[论文解读] Gelation as condensation frustrated by hydrodynamics and mechanical isostaticity

Hideyo Tsurusawa, Mathieu Leocmach+2 more|arXiv (Cornell University)|Apr 12, 2018

Material Dynamics and Properties参考文献 69被引用 23

一句话总结

本研究揭示，胶体凝胶化受流体动力学约束和力学静不定性控制，而不仅仅是玻璃化转变。通过单粒子分辨的共聚焦显微镜，作者发现由于不可压缩性，网络在早期即形成，但机械稳定性仅在局部静不定性达成后才出现，表明静不定性是承载载荷凝胶形成的必要条件。

ABSTRACT

Colloidal gels have unique mechanical and transport properties that stem from their bicontinous nature, in which a colloidal network is intertwined with a viscous solvent, and have found numerous applications in foods, cosmetics, construction materials, and for medical applications, such as cartilage replacements. So far, our understanding of the process of colloidal gelation is limited to long-time dynamical effects, where gelation is viewed as a phase separation process interrupted by the glass transition. However, this picture neglects two important effects: the influence of hydrodynamic interactions, and the emergence of mechanical stability. With confocal microscopy experiments, here we successfully follow the entire process of gelation with a single-particle resolution, yielding time-resolved measures of internal stress and viscoelasticity from the very beginning of the aggregation process. First, we demonstrate that the incompressible nature of a liquid component constrains the initial stage of phase separation, assisting the formation of a percolated network. Then we show that this network is not mechanically stable and undergoes rearrangements driven by self-generated internal stress. Finally, we show that mechanical metastability is reached only after percolation of locally isostatic environments, proving isostaticity a necessary condition for the stability and load bearing ability of gels rather than the glass transition. Our work reveals the crucial roles of momentum conservation in gelation in addition to the conventional purely out-of-equilibrium thermodynamic picture.

研究动机与目标

• 解决传统玻璃化转变图景之外胶体凝胶化的根本机制。
• 研究流体动力相互作用和机械稳定性在凝胶化过程中网络形成中的作用。
• 确定机械静不定性（每个粒子六个邻近粒子）是否为凝胶中机械稳定性的必要条件。
• 以单粒子分辨实验获取整个凝胶化过程中内部应力、黏弹性及结构演化的数据。
• 阐明凝胶中超扩散老化和机械亚稳态的起源，挑战纯粹热力学或动力学解释。

提出的方法

• 采用高时空分辨率的共聚焦显微镜，全程追踪单个胶体粒子的运动。
• 利用从阿伦尼乌斯方程推导出的力依赖性结合速率测量键断裂速率，其中力通过速率对力的对数依赖关系推断。
• 使用公式 $\Sigma = 2\mathcal{F}/(\pi\sigma\delta)$ 计算内部应力，其中 $\delta = 2R_g$。
• 采用广义斯托克斯-爱因斯坦关系进行双粒子微流变测量，提取复模量 $G(\omega,t)$，并通过频率无关的损耗正切确定凝胶点。
• 使用斯坦哈特键序参数 $q_2(i)$ 检测局部二重对称性，并量化粒子层面的拉伸和网络各向异性。
• 采用汉宁窗进行傅里叶空间分析，计算结构因子 $S(q)$，将主波矢量 $<q>$ 定义为低-$q$ 范围内 $qS(q)$ 与 $S(q)$ 的积分之比。

Figure 1: Reservoir cell. (a) Sketch of our experimental setup. The observation cell contains initially colloids, polymer and no salt. (b) Confocal slice of a gel formed in situ by our method ( $\phi=25.5~{}\%$ , $c_{p}=1.4$ mg/g), 1 hour after gelation. (c) Idem for a gel at the same state point fo

实验结果

研究问题

• RQ1 流体动力学相互作用如何影响胶体凝胶化初期的相分离和网络形成？
• RQ2 为何胶体凝胶形成连续网络而非孤立团簇，与经典旋节线分解的预测相反？
• RQ3 每个粒子六个邻近粒子构成的机械静不定性在凝胶机械稳定性中起何作用？
• RQ4 玻璃化转变是否足以解释凝胶中观察到的动力学冻结和机械稳定性，还是需要额外的机械约束？
• RQ5 内部应力如何随凝胶化过程演化，机械亚稳态的实现相对于渗透和静不定性发生在何时？

主要发现

• 溶剂的不可压缩性抑制了向孤立团簇的相分离，从一开始就促进了连续网络的形成。
• 初始网络在机械上不稳定，即使在完全渗透之前，也因自生应力而发生内部重排。
• 只有在局部静不定环境渗透之后，机械亚稳态才得以实现，证实了静不定性是承载载荷能力的必要条件。
• 凝胶点（由频率无关的损耗正切定义）出现在静不定性渗透之后不久，而非玻璃化转变之后。
• 在聚集的早期阶段，内部应力显著增加，键断裂速率表现出与力相关的特性，与能垒跨越一致。
• 静不定性的出现与黏弹性和机械稳定性的出现密切相关，表明凝胶刚性具有直接的机械起源，而不仅仅是动力学冻结的结果。

Figure 2: Snapshots from the entire gelation process reconstructed via particle-tracking of a typical sample close to the cluster-gel line ( $\phi=7.5~{}\%$ , $c_{p}=1$ mg/g) using the salt-injection protocol. Particles are colored according to the size of the cluster they belong to, going from blue