Mesoporosity, Mechanical Properties, and Statistical–Physics Modeling of PVA/MMT/MXene Nanocomposite Membranes for Pb²⁺ and Methylene Blue Adsorption

Poly(vinyl alcohol) (PVA)/montmorillonite (MMT)/Ti₃C₂T_x (MXene) nanocomposite membranes (PVA/MMT/MXene) were developed and evaluated in terms of their mechanical properties, mesoporosity, and adsorption performance toward Pb²⁺ ions and methylene blue (MB). The incorporation of MMT and MXene resulted in a strong synergistic reinforcement, increasing the ultimate tensile strength from 10 to 20 MPa, the Young’s modulus from 14.7 to 29.5 MPa, and reducing the swelling ratio from 2.0 to 1.1 g·g⁻¹. BJH porosimetry revealed a refined and interconnected mesoporous structure, with the cumulative pore volume increasing from 0.134 to 0.448 cm³·g⁻¹. In adsorption experiments (mono-solute systems, 25 °C), the ternary membrane achieved high uptake capacities of 55 mg·g⁻¹ for Pb²⁺ and 80 mg·g⁻¹ for MB, outperforming binary PVA/MMT and neat PVA. Statistical–physics modeling provided microscopic descriptors consistent with the experimental isotherms: Pb²⁺ adsorption follows a monolayer regime (n ≈ 1), whereas MB exhibits multilayer behavior (n > 1) with a higher site density (Nm ≈ 1.6 mmol·g⁻¹). These results demonstrate that the hybrid 2D–2D architecture of MMT and MXene significantly enhances the structural robustness, pore accessibility, and adsorption efficiency of PVA-based membranes, highlighting their potential for efficient removal of metal ions and dyes from aqueous media.