论文标题
分支聚合物的尺寸指数/ Isaacson-Lubensky公式的扩展和应用于晶格树的应用
Size Exponents of Branched Polymers/ Extension of the Isaacson-Lubensky Formula and the Application to Lattice Trees
论文作者
论文摘要
可以将分支聚合物分为两个类别，以遵守不同的公式：\ begin {equination}ν= \ begin {cases} \ hspace {1mm} \ displayStyle \ frac {2（1+ν_{0}} } \ hspace {2mm} \ displayStyleV {0} \ ge \ ge \ frac {1} {d+1} \ hspace {10mm} \ text {（i）} \\ [（i）} \\ [3mm]带有} \ hspace {2mm} \ displayStyleV {0} \ le \ frac {1} {d+1} \ hspace {10mm} \ text {（ii）} \ end} \ end {cases} \ notag} \ notag \ notag \ end eNd {equination {equination {equation}，以提供优质溶剂的稀释度限制。 II类涵盖具有完全扩展配置的特殊聚合物。根据这些平等，我们讨论了嵌套体系结构和晶格树的大小指数。特别是，我们比较了先前的结果，$ν_{d = 2} = 1/2 $，对于$ z $ = 2具有$ν_{0} = 1/4 $的聚合物与数值结果，$ν_{d = 2} \ doteq 0.64115 $，用于在2-Dimensional上产生的Lattice lattice lattice lattice。我们的猜想是，尽管聚合物物理学和凝结物理物理学的结论都是正确的，但差异是由于晶格树是由分支构造的较少的分支结构所构成的，而不是具有$ν_{0} = 1/4 $的聚合物物理学的分支聚合物。目前的分析表明，二维晶格树是具有$ \barν_{0} \ doteq0.32 $的平均理想大小指数的异构体的混合物。
Branched polymers can be classified into two categories that obey the different formulae: \begin{equation} ν= \begin{cases} \hspace{1mm}\displaystyle\frac{2(1+ν_{0})}{d+2} & \hspace{3mm}\mbox{for polymers with}\hspace{2mm}\displaystyleν_{0}\ge\frac{1}{d+1}\hspace{10mm}\text{(I)}\\[3mm] \hspace{5mm}2ν_{0}& \hspace{3mm}\mbox{for polymers with}\hspace{2mm}\displaystyleν_{0}\le\frac{1}{d+1}\hspace{10mm}\text{(II)} \end{cases}\notag \end{equation} for the dilution limit in good solvents. The category II covers the exceptional polymers having fully expanded configurations. On the basis of these equalities, we discuss the size exponents of the nested architectures and the lattice trees. In particular, we compare our preceding result, $ν_{d=2}=1/2$, for the $z$=2 polymer having $ν_{0}=1/4$ with the numerical result, $ν_{d=2}\doteq 0.64115$, for the lattice trees generated on the 2-dimensional lattice. Our conjecture is that while both the conclusions in polymer physics and condensed matter physics are correct, the discrepancy arises from the fact that the lattice trees are constructed from less branched architectures than the branched polymers having $ν_{0} = 1/4$ in polymer physics. The present analysis suggests that the 2-dimensional lattice trees are the mixture of isomers having the mean ideal size exponent of $\barν_{0}\doteq0.32$.
