Lattice mean-field method for stationary polymer diffusion

Area of Science:

• Polymer Science
• Physical Chemistry
• Materials Science

Background:

• Studying diffusion in polymer systems is crucial for understanding material properties and behavior.
• Existing methods like the Scheutjens-Fleer self-consistent field (SF-SCF) method are effective for equilibrium systems.
• There is a need for methods that can efficiently study non-equilibrium, stationary diffusion processes in polymers.

Purpose of the Study:

• To present a novel method for investigating mean-field stationary diffusion (MFSD) in polymer systems.
• To demonstrate the method's ability to model diffusion between different polymer mixtures.
• To extend equilibrium self-consistent field theories to non-equilibrium diffusion phenomena.

Main Methods:

• Implementation of four alternative diffusion equations based on slow- and fast-mode theories.
• Evaluation of diffusion driving forces using methods inspired by the SF-SCF approach.
• Numerical simulation of stationary diffusion between two distinct bulk polymer mixtures.

Main Results:

• Diffusion profiles are predominantly governed by the chosen diffusion theory (slow- vs. fast-mode).
• The method for evaluating diffusion driving forces has a secondary impact on the diffusion profiles.
• Numerical results for stationary states show excellent agreement with analytical solutions.

Conclusions:

• The developed MFSD method provides a robust framework for studying non-equilibrium polymer systems.
• This approach offers a computationally efficient alternative to simulation techniques for analyzing fluxes and steady-state profiles.
• Potential applications include drug delivery systems and membrane technologies involving polymer diffusion.