PRISM: A phase-resolved equation of state for surface pressure-area isotherms of Langmuir monolayers

Surface pressure-area isotherms of Langmuir monolayers encode phase boundaries, molecular packing, coexistence regimes, and elastic response, but their interpretation is still often based on heterogeneous workflows that rely on subjective manual segmentation, noise-sensitive numerical derivatives, and limited uncertainty quantification. A phase-resolved, thermodynamically constrained equation-of-state framework can extract physically interpretable descriptors from quasi-equilibrium monolayer isotherms while keeping model complexity under statistical control.

We introduce the Phase-Resolved Interfacial Surface Model (PRISM), a continuous surface equation of state for surface tension (or surface pressure) as a function of area per molecule. PRISM describes single-phase branches and first-order coexistence regions, enforces continuity at transition points, and activates an effective domain-corrected coexistence term only when statistically justified. Parameters are inferred by constrained nonlinear regression and accompanied by subsampling-based confidence intervals.

PRISM replaces subjective heuristics with objective inference, yielding limiting molecular areas, phase boundaries, coexistence descriptors, and elastic moduli with uncertainty quantification. Applied to DPPC, POPE, POPC, and POPS monolayers, the framework captures both sharp plateaus and sloped coexistence regions, reconstructs phase diagrams, and enables the estimation of phase-transition enthalpies and entropies when temperature-dependent coexistence data are available. The method is intended for quasi-equilibrium isotherms with distinguishable branches or effective first-order coexistence regimes; strongly hysteretic, collapse-dominated, or continuous-transition cases require additional treatment. A web application implementing PRISM is available at https://surffitter.simbioslab.com/ to apply the model to user-provided isotherms.