Supramolecular architectures on a torus: geometrically modulated chiral phases and the impact of elastic anisotropy

The control of supramolecular self-assembly on curved manifolds represents a challenge in soft matter. This work investigates chiral nematic phases confined to a toroidal geometry, where intrinsic helical twisting power competes with spatially varying curvature. We employ Physics-Informed Neural Networks (PINNs) to simulate self-assembly of chiral host-guest systems, mapping interactions between molecular chirality (q0), saddle-splay elasticity (K24), and bulk elastic anisotropy (K11, K22, K33). Our simulation results unveil a phase diagram governed by a ”geometric clamp” mechanism. Specifically, the saddle-splay potential – arising from coupling between the director field and negative Gaussian curvature – locally suppresses chiral induction. This yields spatially heterogeneous ground states where curvature-pinned achiral domains coexist with frustrated helical textures. We demonstrate that tuning the material’s elastic anisotropy offers a chemical route to select the orientation of these supramolecular domains, providing design principles for curvature-directed functional materials.