[论文解读] On the validity of the Hertzian model: the case of soft colloids

Lorenzo Rovigatti, Nicoletta Gnan+2 more|arXiv (Cornell University)|Aug 14, 2018

Material Dynamics and Properties被引用 4

一句话总结

本研究通过将单颗粒弹性模量与微凝胶中的有效粒子间相互作用直接关联，验证了软胶体的赫兹模型。采用广义模拟方法，表明赫兹近似在接近单位的名义堆积分数下依然成立，泊松比在体积相变附近表现出非单调最小值，证实其在小形变条件下的有效性。

ABSTRACT

Soft responsive colloids are ideal model systems to investigate fundamental problems in statistical mechanics. An important open problem is whether it is possible to establish a direct connection between the elastic properties at the single particle level and the resulting interaction potential in bulk suspensions, particularly in the high-concentration regime. Here we examine this question by focusing on thermoresponsive, colloidal-sized polymer networks, namely microgels, the archetype of soft colloids. Microgels are often assumed to interact through a simple Hertzian potential, a classic model in linear elasticity. By developing an appropriate methodology, that can be generalized to any kind of soft particle, we are able for the first time to calculate all the elastic moduli of microgels across their volume phase transition (VPT). With increasing temperature, we find a monotonous increase of the bulk, Young and shear moduli, whereas the Poisson's ratio exhibits a non-monotonic behaviour characterized by a minimum close to the VPT in agreement with experimental results and theoretical predictions. We also calculate the particle-particle effective interactions and compare it with the Hertzian potential using the estimated moduli. We find that the Hertzian model works well in the regime of small deformations. Carrying out additional bulk simulations we are also able to pinpoint the region of validity of the Hertzian approximation, which is found to hold up to nominal packing fractions close to unity. Our study thus validates a classical model in fundamental physics and paves the way for a systematic assessment of single-particle elastic properties and for a microscopic understanding of their relation with softness and effective interactions.

研究动机与目标

• 建立单颗粒弹性特性与软胶体宏观尺度有效相互作用之间的直接联系。
• 评估赫兹势模型在软物质悬浮液高浓度区域的有效性。
• 量化弹性模量（体变模量、杨氏模量、剪切模量和泊松比）在热响应型微凝胶体积相变过程中的演化行为。
• 确定赫兹模型在形变和堆积分数方面的适用范围。

提出的方法

• 开发了一种广义模拟方法，用于计算微凝胶在整个体积相变过程中所有弹性模量。
• 从热涨落下粒子尺度的机械响应中计算体变模量、杨氏模量、剪切模量和泊松比。
• 利用计算得到的模量，在赫兹框架内构建有效的粒子间相互作用势。
• 进行了额外的宏观模拟，以探究赫兹近似在不同堆积分数下的有效范围。
• 将赫兹势与模拟得到的有效相互作用进行比较，以评估一致性。

实验结果

研究问题

• RQ1 赫兹模型在多大程度上能准确描述密集悬浮液中软胶体粒子之间的有效相互作用？
• RQ2 微凝胶的弹性模量在其体积相变过程中如何演化，泊松比在此行为中起到何种作用？
• RQ3 赫兹近似在形变或堆积分数超过多大范围后会失效？
• RQ4 单颗粒弹性特性能否在软物质系统中可靠地与宏观有效相互作用关联？
• RQ5 温度诱导的微凝胶塌陷如何影响其力学响应和粒子间作用力？

主要发现

• 微凝胶的体变模量、杨氏模量和剪切模量在体积相变过程中随温度单调增加。
• 泊松比表现出非单调行为，在体积相变附近出现明显的最小值，与实验和理论预测一致。
• 在小形变条件下，赫兹势能准确描述有效相互作用，验证了其在软胶体系统中的适用性。
• 赫兹近似在接近单位的名义堆积分数下依然有效，表明其在密集悬浮液中具有广泛适用性。
• 本研究建立了单颗粒弹性与软物质中有效粒子间相互作用之间的直接、定量关联。