Ozaki Hiroto, Narita Tetsuharu, Koga Tsuyoshi, Indei Tsutomu
Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Kyoto 615-8510, Japan.
Laboratoire Sciences et Ingénierie de la Matière Molle, PSL Research University, UPMC Univ Paris 06, ESPCI Paris, CNRS, 10 rue Vauquelin, 75231 Paris CEDEX 05, France.
Polymers (Basel). 2017 Jun 29;9(7):256. doi: 10.3390/polym9070256.
When the polymer chains are cross-linked by physical bonds having a finite lifetime, the relaxation time and viscosity do not diverge at the gel point though percolation occurs. These undivergent quantities are related to the finite-sized "largest relaxed cluster," which can relax before it breaks. Its size is the key rheological parameter characterizing of the critical physical gels. In order to evaluate this characteristic size, we propose here a generalized phenomenological model for the viscoelasticity of critical physical gels. We apply the theory to the previously reported experimental result for the physical gel consisting of polyacrylamide-derivative associating polymers containing imidazole groups cross-linked by coordination bonds with Ni ions. We successfully estimate the size of the largest relaxed cluster and the fractal dimension. The size is in good agreement with that estimated from the mean-square displacement of probe particles at the gel point by microrheological measurement. We also compare this system with the poly(vinyl alcohol) hydrogel cross-linked by borate ions, and show that the difference in the cluster structures is originating from the differences of precursor chain properties such as overlap concentration and radius of gyration and of the cross-linking states in these systems.
当聚合物链通过具有有限寿命的物理键交联时，尽管发生了渗流，但在凝胶点处松弛时间和粘度不会发散。这些不发散的量与有限尺寸的“最大松弛簇”有关，该簇在断裂前可以松弛。其大小是表征临界物理凝胶的关键流变参数。为了评估这个特征尺寸，我们在此提出一个关于临界物理凝胶粘弹性的广义唯象模型。我们将该理论应用于先前报道的由含咪唑基团的聚丙烯酰胺衍生物缔合聚合物与镍离子通过配位键交联而成的物理凝胶的实验结果。我们成功地估计了最大松弛簇的大小和分形维数。该大小与通过微观流变测量在凝胶点处由探针颗粒的均方位移估计的值非常吻合一致。我们还将该体系与硼酸根离子交联的聚乙烯醇水凝胶进行了比较，并表明簇结构的差异源于这些体系中前体链性质（如重叠浓度和回转半径）以及交联状态的差异。
