Functionalization of polyolefin fibers is a complex multiphase process including solid, liquid, and gas phases.  The type and degree of functionalization is system dependent.  Functionalization ranges from fiber surface treatment to complete fiber stabilization.  A fully stabilized polyolefin fiber is functionalized uniformly from the surface to the core.  During this process, the reactant diffuses in the bulk liquid phase to the polymer surface.  Subsequently, the reactant diffuses into and reacts with the polymer.  In some reaction systems, gaseous products may form that diffuse out from the polymer fiber.  A reaction-diffusion model of the polyolefin functionalization process is useful to predict and optimize the desired characteristics of a functionalized polyolefin fiber. 

This paper presents the development and application of a reaction-diffusion model for the liquid-phase sulfonation of polyethylene fibers.  Diffusion coefficients and reaction kinetics were estimated from varying degrees of partially sulfonated polyethylene fibers produced in a continuous multi-stage sulfonation reactor.  Sulfonated polyethylene fibers were characterized by thermogravimetric analysis (TGA), elemental analysis (CHSN/O), and scanning electron microscopy and energy dispersive X-ray spectrometry (SEM-XEDS).  The fiber sulfonation model predicts the radial distribution of sulfonated polyethylene,unreacted polyethylene, and diffusing SO₃.