due to the nonnegligible conductivity, the original Debye formula should be modified as the followed equation.

Eq. S8
Thus, in the ε'' vs. ε' curves (Cole-Cole plot), the curves would transform into several distorted semicircles with a "tail" extending to the upper right.The semicircles represent polarization-relaxation behaviors, while the "tail" is on behalf of electrical conductance.

Section S7: Electric-field distribution simulation by CST Microwave Studio
The constructed model of a local CoFe@C nano-capsule is shown as Figure S22, and the detail simulation parameters are provided in Table S8.The excitation is orthogonal alternating electric field and magnetic field to simulate the electric field distribution of an object in a rectangular waveguide cavity.''= '' '' 1

Section S8: Magnetic loss mechanism
The magnetic loss originates from the interactions between magnetic domains or dipoles with alternating magnetic field.In the high frequency region, the magnetic loss mainly consists of the domain wall rotation, eddy current loss, ferromagnetic resonance (including natural resonance and exchange resonance), etc.
The natural resonance frequency can be calculated by the followed equations.

Eq. S11
where fr is the natural resonance frequency, γ is the gyromagnetic ratio, Ha is the anisotropy energy, K1 is the anisotropy coefficient, μ0 is the initial permeability, Ms is the saturation magnetization, and Hc is the coercivity.According to the equations, the natural resonance frequency will shift to higher frequency with the coercivity increasing.
According to Aharoni's theory, the exchange resonance frequency ωkn can be given by the followed equation.

Eq. S12
where γ is the gyromagnetic ratio, C is the exchange constant, μkn is the eigenvalues of the equation [J'n(r)]r=R = 0 with Jn being Bessel's spherical functions, R is the magnetic particle radius, K1 is the anisotropy coefficient, Ms is the saturation magnetization, H0 is the external magnetic field.According to the equation, the exchange resonance frequency will shift to lower frequency range with saturation magnetization increasing.
Generally, for soft magnetic metallic materials, the natural resonance usually occurs at 2-10 GHz, and the exchange resonance locates on higher frequency range.
Under the motivation of alternating magnetic field, the induced current turning around the conductor is called eddy current, which transforms magnetic field energy into heat.The presence of eddy current can be judged by C0 value, which is calculated by the followed equation.

Eq. S13
where μ' and μ'' are the real part and imaginary part of permeability, μ0 is the initial permeability, f is the frequency, σ is the electrical conductivity, d is the thickness.According to the equation, if the magnetic loss only caused by only eddy current loss, the C0 values should be constant with the changing frequency.

Section S9: Attenuation coefficient
The attenuation coefficient (α) is calculated by the followed equation.

Eq. S14
where f is the frequency; c is the light speed in vacuum; ε' and ε'' refer to the real part and imaginary part of permittivity; ε' and ε'' represent the real part and imaginary part of permeability, respectively.The attenuation coefficient of the aerogels in this work is shown in Figure S25a.

Section S10: Intrinsic impedance coefficient
The intrinsic impedance coefficient (Mη) is calculated by the followed equation.

Eq. S15
where Re[x] refers to the real part of x, εr and μr represent the complex permittivity and permeability, respectively.The attenuation coefficient of the aerogels in this work is shown in

Section S11: Characteristic impedance coefficient
The characteristic impedance coefficient (Z = Z' + jZ'') is calculated from the electromagnetic parameters, and calculated by the followed equations.

Eq. S16
Eq. S17 Eq. S18 where Zin and Z0 are on behalf of the input impedance and the free space impedance, respectively, εr and μr are the complex permittivity and permeability, c is the light speed in vacuum, j is the imaginary unit, d is the absorber matching thickness, Re[x] and Im[x] represent the real part and imaginary part of x, respectively.In the impedance matching isotherm maps, the overlapping region (purple area in this work) can simultaneously satisfy the requirement of Z' close to 1 and Z'' close to 0, which means that the impedance of absorbers is extremely close to that of air, thus the electromagnetic waves can totally enter into the absorber to be consumed.Ref.

Figure S4 .
Figure S4.SEM image of PBA/CNF aerogels fabricated via a common mechanical mixing process.

Figure S8 .
Figure S8.SEM images of CNF aerogel (a) in the top view, (b) the side view, and (c) the enlarged view.

Figure S9 .
Figure S9.SEM images of CoFe/C aerogels prepared via the common mechanical mixing strategy.

Figure S13 .
Figure S13.Three-dimensional RL representations and two-dimensional RL projection mappings of CNF-derived carbon aerogel.

Figure S22 .
Figure S22.The constructed model of a local CoFe@C nano-capsule: (a-c) physical structure and materials, (d) mesh conditions, (e) simulated waveguide cavity.

Figure S23 .
Figure S23.(a) Complex permittivity of CoFe/carbon aerogels prepared through both in-situ and ex-situ methods.(b) Fitting results about contributions of conductivity and polarization losses in CoFe/carbon aerogels prepared through both in-situ and ex-situ methods.

Figure S27 .
Figure S27.Compressive stress-strain curves under 50% strain for CoFe/carbon aerogels prepared through "in-situ growth" (red curves) and "ex-situ mixing" (blue curves) with the same loading content.

Table S4 .
The thickness of covered aerogel layer at different waveband.

Table S5 .
The detail electromagnetic parameters of different aerogels.

Table S6 .
Comparison of EMW absorption performances between CoFe/carbon aerogels and the reported PBA derivatives.

Table S7 .
Comparison of EMW absorption performances between CoFe/carbon aerogels and other reported carbonbased aerogels.

Table S8 .
The simulation parameters of electric-field distribution by Ansys HFSS

Table S9 .
The stress remaining and plastic deformation of CoFe/carbon aerogel compared with other polymer-derived carbon aerogels.