## 2 Materials and Methods
### Preparation of Porous Materials and Performance Evaluation Methods  
A prototype porous composite material consisting of PMS xerogel and CNFs was fabricated to resemble the microstructure and Young's modulus of the porous sound absorber model calculated in Section 3.1. The fabrication procedure accorded with [PERSON] et al. [21]. The normal-incidence sound absorption coefficients of the prepared xerogel specimens were measured using a WinZacMTX (Nihon Onkyo Engineering Co., Ltd., Tokyo, Japan; per JIS A 1405-2 [22] and ISO 10534-2 [23]). The inner diameter of the acoustic tube was 40 mm, and the measurement frequency range was 200-4800 Hz. The shape of the specimens was adjusted so that the specimens could be set in the tube without resistance and compression by pressing lightly with a finger. Furthermore, the sound absorption coefficient measurement was repeated several times after shaving a little around the specimens, and the final measurement results were obtained after confirming that the resonant behavior was no longer present. The flow resistance per unit thickness was measured using an AirReSys (Nihon Onkyo Engineering Co., Ltd. per ISO 9053-1 [24]). To prevent air leakage from around the  
Figure 4: Mechanisms inside porous materials: (**a**) sound absorption and (**b**) heat transfer. specimens, the specimens were clamped in a special ring-shaped jig and set in the tube. At this time, the thickness was measured using a caliper to ensure that the specimens were not compressed. The differential pressure before and after the specimen was read when air flowed through the specimen at a velocity of 0.5 mm/s. The results were normalized using the flow velocity and specimen thickness. The Young's and loss modulus were measured using a modulus measurement system (Nihon Onkyo Engineering Co., Ltd.). The specimen was placed on the base plate of a shaker, and a mass plate was placed on top of the specimen to construct a spring-mass system in the thickness direction. Resonance was generated by vibrating the base plate, and Young's modulus was calculated using the resonance frequency and the thickness of the specimen. The loss factor was calculated using the full width at half maximum of the peak near the resonance frequency. The pore size distribution was determined using an AutoPore IV 9500 mercury intrusion porosimeter (Micromerities Instruments Corporation, Norcross, GA, USA). A measurement specimen sized approximately 0.03-0.04 g was placed in a sealed glass container for measurement. The mercury intrusion pressure ranged from approximately 1 kPa to 400 MPa, and the measurement mode was pressure boosting. In this measurement method, specimens may be compressed during the measurement. Therefore, the pore size distribution in this measurement is for reference only. Thermal conductivity was measured in a room under standard conditions using a simple measurement apparatus equipped with a heat flux sensor, thermocouples, an electric heater, and a thermal insulator, as shown in Figure 5. The heat flux sensor and a thermocouple were placed on the heater, which supplied a constant heat quantity. The test specimen, which was covered with an insulation material with a thermal conductivity of 0.0313 W/(m\(\cdot\)K), was placed on the heater and the thermocouple, and a thermocouple and a 1 mm-thick resin plate was placed on the test specimen for measurement. Thermal conductivity was derived from the measured heat flux and the temperatures above and below the specimen. Since this measurement apparatus is a simplified system, heat flow leaks out of the system. The thermal conductivity of the thermal-insulating material was 0.0313 W/(m\(\cdot\)K) according to a steady-state thermal conductivity measurement system (HFM436/3/1 Lambda, NETZSCH-Geratebau GmbH, Selb, Germany; per JJS A 1412-2 [25] and ISO 8301 [26]) and 0.0469 W/(m\(\cdot\)K) according to this simple measurement apparatus.