Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS-1), 52425 Jülich, Germany.
Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS-2), 52425 Jülich, Germany.
J Chem Phys. 2023 Jul 21;159(3). doi: 10.1063/5.0150811.
In this work, we compare the single chain dynamic structure factors for five different polymers: polyolefins (PE and PEP), poly-dienes (PB and PI), and a polyether (PEO). For this purpose, we have extended the De Gennes approximation for the dynamic structure factor. We describe the single chain dynamic structure factor in multiplying the coherent scattering functions for local reptation and Rouse motion within the Rouse blob. Important results are (i) the simple De Gennes structure factor S(Q, t)DG approximates within a few Å the outcome for the tube diameter of the more elaborate structure factor (exception PI); (ii) the extended De Gennes structure factor together with the Rouse blob describes the neutron spin echo spectra from the different polymers over the complete momentum transfer range and the full time regime from early Rouse motion to local reptation; and (iii) the representation of the scattering functions could significantly be improved by introducing non-Gaussianity corrections to the Rouse-blob dynamics. (iv) The microscopic tube step length in all cases is significantly larger than the rheological one; further tweaking the relation between tube length and entanglement blob size may indicate a possible trend toward an anisotropic lean tube with a step-length larger than the lateral extension. (v) All considered polymer data coincide after proper (Q, t) scaling to a universal behavior according to the length scale of the tube, while the relevant time scale is the entanglement time τe. (vi) In terms of the packing model, the required number of chains spanning the entanglement volume consistently is about 40% larger than that obtained from rheology.
在这项工作中，我们比较了五种不同聚合物的单链动态结构因子：聚烯烃（PE 和 PEP）、聚二烯（PB 和 PI）和聚醚（PEO）。为此，我们扩展了 De Gennes 近似方法来计算动态结构因子。我们通过将局部蠕动和 Rouse 运动的相干散射函数相乘来描述单链动态结构因子。重要的结果包括：（i）简单的 De Gennes 结构因子 S(Q, t)DG 在几 Å 的范围内近似于更精细结构因子的管直径结果（PI 除外）；（ii）扩展的 De Gennes 结构因子与 Rouse 团块一起描述了不同聚合物的中子自旋回波谱，涵盖了整个动量转移范围和从早期 Rouse 运动到局部蠕动的完整时间范围；（iii）通过对 Rouse 团块动力学引入非高斯修正，可以显著改善散射函数的表示；（iv）在所有情况下，微观管步长都明显大于流变学中的管步长；进一步调整管长与缠结团块大小之间的关系可能表明存在一种具有较大步长的各向异性贫管的趋势，其步长大于横向扩展；（v）所有考虑的聚合物数据在适当的（Q，t）缩放后，根据管的长度尺度，都符合普遍行为，而相关的时间尺度是缠结时间 τe；（vi）根据包装模型，跨越缠结体积所需的链数始终比流变学得到的链数多约 40%。
