Journal of Membrane Science, 78 (1993) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1-12 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Elsevier Science Publishers B.V., Amsterdam Swelling of ionic and neutral polymer networks in ionic solutions Deepak Hariharan and Nikolaos A. Peppas School of Chemical Engineering, Purdue University, West Lafayette, IN 47907 (USA) (Received February 24,1992; accepted in revised form September 29,1992) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ Abstract The dynamic swelling of polymer networks in ionic solution was modelled with a Hamiltonian equation of motion which was transformed into an equation describing the system displacement vector as a func- tion of time. The model was developed from first principles using the principle of conservation of energy. It reflects the effect of various physiological parameters like the pH of the solution, ionic strength and composition of the buffer solution on the swelling behavior. The coefficients in the model were deter- mined from equilibrium considerations. It was found that the coefficient of friction between the polymer gel and the solution obtained from experiments was almost constant for polymers swelling to a moderate degree. The equation was solved with appropriate boundary conditions. This model was used to calculate the swelling behavior of thin polymer films in buffer solutions. Keywords: swelling; diffusion, modelling of; ionic networks; gels Introduction Crosslinked ionic polymers (networks) con- tain groups which ionize under the influence of suitable external conditions. Upon ionization, these systems swell due to favorable thermo- dynamic compatibility between water and hy- drophilic pendant groups of the network or due to the repulsion between the charged groups. Ionic networks have been utilized in biosepar- ations, membrane processes and in controlled drug delivery. In the latter case, previously in- corporated bioactive agents such as drugs, pep- tides or proteins may be allowed to diffuse Correspondence to: Nikolaos A. Peppas, School of Chem- ical Engineering, Purdue University, West Lafayette, IN 47907, USA. through the mesh of a network at specific ionic or physiological conditions due to selective net- work response to the environment by swelling or deswelling depending on the ionization of the fixed groups. The theory of network swelling has received renewed attention over the past decade. Early work by Flory and Rehner [ 11, Katchalsky et al. [ 2-41 and others addressed important ques- tions related to the equilibrium behavior of neutral and ionic networks in swelling agents. Significant work has been carried out by Tan- aka et al. [5,6] in describing the swelling of a polymer gel. The longitudinal bulk modulus of the polymer gel and the coefficient of friction between the network and the gel fluid were used as parameters to describe the swelling of the polymer network. An equation of motion was 0376-7388/93/$06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.