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Bivariate Distribution and Related Analytical Solutions for Batch Step-Growth Polymerization of AB(2)-Type Monomer

机译:AB(2)型单体的分批步进生长聚合的双变量分布及相关分析解

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摘要

Based on the analytical solution for the bivariate distribution N(n,k) of the degree of polymerization n and the number of dendritic units k, it is shown that the batch step-growth polymerization of AB(2)-type monomer leads to form random hyperbranched architecture, irrespective of the magnitude of reactivity ratio r that represents the reactivity of the second B group. The bivariate distribution function enables one to obtain various useful analytic relationships for the hyperbranched architecture. The degree of branching at large n limit, DBn -> infinity, is an important property to represent the branched polymer system, rather than the average DB of the whole reaction mixture. For the case with r = 1, the value of DBn -> infinity is always 0.5, and is unchanged at any stage of batch polymerization. On the other hand, DBn -> infinity changes with the progress of polymerization for r not equal 1, but the change is not very significant for the high conversion region. The degree of branching at large k limit, DBk -> infinity, is always larger than DBn -> infinity, but the relationship DBk -> infinity = DBn -> infinity holds at 100% conversion.
机译:基于用于聚合程度N的双抗体分布N(n,k)的分析溶液N和树突状单位的数量K,显示AB(2)型单体的批量生产聚合导致形成随机超支化架构,无论代表第二B组的反应性的反应性比R的大小。双方分布函数使得能够获得超支架构的各种有用的分析关系。大n限制的分支度DBN - >无限远,是表示支化聚合物体系的重要性质,而不是整个反应混合物的平均dB。对于r = 1的情况,DBN - “无限远的值始终为0.5,并且在分批聚合的任何阶段保持不变。另一方面,DBN - > Infinity随着r不等于1的聚合进度而变化,但高转化区域的变化不是很重要。大于k限制的分支程度,dbk - >无限远,总是大于dbn - >无限远,但关系dbk - > Infinity = dbn - > Infinity在100%转换时保持。

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