arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1908.01484cond-mat.softcond-mat.dis-nncond-mat.mtrl-sci
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通过孔径分布表征polymer溶液的筛孔尺寸

Characterizing the mesh size of polymer solutions via the pore size distribution

Valerio Sorichetti, Virginie Hugouvieux, Walter Kob

摘要:

为了表征几何网格尺寸$ξ$,我们模拟了一个解决方案的粗粒聚合物的密度范围从稀到浓制度和不同的链长。传统的方法来估计$ξ$依赖于缩放的假设,这给$ξ$只有一个未知的乘法因子,或测量的单体密度波动相关长度$ξ_c$。我们确定$ξ_c$从单体结构因子和径向分布函数,并发现识别$ξ=ξ_c$是不合理的半稀释制度之外。为了更好地表征$ξ$,我们按照两种不同的定义计算孔径分布(PSD),一种是Torquato等人(参考文献1),另一种是Gubbins等人(参考文献2)。我们发现,这两个分布,$\langle r \rangle_T$和$\langle r \rangle_G$的平均值,都显示的行为预测$ξ$的标度理论,并认为,$ξ$可以确定与这些数量之一。这种识别允许将PSD解释为网格尺寸的分布,这是常规方法无法访问的量。最后,我们表明,它是可能的映射系统的硬或重叠的领域,其中Torquato的PSD可以计算分析和准确地再现PSD的解决方案的聚合物溶液。我们给出了一个表达式,允许$\langle r \rangle_T$被估计具有很大的准确性,在semidilute制度只知道的回转半径和密度的聚合物。

英文摘要:

In order to characterize the geometrical mesh size $ξ$, we simulate a solution of coarse-grained polymers with densities ranging from the dilute to the concentrated regime and for different chain lengths. Conventional ways to estimate $ξ$ rely either on scaling assumptions which give $ξ$ only up to an unknown multiplicative factor, or on measurements of the monomer density fluctuation correlation length $ξ_c$. We determine $ξ_c$ from the monomer structure factor and from the radial distribution function, and find that the identification $ξ=ξ_c$ is not justified outside of the semidilute regime. In order to better characterize $ξ$, we compute the pore size distribution (PSD) following two different definitions, one by Torquato et al. (Ref.1) and one by Gubbins et al. (Ref.2). We show that the mean values of the two distributions, $\langle r \rangle_T$ and $\langle r \rangle_G$, both display the behavior predicted for $ξ$ by scaling theory, and argue that $ξ$ can be identified with either one of these quantities. This identification allows to interpret the PSD as the distribution of mesh sizes, a quantity which conventional methods cannot access. Finally, we show that it is possible to map a polymer solution on a system of hard or overlapping spheres, for which Torquato's PSD can be computed analytically and reproduces accurately the PSD of the solution. We give an expression that allows $\langle r \rangle_T$ to be estimated with great accuracy in the semidilute regime by knowing only the radius of gyration and the density of the polymers.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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