A Simple Approach to Characterize Sorption and Release Kinetics in Polymeric Materials with Planar, Cylindrical or...

Area of Science:

• Polymer Science
• Materials Science
• Chemical Engineering

Background:

• Modeling substance sorption and release in polymers is essential for various applications.
• Existing analytical solutions are often limited to simple geometries and ideal conditions.
• Accurate estimation of diffusion coefficients is critical for material performance.

Purpose of the Study:

• To develop a universal theoretical framework for modeling sorption and release kinetics in polymers.
• To provide a method for estimating diffusion coefficients applicable to diverse geometries.
• To overcome limitations of classical analytical solutions in mass transfer modeling.

Main Methods:

• Fick's second law was adapted into dimensionless variables.
• Numerical solutions using a finite-difference approach generated universal mass transfer profiles.
• These profiles were fitted with double-exponential equations for explicit expression.

Main Results:

• Universal mass transfer profiles were generated for planar, cylindrical, and spherical geometries.
• Explicit expressions were derived for straightforward estimation of diffusion coefficients.
• The method demonstrated excellent agreement with literature data for films, fibers, and microspheres.

Conclusions:

• The proposed theoretical framework offers a versatile approach for modeling diffusion in polymers.
• This method is applicable to a wide range of geometries found in practical applications.
• It provides a more robust alternative to classical solutions for estimating diffusion coefficients.