Several researchers have investigated the phenomenon of polymer–gas mixtures, and a few have proposed diffusion coefficient values instead of a diffusion coefficient model. There is a paucity of studies focused on the continuous change in the diffusion coefficient corresponding to the overall pressure and temperature range of the mixture. In this study, the gas sorption and desorption experiments of poly(methyl methacrylate) (PMMA) were conducted via solid-state batch foaming, and the weight change was measured using the gravimetric method with a magnetic balance. The control parameters were temperature, which ranged from 290 to 370 K, and pressure, which ranged from 2 to 5 MPa; in the subcritical regime. Based on the experimental data, the diffusion coefficient of the PMMA was calculated using Fick’s law. After calculating the diffusion coefficient in the range of the experiment, the diffusion coefficient model was employed using the least-squares method. Subsequently, the model was validated by comparing the obtained results with those in the literature, and the overall trend was found to be consistent. Therefore, it was confirmed that there were slight differences between the diffusion coefficient obtained using only Fick's equation and the value using by a different method.

This study proposes a novel process that integrates the molding and patterning of solid-state polymers with the force generated from the volume expansion of the microcellular-foaming process (MCP) and the softening of solid-state polymers due to gas adsorption. The batch-foaming process, which is one of the MCPs, is a useful process that can cause thermal, acoustic, and electrical characteristic changes in polymer materials. However, its development is limited due to low productivity. A pattern was imprinted on the surface using a polymer gas mixture with a 3D-printed polymer mold. The process was controlled with changing weight gain by controlling saturation time. A scanning electron microscope (SEM) and confocal laser scanning microscopy were used to obtain the results. The maximum depth could be formed in the same manner as the mold geometry (sample depth: 208.7 µm; mold depth: 200 µm). Furthermore, the same pattern could be imprinted as a layer thickness of 3D printing (sample pattern gap and mold layer gap: 0.4 mm), and surface roughness was increased according to increase in the foaming ratio. This process can be used as a novel method to expand the limited applications of the batch-foaming process considering that MCPs can impart various high-value-added characteristics to polymers.