## 1 Introduction  
Insulation is the most basic and commonly used passive method to decrease the energy consumption of buildings and to reduce cooling and heating loads. Insulation materials in the outer walls, roofs, and floors of buildings directly affect the cooling and heating loads. These materials should be replaced before the end of their service lifetime during remodeling and renovation to maintain the performance of buildings. Therefore, insulation materials are carefully selected at the design stage based on the purpose and characteristics of the building. Insulation materials used in buildings are classified as inorganic and organic insulation materials. Inorganic materials include glass wool, mineral wool, and gypsum board, which consist mainly of an open-cell structure and do not have an organic polymer matrix. Owing to this nature, generally, inorganic insulation materials are known to have better fire-resistant properties than organic insulation materials. Compared to inorganic insulation materials, organic insulation materials have a relatively lower thermal conductivity due to the cellular structure with highly formed closed cells. Expanded Styrene (EPS), polyurethane (PUR), polyisocyanurate (PIR), extruded styrene (XPS), and phenolic foam (PF) are representative insulation materials and are known to be highly insulative materials due to their unique closed-cell structure compared to open-cell structure inorganic materials. These can be divided into extruded insulation materials, bead insulation materials, urethane foam, and phenol foam according to the foaming process and raw materials [1,2]. Extruded insulation materials are made by foaming gas, with a lower thermal conductivity than air, to secure a high insulation performance during manufacturing. HCFC-141b, HCFC-142b are representative foaming gases, which have widely been used due to lower thermal conductivities ranging from 0.0097 to 0.0115 W / (m \(\cdot\) K) than 0.025 W / (m \(\cdot\) K) of air [3]. However, this foaming gas is gradually released over time and replaced with external air, which degrades the insulation performance of the materials by 30 to 40%. Basically, this degradation occurs at different speeds of time, which are a function of polymer type, cellular structure, temperature and foaming gas. Among these, foaming gas is generally known to directly influence the thermal conductivity by replacing it with air. At the early state, diffusion of air inside cellular structure happens faster than that of foaming gas, and induces a rapid decrease of thermal conductivity. As equilibrium in between diffusion of air and foaming gas inside the cellular structure is achieved, degradation of thermal conductivity slows down and stops when each concentration of air and foaming gas become similar [4,5]. Even if a foaming gas releases continuously inside the structure, degradation in thermal conductivity is observed very slowly. It was reported that the thermal resistance of foam insulation material was the function of time and thickness of material in the below equation [6,7]. \[\text{Thermal resistance}=\text{F}\left\{\text{e}^{\left(\frac{\text{ time}}{\text{thickness}\right)^{2}}}\right\} \tag{1}\]  
The heat transport through cellular foam plastics is the sum of heat capacities of radiation, gas mixture, and solid polymer. Heat capacities of solid polymer and radiation are relatively constant as foaming gas and time change. Therefore, long-term change in thermal performance can be regarded as governed by foaming gas concentration. The primary parameters of gas concentration in the cellular structure are effective diffusion coefficient, thickness, and time. To evaluate the contribution of each parameter, thickness and diffusion coefficient can be modulated by elevating the temperature, slicing thick material, and ageing for an intended time.