We present an exact and Monte Carlo renormalization group (MCRG) study of semiflexible polymer chains on an infinite family of the plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension $d_f$ is equal to 2 for all members of the fractal family enumerated by the odd integer $b$ ($3\le b< \infty$). For various values of stiffness parameter $s$ of the chain, on the PF fractals (for $3\le b\le 9$) we calculate exactly the critical exponents $ν$ (associated with the mean squared end-to-end distances of polymer chain) and $γ$ (associated with the total number of different polymer chains). In addition, we calculate $ν$ and $γ$ through the MCRG approach for $b$ up to 201. Our results show that, for each particular $b$, critical exponents are stiffness dependent functions, in such a way that the stiffer polymer chains (with smaller values of $s$) display enlarged values of $ν$, and diminished values of $γ$. On the other hand, for any specific $s$, the critical exponent $ν$ monotonically decreases, whereas the critical exponent $γ$ monotonically increases, with the scaling parameter $b$. We reflect on a possible relevance of the criticality of semiflexible polymer chains on the PF family of fractals to the same problem on the regular Euclidean lattices.
Divergence Of Persistent Length Of A Semiflexible Homopolymer Chain In The Stiff Chain Limit
在这份简短的报告中，我们重新审视了分析计算[Mishra，{ \it et al.}，Physica A { \bf 323}（2003）453和Mishra，NewYork Sci. J. { \bf{3(1)} }（2010）32.]半柔性均聚物链的持久长度的%表示极刚性链极限，{ \bf $k\to0$（其中，$k$是链的刚度）}表示定向行走晶格模型的极刚性链极限，$k\to0$（其中，$k$是链的刚度）表示二维和三维定向行走晶格模型。我们对二维（正方形和长方形）和三维（立方形）格点的研究清楚地表明，持久长度按照表达式$(1-g_c)^{-1}$发散，其中$g_c$是无限长线性半柔性均聚物链聚合所需的步逸度的临界值，发散的性质与空间维数无关.这显然是正确的，因为在极端刚性链极限的情况下，聚合物链是一维物体，其形状像刚性杆。
Linear Viscoelasticity of Semiflexible Polymers with Hydrodynamic Interactions
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度理工学院孟买分校 IITB-莫纳什研究院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（莫纳什大学化学与生物工程系）
