Study on methodology for critical behavior near the sol-gel transition point

为了分析溶胶-凝胶过渡点附近的临界现象，我们不仅测量了表征凝胶宏观特征的力学性能，还测量了表征凝胶分子水平特征的光散射。采用动态光散射法确定溶胶-凝胶过渡点。根据散射光强度随时间的波动，测量自相关函数，然后利用Stokes-Einstein方程，根据相关函数得到的扩散常数计算簇半径。结果表明，首先形成初级团簇，然后初级团簇之间相互聚合形成较大的次级团簇。当浓度接近胶凝点时，二级团簇的大小有发散的趋势。通过用标度律拟合数据，确定了临界指数为0.84，与渗流理论中相关长度的临界指数相差不大，称为0.9。琼脂糖通过非共价键形成团簇，也可以用动态光散射法确定琼脂糖溶胶的团簇半径。当浓度增加并接近溶胶-凝胶过渡点时，平均团簇半径呈发散趋势。在27ºC温度下，凝胶浓度和临界指数分别为4.5 × 10^<-3>(wt%)和0.98。当温度降低并接近胶凝温度时，团簇半径变大。通过拟合得到，当浓度为0.15（wt%）时，胶凝温度为32.7，临界指数为1.36，均大于理论值。从以上结果可以看出，通过测量簇半径分布，渗流和结垢的概念在确定溶胶-凝胶过渡点附近的物性变化时是有效的。少

Not only Mechanical properties, which give macroscopic features of gels, but also light scattering, which gives features of gels on molecular level, were measured in order to analyze the critical phenomena near the sol-gel transition point.dynamic light scattering method was carried out to determine the sol-gel transition point. From the fluctuations of scattered light intensity in the course of time, auto-correlation function was measured, and then by using Stokes-Einstein equation, cluster radius was calculated from the diffusion constant which was obtained from the correlation function. Results suggested that first, primary clusters were formed, and then the primary clusters polymerized with each other to form larger secondary clusters. The size of secondary clusters showed a tendency to diverge when the concentration approached the gelation point. By fitting the data with scaling law, the critical exponent was determined to be 0.84, which is not so far off from the critical exponen … More t of correlation length in percolation theory, which is said to be 0.9.In the case of agarose, which forms clusters by non-covalent bonds, it was also possible to determine the cluster radius of agarose sol by using the dynamic light scattering method. Average cluster radius showed a tendency to diverge when the concentration increased and approached the sol-gel transition point. It was also possible to fit the data with scaling law, and the gelation concentration and the critical exponent were determined to be 4.5*10^<-3>(wt%) and 0.98 at the temperature of 27ﾟC.When the temperature was lowered and approsched the gelation temperature, the cluster radius became larger. By fitting the data, the gelation temperature and the critical exponent were determined to be 32.7ﾟC,and 1.36, for 0.15(wt%) agarose sol. The critical exponent thus obtained was larger than the theoretical value.From the above results, it was suggested that by measuring the cluster radius distribution, concepts of percolation and scaling were shown to be effective when determining the physical property changes near the sol-gel transition point. Less