Rigorous Models for Vapor Diffusion in Polymers with Immobilization and Chemical Potential Gradients

Area of Science:

• Materials Science
• Physical Chemistry
• Chemical Engineering

Background:

• Vapor sorption and diffusion in materials are governed by complex thermodynamic and kinetic phenomena.
• Immobilization and concentration-dependent mixing free energies significantly impact sorption and transport.
• Existing models often struggle to simultaneously capture both equilibrium and dynamic aspects.

Purpose of the Study:

• To develop a unified model that integrates immobilization and mixing free energies for sorption and diffusion.
• To rigorously apply Fick's law using chemical potential gradients instead of concentration gradients.
• To validate the model across diverse material systems with varying sorption characteristics.

Main Methods:

• Developed a transport model incorporating quasi-equilibrated immobilization reactions.
• Applied Fick's law based on chemical potential gradients.
• Tested the model against five distinct material case studies exhibiting varied sorption behaviors.

Main Results:

• The unified model successfully captures both sorption dynamics and equilibrium isotherms simultaneously.
• Intrinsic diffusivity was found to be constant across all case studies.
• Effective diffusivity showed predictable changes due to immobilization and varying mixing free energies.

Conclusions:

• A unified model effectively describes vapor sorption and diffusion by considering immobilization and mixing energies.
• The model's reliance on chemical potential gradients provides a more rigorous approach to transport phenomena.
• Understanding these coupled phenomena is crucial for designing materials with tailored vapor interaction properties.