Swelling mechanism unique to charged gels: Primary formulation of the free energy

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Abstract
This paper discusses the principal origin of the swelling behaviors inherent in charged gels. We start from a general formula for the free energy of the system consisting of a charged gel and the surrounding reservoir. First, it is clarified that the main term in the ionic contribution to the system free energy when the backbone network of gel is smeared with uniform density over the gel region is the translational entropy term of small ions freely mobile over the entire system, and therefore has no contribution to the swelling. Moreover, it is derived, from the system free energy within the Gaussian approximation, that the effective electrostatic interactions energy between charged groups on the network is obtained from summing the Yukawa-type potential which is screened by small ions inside a gel as has been speculated before, but that the corresponding interactions energy in smearing charged groups is to be subtracted from the total. These theoretical investigations reduce the starting formula for the system free energy to a more tractable form, which reveals that the ionic swelling behaviors are mainly ascribed to conformational changes of the backbone networks induced by alterations of the effective electrostatic interaction between charged groups.