时间分辨小角X射线散射中的等吸收点：从光谱类比到胶体凝胶化过程中无模型结构标记

中文摘要 AI 辅助

凝胶化是从流体状态通过分级过程转变为跨越系统的非平衡软固体网络，该过程将局部粒子相互作用与介观聚集和全局连通性联系起来。在时间分辨小角X射线散射（SAXS）中，等吸收点（散射强度不变的散射波矢）在此转变过程中出现，但其物理意义尚不清楚。本文表明，在Ludox胶体盐诱导凝胶化过程中观察到的两个等吸收点$q_1$和$q_2$，反映的是基本结构约束而非两种物质的相互转化。高$q$点$q_2$是由粒子接触距离决定的通用几何标记，低$q$点$q_1$源于Porod不变量守恒，将快速停滞的局部簇与生长的介观网络分开。通过在由这些点定义的倒易空间区域分解Porod不变量，我们定义了一个无量纲参数$\Phi(t/t_g)$，其S形演化提供了一个简单、无模型、尺度分辨的凝胶化指纹。这些结果与$S(q_{\min},t)$和$S(q \rightarrow 0,t)$的联合演化一起，建立了一个定量的无模型框架，将局部结构、全局连通性和散射特征联系起来，阐明了等吸收点在软物质转变中的作用。

英文摘要

Gelation is the transition from a fluid state into a system-spanning, out of equilibrim soft-solid network through a hierarchical process that couples local particle interactions to mesoscopic clustering and global connectivity. In time-resolved small-angle X-ray scattering (SAXS), isosbestic points -- scattering wavevectors where scattering intensity remains invariant -- emerge during this transformation, yet their physical meaning has remained unclear. Here, we show that two isosbestic points, $q_1$ and $q_2$, observed during salt-induced gelation of Ludox colloids, reflect fundamental structural constraints rather than a two-species interconversion. The high-$q$ point $q_2$ is a universal geometric marker, determined by particle contact distances, while the low-$q$ point $q_1$ arises from Porod invariant conservation and separates rapidly arrested local clusters from the growing mesoscopic network. By decomposing the Porod invariant across the reciprocal-space regions defined by these points, we define a dimensionless parameter, $Φ(t/t_g)$, whose sigmoidal evolution provides a simple, model-free, scale-resolved fingerprint of gelation. Together with the combined evolution of $S(q_{\min},t)$ and $S(q \rightarrow 0,t)$, these results establish a quantitative model free framework linking local structuring, global connectivity, and scattering signatures, clarifying the role of isosbestic points in soft-matter transformations.

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