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 ([Formula: see text]) and the elastic blob ([Formula: see text]) were obtained from these measurements and compared to the theoretical mesh size, the geometric blob ([Formula: see text]), 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, [Formula: see text] , obtained by dynamic light scattering (DLS) was found to obey the well-known concentration dependence for polymer solutions in semidilute regime ([Formula: see text]) irrespective of the Cases. On the other hand, the [Formula: see text] was strongly dependent on the Cases: For Case A, [Formula: see text] was weakly dependent on the molecular weight of linear-PEGs ([Formula: see text]) while [Formula: see text] for Case B was a strong increasing function of [Formula: see text] ([Formula: see text]). However, both of them are different from the geometric blob (theoretical mesh) of the gel networks. In addition, interesting relationships between [Formula: see text] and [Formula: see text] , [Formula: see text] , [Formula: see text] , were obtained for Cases A and B, respectively.