On the scattering properties of polyelectrolyte gels

We present a simple model for scattering properties of polyelectrolyte gels at swelling equilibrium. In the weak screening limit where the Debye-Hfickel screening length is larger than the mesh size of the gel, the direct electrostatic interactions are negligible and the swelling is driven by the osmotic pressure of the counterions. The tension created by this pressure is transmitted through the crosslinks to the elastic char s which behave as isolated chains with an applied force at their end points. The structure fz =tor of the gel can be split into a frozen component due to the average concentration heterogencities and a thermodynamic component due to concentration fluctuations. The frozen component has a peak at a wavevector of the order of the mesh size of the gel, the thermodynamic component has a peak at a higher wavevector of the order of the inverse transverse radius of the chains. At infinite times the dynamic structure factor relaxes towards the frozen component of the static structure factor. In the limit of small wavevectors the relaxation is diffusive with a diffusion constant equal to the Stokes diffusion constant of the Pincus blobs of the stretched chains. The diffusion constant shows a minimum at a wavevector of the order of the inverse transverse radius of the chains. 1532 JOURNAL DE PHYSIQUE II N°8