Influence of Gas Exchange in Porous Materials on Resonance Frequency Shift in Microspeakers and Development of a Mathematical Model

The continuous reduction of back-cavity volume in microspeakers increases acoustic stiffness and limits low-frequency output. Here, we introduce porous fillers into the back cavity to create a virtual volume expansion effect. We examine how gas transport in the fillers affects the fundamental resonance frequency (f₀) and develop a predictive model. Representative molecular sieves and metal−organic frameworks (MOFs) were selected as cavity fillers. Pore structure and total gas adsorption capacity (ΔV) were characterized by Brunauer−Emmett−Teller (BET) analysis. Gas exchange rate (R_ex) was measured by dynamic vapor sorption (DVS) at 25 ℃ and 80 ℃. The resonance frequency shift (Δf₀) was obtained by impedance measurements in a sealed 1 cm³ cavity. Knudsen diffusion theory was used to interpret the role of gas exchange in f₀ reduction. Overall, R_ex is more closely associated with the magnitude of f₀ reduction than ΔV. Molecular Sieve 01 shows a smaller adsorption capacity than MOF-74 (Mg), yet it produces the largest f₀ drop at 25 ℃ (Δf₀ = −283 Hz). In contrast, MOF-74 (Mg) gives a smaller shift (Δf₀ = −137 Hz). At 80 ℃, the molecular sieves maintain effective gas exchange, whereas several MOF samples show weakened pressure regulation due to diffusion limitations. A linear model built using R_ex and ΔV predicts the f₀ shift with high accuracy (R² = 0.986). These results identify the gas exchange rate—not adsorption capacity alone—as the dominant factor driving the observed virtual expansion effect. The model provides a quantitative basis for back-cavity material screening and low-frequency acoustic design in microspeakers.