In order to determine in polymeric systems 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. We determine the monomer density fluctuation correlation length ξ_c from the monomer structure factor as well as the radial distribution function, showing 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. and one by Gubbins et al. We find that the mean values of the two distributions, ⟨r⟩_T and ⟨r⟩_G, 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 ⟨r⟩_T to be estimated with high accuracy in the semidilute regime by knowing only the radius of gyration and the density of the polymers.

中文翻译：

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通过孔径分布确定聚合物溶液的筛孔尺寸

为了确定聚合物体系中的几何网格尺寸ξ，我们模拟了一种粗粒聚合物的溶液，其密度范围从稀到浓，并且对于不同的链长。我们确定单体浓度波动相关长度ξ _Ç由单体结构因子以及径向分布函数，显示出识别ξ=ξ _Ç不是亚浓制度的正当外部。为了更好地描述ξ，我们根据两种不同的定义来计算孔径分布（PSD），一种是Torquato等人的定义。和Gubbins等人的 我们发现，两个分布的平均值，⟨ [R ⟩ _ŧ和⟨ [R ⟩ _{g ^}，显示出通过缩放理论为ξ预测的行为，并认为ξ可以用这些量之一来识别。这种识别可以将PSD解释为网格大小的分布，而网格大小是常规方法无法访问的。最后，我们表明可以在坚硬或重叠的球体系统上绘制聚合物溶液，可以通过分析计算Torquato的PSD并准确地再现溶液的PSD。我们给允许⟨表达式ř ⟩ _Ť通过知道仅回转半径和聚合物的密度以与在亚浓政权高精度估计。