Accurately predicting gas and liquid solubility in semi-crystalline polymers is crucial for optimizing their production, performance, and degradation behaviour. In this work a novel statistical-mechanical model for semi-crystalline polymers is showcased. The amorphous domains are divided into two portions: the semi-rigid inter-lamellar domains and the melt-like ``free" amorphous domains. Solubility in the inter-lamellar domains is reduced due to the presence of tie-molecules, which are polymer chains connecting different crystals. By incorporating reversible mass exchange at the crystal/amorphous interface, the model predicts variations in lamellar thickness and solubility with temperature.

According to our model, the equilibrium solubility in each polymer sample is determined by its crystallinity, the fraction of tie-molecules at the crystal/amorphous interface, and the fraction of free amorphous domains. While crystallinity can be easily measured, the other two parameters are adjusted to minimize differences between the model's predictions (made in conjunction with the SAFT-γ Mie equation of state) and experimental sorption isotherms of pure fluids in polyethylene (PE), polypropylene (PP), and polyethylene glycol (PEG) samples. The model accurately reproduces the solubility of all solutes considered after the assignment of unique sample-specific parameters to each sample. A meta-analysis of literature data reveals that in PE, the fraction of free amorphous domains decreases with crystallinity whereas the fraction of tie-molecules lies in the range 0.2 – 0.4.

The model's predictions of solubility of binary mixtures of short hydrocarbons in PE are in good agreement with experimental data. The model also accurately captures the temperature dependence of solubility in most of the polymer samples considered, except for those with low crystallinity where changes in the free amorphous domains with temperature may need consideration. Additionally, the model is applied to study the moisture uptake by PEG. By employing simple thermodynamic considerations, the model qualitatively predicts the humidity at which deliquescence occurs and describes the moisture uptake at each relative humidity after adjusting the fraction of tie-molecules.