A topology-tuned pressure valve across the isoreticular RHO zeolite family

Abstract

The isoreticular index of the eight-member embedded RHO zeolite hierarchy operates as a phenomenological design knob that tunes the mechanical critical pressure of the framework valve from $\sim 0.94$ GPa for parent RHO down to a predicted $\lesssim 0.03$ GPa for the largest member PST-28, more than an order of magnitude lower across a single family of synthesizable nanoporous solids. The molecular-valve effect that defines zeolite RHO (a reversible centric-to-acentric phase transition triggered by water, gas pressure, or mechanical loading) is shown here to be not a peculiarity of the smallest member but a generic property of the whole hierarchy, with a critical pressure that decays exponentially with the isoreticular order $k$. Combining lattice dynamics, full elastic-constant tensors, and finite-temperature free-energy reconstructions within a classical core-shell description of the pure-silica frameworks (independently validated against r$^2$SCAN+rVV10 density-functional theory on $G_1$ and $G_2$), we find that the entire family is well described by an effective mean-field Landau picture in which the framework distortion couples quadratically to the volumetric strain. We emphasise that $p_c$ is a mechanical (hydrostatic) critical pressure of the bare pure-silica framework, used as a proxy for the intrinsic framework softness and for the cation- and dehydration-driven response of the real aluminosilicates; it is not a gas-adsorption pressure. The exponential extrapolation places $p_c(G_6\text{-}G_8) \lesssim 0.1$ GPa (model-dependent band $0.03$-$0.15$ GPa), identifying the higher-order members as the softest, most stimuli-responsive frameworks of the hierarchy; whether this intrinsic softness translates into guest-driven switching at low gas activities will depend on the Al distribution, extra-framework cations and adsorbed molecules, and remains to be tested experimentally.