[论文解读] Colloidal Hard Spheres: Triumphs, Challenges and Mysteries

C. Patrick Royall, Patrick Charbonneau+5 more|arXiv (Cornell University)|May 3, 2023

Material Dynamics and Properties被引用 14

一句话总结

对胶体硬球作为模型系统的综合综述，涵盖平衡与非平衡现象、实验实现、模拟、理论以及未解决的挑战。

ABSTRACT

The simplicity of hard spheres as a model system is deceptive. Although the particles interact solely through volume exclusion, that nevertheless suffices for a wealth of static and dynamical phenomena to emerge, making the model an important target for achieving a comprehensive understanding of matter. In addition, while real colloidal suspensions are typically governed by complex interactions, Pusey and Van Megen [Nature 320 340--342 (1986)] demonstrated that suitably tuned suspensions result in hard-sphere like behavior, thus bringing a valuable experimental complement to the celebrated theoretical model. Colloidal hard spheres are thus both a material in their own right and a platform upon which phenomena exhibited by simple materials can be explored in great detail. These various purposes enable a particular synergy between experiment, theory and computer simulation. Here we review the extensive body of work on hard spheres, ranging from their equilibrium properties such as phase behavior, interfaces and confinement to some of the non--equilibrium phenomena they exhibit such as sedimentation, glass formation and nucleation.

研究动机与目标

• 解释为什么硬-球胶体作为简单液体的基准模型及其熵驱动的相行为。
• 评估真实胶体系统通过合成、稳定化以及映射到硬球参数来近似硬球行为的方式。
• 调查实验、计算和理论方法在硬球系统中的应用，并确定关键成就与突出挑战。
• 突出跨越相、界面、限制、混合物与非平衡现象的实验观察和理论发展。

提出的方法

• 合成并表征硬球样的胶体，特别是立体稳定化的 PMMA，以近似硬球行为。
• 将真实胶体相互作用映射到有效硬球模型，并确定有效直径与体积分数。
• 回顾用于测量结构与动力学的实验技术，包括光散射和共聚焦显微镜。
• 总结用于硬球系统的计算方法，包括蒙特卡罗、事件驱动、布朗动力学以及包含流体动力的模拟。
• 讨论铸就理论框架，如积分方程理论、单元理论以及用于硬球的经典密度泛函理论。

Figure 2: The colloidal hard spheres observed by Pusey and Van Megen are depicted (a) immediately, (b) one, and (c) four days after mixing. After four days, the system is presumed to have completed its phase separation. Volume fraction increases from left to right, with effective values (determined

实验结果

研究问题

• RQ1 真实胶体系统在合成、稳定化和实验条件下与理想硬球行为有多接近？
• RQ2 已在实验中观察到的硬球的平衡相行为与动力学现象有哪些，与理论和模拟的一致性如何？
• RQ3 将软或带电胶体映射到硬球模型的主要挑战是什么，如何确定有效直径？
• RQ4 硬球系统在玻璃形成、成核和限制方面还有哪些待解的问题？
• RQ5 如何整合实验、模拟和理论以推进对硬球胶体的理解？

主要发现

• 硬球系统的熵驱动的流体-晶体转变在胶体中被实验上证实。
• 胶体实验使结构和动力学的直接成像成为可能，包括高级结构发展。
• 硬球系统中的界面自由能和晶粒边界模型了基本材料失效机制。
• 二元混合、限制与非平衡现象揭示丰富的行为，已在实验和计算上进行探索。
• 硬球玻璃、阻塞与成核现象是理解这些系统的相变与老化的核心。

Figure 3: Equation of state and phase diagram of hard spheres. The pressure $\beta P\sigma^{3}$ as a function of volume fraction $\phi$ (solid blue) is (approximately) given by the Carnahan-Starling expression Carnahan and Starling ( 1969 ) for the fluid and by that of Hall Hall ( 1972 ) for the cry