Adsorption kinetics in the polyethylenimine–cellulose fiber system

Abstract

The rate of adsorption of polyethylenimine (PEI) onto regenerated cellulose fibers can be described as a mass-transport process. The application of simple mass-transfer theory led to the conclusion that diffusion into the internal porous structure of the fiber represents the predominant barrier to rapid adsorption. Under suitable conditions, mass transfer as a result of electrostatic interactions between polymer and fiber may play a role in determining the sorption rate. Adsorption rate curves were measured as a function of polymer molecular weight, initial polymer concentration, ionic strength, and pH. A rate equation based on diffusion control with Langmuirian adsorption in stirred solution was developed. The equation predicted that the initial rate should depend linearly on initial polymer concentration and on the adsorbate diffusion coefficient to the 0.66 power. This equation served to aid in the design and interpretation of experiments. Fractionated PEI was sorbed onto regenerated cellulose fibers from aqueous solution. This system was chosen to facilitate characterization and control of variables. The polymer was fractionated by means of gel permeation chromatography to limit the effects of polymolecularity. Equilibrium adsorption measurements showed that, over a molecular weight range of from 8,000 to 20,000, the smaller molecules were sorbed to a greater extent than the larger ones. For all molecular weight fractions studied, a maximum in retention was observed at pH 10.9. It was shown that the pH dependence is due primarily to an ion-exchange reaction involving ionized hydroxyls on the fibers. Differences in polymer size greatly affected accessibility to reactive sites. The diffusion coefficient was found to decrease with increasing ionic strength, pH, and molecular weight. The sensitivity to pH and salt concentration can be explained by means of an electrophoretic effect. Adsorption equilibrium was achieved after six to eight hours for most cases. The initial rate was found to increase with initial polymer concentration and to decrease with decreasing pH, ionic strength, and molecular weight. With some exceptions, the magnitude of these effects is in accord with simple mass-transfer theory. The deviations from theory are shown to be a result of electrostatic interactions between the fiber and the polymer. The electrostatic interactions are reflected, in general, by an accelerated initial rate and a retarded approach to equilibrium as compared with simple diffusion alone. An effective diffusional film thickness was defined as the distance over which the polymer must diffuse to produce the observed rate. This quantity was calculated from the rate data and found to be on the order of four centimeters. This physically impossible magnitude was interpreted as an indication of the presence of a physical barrier to mass transfer. It was concluded that this barrier is a result of the necessity of the polymer to penetrate the porous structure of the fiber. Electron micrographs of fiber cross sections treated wit...

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