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Page 6 of 28 Wang et al. Soft Sci. 2026, 6, 8

A larger α value indicates a stronger attenuation capability for incident microwaves, thereby dissipating EM
energy and minimizing the transmission of residual waves out of the MAM.

RL
Both the optimal impedance matching and attenuation capability determine the microwave absorption
performance of the aerogel, which is quantified by the RL calculated as follows [63-65] :

− 0
(11)
= 20log 10
+ 0
If the value of the RL is less than -10 dB, more than 90% of the incident microwave can be effectively
absorbed, basically meeting the requirements in practical application . Besides, the EAB is defined as the
[66]
frequency region where the RL value is less than -10 dB. The RL and EAB are the most critical indicators to
evaluate the microwave absorption performance. Additionally, beyond the dissipation mechanisms
previously discussed, the interconnected conductive networks and porous microstructures of carbon-based
aerogels enhance energy consumption through multi-reflection and scattering [67,68] .

Role of the aerogel in microwave absorption performance
Apart from reducing density and enabling lightweight properties, the 3D microstructure of carbon-based
aerogels plays a significant role in enhancing microwave absorption performance, distinguishing them from
low-dimensional carbon-based counterparts .
[69]

For example, Qiao et al. prepared porous carbon aerogels with the decoration of the highly dispersed
magnetic nanoparticles . The introduction of CoFe alloy nano-capsules would reduce the complex
[70]
permittivity, while the complex permeability increased with the content of CoFe alloy nanoparticle within
the carbon-based aerogel. More importantly, the construction of the anisotropic cellular structure plays a
crucial role in influencing the EM response behaviors compared to the irregular microstructures prepared by
the common mechanical mixing strategy, obtaining the optimal RL intensity of -70.8 dB and EAB of 6.0 GHz
with a low filler ratio of 2.2 wt%. The contribution of aerogel toward the microwave response behaviors
could be mainly described as follows :
[36]

(a) The porous structure allows more air to be accommodated within the interior of the aerogel, effectively
reducing the impedance mismatch between the MA aerogel and free space, thereby improving impedance
matching and ensuring microwave penetration. Accordingly, the effective permittivity of the aerogel can be
expressed using the Maxwell-Garnett (MG) equation, as given below:

= ( 2 + 2 1 ) + 2 ( 2 − 1 ) 1 (12)
( 2 + 2 1 ) − ( 2 − 1 )
where ε is the theoretical effective dielectric constant, ε and ε are the dielectric constants of the solid and
2
1
eff
air (ε ≈ 1), respectively, and f represents the volume proportion of pores in the materials. The carbon-based
2
r
aerogel can be regarded as a composite consisting of a solid component (carbon framework) and an air
component (pore), which can reduce the effective dielectric constant and alleviate the impedance
mismatching behaviors. Moreover, based on this equation, it is implied that the dielectric loss could be
regulated by controlling the porosity of the aerogel.

(b) The porous structure extends propagation paths and alters propagation direction of the incident
microwave, which greatly increases the contact between the microwave and the pore walls within the aerogel,
promoting the energy dissipation and transforming it into heat by the multi-reflection/scattering effect.