This study investigates the modeling and experimental validation of cell morphology in microcellular-foamed polycaprolactone (PCL) using supercritical carbon dioxide (scCO₂) as the blowing agent. The microcellular foaming process (MCP) was conducted using a solid-state batch foaming process, where PCL was saturated with scCO₂ at 6 to 9 MPa and 313 K, followed by depressurization at a rate of −0.3 and −1 MPa/s. This study utilized the Sanchez–Lacombe equation of state and the Peng–Robinson–Stryjek–Vera equation of state to model the solubility and density of the PCL-CO₂ mixture. Classical nucleation theory was modified and combined with numerical analysis to predict cell density, incorporating factors such as gas absorption kinetics, the role of scCO₂ in promoting nucleation, and the impact of depressurization rate and saturation pressure on cell growth. The validity of the model was confirmed by comparing the theoretical predictions with experimental and reference data, with the cell density determined through field-emission scanning electron microscopy analysis of foamed PCL samples. This study proposes a method for predicting cell density that can be applied to various polymers, with the potential for wide-ranging applications in biomaterials and industrial settings. This research also introduces a Python-based numerical analysis tool that allows for easy calculation of solubility and cell density based on the material properties of polymers and penetrant gases, offering a practical solution for optimizing MCP conditions in different contexts.

Traditionally, the microcellular foaming process has aimed to generate uniform cell structures by applying heat uniformly to all surfaces of a polymer. Homogeneous cell distribution is known to enhance the mechanical properties and durability of the final product. However, the ability to engineer a gradient in cell density offers potential advantages for specific functional applications, such as improved sound absorption and thermal insulation. In this study, a controlled thermal gradient was introduced by heating only one side of a fully CO₂-saturated poly(methyl methacrylate) (PMMA) specimen. This approach allowed for the formation of a cell density gradient across the sample thickness. The entire process was conducted using a solid-state batch foaming technique, commonly referred to as the microcellular foaming process. A one-sided heating strategy successfully induced a spatial variation in cell morphology. Furthermore, a coalescence function was developed to account for cell merging behavior, enabling the construction of a predictive model for local cell density. The proposed model accurately captured the evolution of cell density gradients under asymmetric thermal conditions and was validated through experimental observations, demonstrating its potential for precise control over foam structure in saturated PMMA systems.

In previous studies, difficulties were encountered in measuring changes within high-pressure vessels owing to limitations such as sensor connectors and sensor failures under high-pressure conditions. In addition, polymer–gas mixtures experience instantaneous gas desorption upon exiting high-pressure vessels owing to pressure differentials, leading to measurement errors. In this study, a device using magnetic sensors was developed to measure the real-time changes in gas-saturated polymers inside pressure vessels. Experiments on polymethyl methacrylate gas adsorption were conducted with parameters including pressure at 5 MPa and temperatures ranging from −20 to 40 °C for 60 and 180 min. It was observed that at −20 °C, the maximum magnetic field force density and deflection were 391.53 μT and 5.83 mm, respectively, whereas at 40 °C, deflection did not occur, with a value of 321.79 μT. Based on gas saturation experiments, a new model for deflection in high-pressure atmospheres is proposed. Additionally, an ANSYS analysis was conducted to predict the changes in Young’s modulus based on gas saturation. In previous studies, mechanical properties were measured outside the pressure vessel, resulting in an error due to a pressure difference, while the proposed method is characterized by the ability to directly measure polymer behavior according to gas saturation in high-pressure vessels using a magnetic sensor in real time. Therefore, it is possible to predict polymer behavior, making it easy to control variables in high-pressure polymer processes.