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arXiv 1102.4962cond-mat.soft
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无拓扑约束和动量守恒的稠密polymer溶液和熔体中的无标度质心位移关联:键涨落模型研究

Scale-free center-of-mass displacement correlations in dense polymer solutions and melts without topological constraints and momentum conservation: A bond-fluctuation model study

Joachim P. Wittmer, Patrycia Polińska, Anna Cavallo, Hendrik Meyer, Jean Farago, Albert Johner, Jörg Baschnagel

摘要:

通过Monte Carlo模拟的一个变体的键涨落模型没有拓扑约束,我们研究的质心(COM)动态聚合物熔体在$d=3$尺寸。我们的分析集中在COM位移相关函数$\CN(t) \approx \partial_t^2 \MSDcmN(t)/2$,测量COM均方位移$\MSDcmN(t)$的曲率。我们证明了$\CN(t) \approx -(\RN/\TN)^2 (\rhostar/ρ) \ f(x=t/\TN)$与$N$的链长($16 \le N \le 8192$),$\RN\sim N^{1/2}$的典型链的大小,$\TN\sim N^2$的最长链松弛时间,$ρ$的单体密度,$\rhostar \approx N/\RN^d$的自密度和$f(x)$的普适函数的渐近衰减为$f(x) \sim x^{-ω}$与$ω= (d+2) \times α$其中$α= 1/4$的$x \ll 1$和$α= 1/2$的$x \gg 1$。我们认为,$t \ll \TN$的代数衰减$N \CN(t) \sim - t^{-5/4}$的结果从链的连接性和熔体不可压缩性的相互作用引起的链和子链的相关运动。

英文摘要:

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints we examine the center-of-mass (COM) dynamics of polymer melts in $d=3$ dimensions. Our analysis focuses on the COM displacement correlation function $\CN(t) \approx \partial_t^2 \MSDcmN(t)/2$, measuring the curvature of the COM mean-square displacement $\MSDcmN(t)$. We demonstrate that $\CN(t) \approx -(\RN/\TN)^2 (\rhostar/ρ) \ f(x=t/\TN)$ with $N$ being the chain length ($16 \le N \le 8192$), $\RN\sim N^{1/2}$ the typical chain size, $\TN\sim N^2$ the longest chain relaxation time, $ρ$ the monomer density, $\rhostar \approx N/\RN^d$ the self-density and $f(x)$ a universal function decaying asymptotically as $f(x) \sim x^{-ω}$ with $ω= (d+2) \times α$ where $α= 1/4$ for $x \ll 1$ and $α= 1/2$ for $x \gg 1$. We argue that the algebraic decay $N \CN(t) \sim - t^{-5/4}$ for $t \ll \TN$ results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.

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