Evaluation of Mesh Size in Model Polymer Networks Consisting of Tetra-Arm and Linear Poly(ethylene glycol)s.

The structure and mechanical properties of model polymer networks consisting of alternating tetra-functional poly(ethylene glycol)s (PEGs) and bis-functional linear PEGs were investigated by dynamic light scattering and rheological measurements. The sizes of the correlation blob ( ξ c ) and the elastic blob ( ξ e l ) were obtained from these measurements and compared to the theoretical mesh size, the geometric blob ( ξ g ), calculated by using the tree-like approximation. By fixing the concentration of tetra-PEGs and tuning the molecular weight of linear-PEGs, we systematically compared these blob sizes in two cases: complete network (Case A) and incomplete network (Case B). The correlation blob, ξ c , obtained by dynamic light scattering (DLS) was found to obey the well-known concentration dependence for polymer solutions in semidilute regime ( ξ c ~ ϕ - 3 / 4 ) irrespective of the Cases. On the other hand, the G ' was strongly dependent on the Cases: For Case A, G ' was weakly dependent on the molecular weight of linear-PEGs ( G ' ~ M c 0.69 ) while G ' for Case B was a strong increasing function of M c   ( G ' ~ M c 1.2 ). However, both of them are different from the geometric blob (theoretical mesh) of the gel networks. In addition, interesting relationships between G ' and ξ c , G ' ~ ξ c , G ' ~ ξ C - 2 , were obtained for Cases A and B, respectively.