中文摘要：

应用统计力学原理，从两种不同角度对ABg型超支化反应体系中的平衡特征进行研究，得到该体系平衡自由能以及反应程度与热力学量之间关系的解析表达式，进一步指出获得超支化高分子数量分布函数的两种新方法，并结合改进的高分子格子流体理论探讨了聚合反应对体系状态方程的影响。

英文摘要：

The equilibrium statistical characteristics of hyperbranched reaction system of ABg type is studied from two viewpoints by using the principle of statistical mechanics. The equilibrium free energy and a relationship between the conversion and some thermodynamic quantities are obtained. Furthermore, two new methods that can be used to evaluate the number fraction distribution of hyperbranched polymers are reported. As an application, it is found that the effect of polymerization is significant on the equation of state proposed by the improved lattice-fluid theory.