Constraint-Driven Deformation and Periodic Assembly Formation in Elliptical Bilayer Membranes

Understanding how geometric confinement regulates the structure, elasticity, and morphological evolution of polymer bilayer membranes remains a fundamental challenge in soft matter physics. Here, we develop a multiscale framework combining constraint-based self-consistent field (SCF) theory with the Helfrich elastic model (HEM) to investigate confined elliptical cylindrical bilayers. The SCF free energies quantitatively agree with Helfrich predictions over a broad range of geometries, demonstrating that curvature elasticity provides the leading-order contribution to membrane deformation. However, systematic deviations emerge under strong confinement. By introducing a dimensionless thickness-curvature parameter Λ = Ωκmax, we reveal that the deviation between SCF and HEM exhibits a nonmonotonic dependence on membrane geometry and cannot be explained solely by higher-order curvature elasticity. Instead, SCF calculations demonstrate that finite membrane thickness, interface geometry, and polymer segment redistribution evolve cooperatively under confinement, revealing the molecular-scale mechanisms underlying corrections beyond the classical zero-thickness Helfrich description. Furthermore, variations in molecular interactions and block composition regulate membrane thickness and packing through distinct mechanisms, leading to different structural responses even under identical geometrical constraints. Under sufficiently strong confinement, the accumulated elastic frustration drives morphological reorganization from isolated bilayers toward periodic membrane morphologies. This work establishes a quantitative bridge between molecular self-consistent field theory and continuum membrane elasticity, providing a predictive framework for understanding confined polymer membranes beyond the classical zero-thickness approximation.