Eigenrate-Based Thermodynamic Decomposition of Competing Release Mechanisms in Polymeric Nano- and Microspheres: The MMIR-S Framework with Arrhenius Dual-Population Burst Kinetics and Log-Normal Polydispersity Averaging

Abstract

Simultaneous operation of Fickian diffusion, swelling-mediated relaxation, and polymer erosion in polymeric nano- and microspheres produces release profiles whose mechanistic origins cannot be resolved by empirical models without system-specific refitting. I present the Modified Multicomponent Interactive Release for Spheres (MMIR-S) framework, a thermodynamically self-consistent mechanistic model for homogeneously loaded spherical particles that determines mechanism-specific release weights from tabulated molecular descriptors, without fitting to release data. The theoretical core is Thermodynamic Eigenrate Decomposition (TED), in which each mechanism is assigned a commensurable first-order depletion rate: the diffusion eigenrate (π²D_eff,app/R²) from the dominant eigenvalue of Fick's second law in spherical coordinates; the swelling eigenrate governed by the Flory–Rehner criterion, closing when χ_PM > 0.5; and the erosion rate accommodating surface, first-order, or bulk erosion kinetics. Normalizing these rates yields mechanism weights summing to unity, connected to Hansen solubility parameters, Flory–Huggins interaction parameters, and partition coefficients without empirical intermediaries. The burst release term distinguishes physically adsorbed drug, governed by a first-order desorption rate constant, from chemically adsorbed drug governed by an Arrhenius rate constant parameterized by binding free energy, producing a biexponential burst profile. A polydispersity correction integrates the release function over a log-normal size distribution via Gauss–Hermite quadrature. Validation against the six-compound, two-pH, multi-polymer dataset of Stiepel et al. [1] demonstrates TED weight distributions consistent with effective diffusivity trends recovered by regression and machine learning. The framework recovers the Higuchi, Hopfenberg, and first-order models as limiting cases, providing a foundation for a priori prediction of release profiles from molecular structure alone.

Graphical Abstract

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