A Thermodynamically Consistent Multiscale Framework for Additive Transport in Pharmaceutical Polymers: The Pharm-PATIK Theory

The incorporation of functional additives into pharmaceutical polymers underpins modern drug delivery systems, yet the predictive modeling of additive mass transfer during processing remains a fundamental challenge. Existing frameworks rely on decoupled Fickian diffusion models that fail to capture the complex interplay between polymer rheology, crystallization dynamics, and mechano-chemical degradation-phenomena critically important for pharmaceutical applications where additive uniformity directly impacts drug product safety and efficacy. Here, we present the Pharm-PATIK (Pharmaceutical Polymer Additive Transport and Interaction Kinetics) framework: a thermodynamically consistent, multiscale computational theory for additive mass transfer in polymer matrices. The framework is built upon the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) formalism and integrates: (i) a multicomponent Maxwell-Stefan diffusion model with shear-dependent Flory-Huggins interaction parameters; (ii) a phase-field description of polymer crystallization with additive exclusion dynamics; (iii) a finite-strain viscoelastic model capturing stress-induced additive migration via configurational temperature theory; and (iv) mechano-chemical degradation kinetics for predictive assessment of leachables formation. The governing equations are formulated as a system of coupled nonlinear partial differential equations with degenerate mobility, for which we establish mathematical well-posedness under physically relevant conditions. Homogenization theory bridges molecular-scale free-volume effects to equipmentscale transport phenomena. Validation against experimental benchmarks including forced Rayleigh scattering diffusivity measurements, X-ray fluorescence mapping, and twin-screw extrusion trials demonstrates predictive accuracy with mean absolute percentage error below 7%. The framework provides a rigorous foundation for digital design of pharmaceutical polymer processing operations, enabling predictive control of additive fate from extrusion through shelflife storage under quality-by-design (QbD) paradigms.