We show that the average length ⟨ L ⟩ of threadlike micelles in surfactant solutions predicted by fitting results of a mesoscopic simulation, the “pointer algorithm,” to experimental G′(ω), G″(ω) data, is longer than, and more accurate than, that from a scaling law that equates ⟨ L ⟩ / l e to the modulus ratio G 0 / G m i n ′ ′. Here, G0 is the plateau modulus, G m i n ′ ′ is obtained at the local minimum in G″, and l e is the entanglement length. The accuracy of the pointer algorithm is supported by the agreement of its predictions with results from a recent application of the slip-spring simulation method to threadlike micelles. Improved fits of the pointer algorithm to the slip-spring results are obtained for weakly entangled micelles (with an average number of entanglements of Z < 15) if the full spectrum of Rouse modes is included in the description rather than just the high-frequency modes included in an earlier version. For sodium laureth-1 sulfate and cocamidopropyl betaine in NaCl solutions, we find scaling relations for micelle length, the plateau modulus, and the persistence length that are in rough agreement with the predictions of mean field theory and with the modified scaling relation in which ⟨ L ⟩ / l e is raised to the 0.82 power, rather than unity, that we recommend as an improvement to the original scaling law.

中文翻译：

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从流变测定法确定线状胶束长度

我们表明，表面活性剂溶液中线状胶束的平均长度 ⟨ L ⟩ 通过细观模拟的拟合结果预测，“指针算法”，实验 G'(ω)，G″(ω) 数据，长于，和比根据缩放定律得出的结果更准确，该定律将 ⟨ L ⟩ / le 等同于模量比 G 0 / G min ′ ′。这里，G0 是平台模量，G min ' ' 是在 G'' 中的局部最小值处获得的，le 是纠缠长度。指针算法的准确性得到了其预测与最近将滑动弹簧模拟方法应用于线状胶束的结果一致的支持。对于弱纠缠胶束（平均纠缠数 Z < 15) 如果描述中包含了 Rouse 模式的完整频谱，而不仅仅是早期版本中包含的高频模式。对于 NaCl 溶液中的 laureth-1 硫酸钠和椰油酰胺丙基甜菜碱，我们发现胶束长度、平台模量和持续长度的标度关系与平均场理论的预测和修正的标度关系大体一致，其中 ⟨ L ⟩ / le 被提升到 0.82 次幂，而不是我们推荐的对原始缩放定律的改进。