Membranes

The industrial application of modified ion-exchange membranes is limited by complex, discontinuous ex-situ processes. This study introduces an in-situ electro-assembly strategy that enables the direct fabrication of a selective layer within an electrodialysis stack without disassembly. By utilizing a programmed current reversal to orchestrate the sequential deposition of polyethyleneimine (PEI), glutaraldehyde cross-linking, and polystyrene sulfonate (PSS) adsorption, we achieve meticulous interfacial engineering on a commercial cation exchange membrane. Comprehensive characterization confirms the successful construction of a hydrophilic, charge-tuned multilayer, which enhances ion transport kinetics and raises the limiting current density. This method culminates in a membrane with an exceptional Li⁺/Mg²⁺ selectivity of 107.9 and robust stability, retaining a significant selectivity of 47 over 10 cycles in real salt lake brine. This synergistic integration of operational simplicity, interfacial precision, and superior performance establishes a transformative and scalable platform for manufacturing high-performance membranes for selective ion separation from complex brine sources.

Analytical models of transdermal drug delivery (TDD) often represent deeper skin layers using ideal sink assumptions or phenomenological interfacial resistances. While mathematically convenient, these approaches obscure the physical role of the dermis and hypodermis in controlling molecular transport. Here, we develop an impedance-based analytical model for diffusion across multilayer skin membranes, in which the epidermal barrier is dynamically coupled to a finite diffusive backing layer representing the dermis–hypodermis composite. Diffusion impedance links transport conductivity, storage capacity, and layer thickness, while preserving continuity of concentration and flux at all interfaces. Closed-form expressions in the Laplace domain describe concentration fields and interfacial fluxes, and cumulative drug uptake is computed in the time domain via inverse Laplace transformation. The model identifies distinct short- and long-time transport regimes. Commonly used Dirichlet and Robin boundary conditions emerge as limiting cases but cannot reproduce the regime-dependent behavior of a backing layer. In particular, Robin formulations reduce the backing layer to a constant effective resistance, neglecting its storage capacity and time-dependent impedance. By replacing ad hoc boundary conditions with a physically grounded impedance framework, this approach provides a unified and extensible method for analyzing multilayer transport systems, including extensions to anomalous or memory-dependent diffusion.

This work presents a novel, membrane-inspired hybrid framework composed of Ag₂Mo₃O₁₀·1.8H₂O nanowires grown in situ on carbon fiber cloth (CFC) for the continuous and selective recovery of high-value sulfur-containing molecules from organic wastewater. The framework forms an integrated hierarchical porous network rich in micro-/nano-channels, which facilitates efficient, capillary-driven water transport. Owing to its mesoporous texture and specific Ag–S coordination affinity, the material shows exceptional selectivity toward sulfur-containing dyes, enabling rapid adsorption (>94% removal of methylene blue within 10 min) and high specificity in mixed solutions. The hybrid also exhibits excellent reusability, maintaining high recovery efficiency over repeated adsorption–desorption cycles. When configured into a continuous-flow system, the framework operates without external pressure and achieves a water transport rate of 1875 mL·h⁻¹·m⁻². These findings underscore the potential of the Ag₂Mo₃O₁₀·1.8H₂O/CFC hybrid as an efficient, scalable, and sustainable platform for resource-oriented wastewater treatment.