从真实聚合物到随机图：缔合聚合物溶液中的渗流阈值
From real polymers to random graphs: percolation thresholds in associative polymer solutions
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中文总结 AI 辅助
研究缔合聚合物溶液中溶胶-凝胶转变阈值，结合分子动力学模拟与随机图模型，发现无坐标随机图恢复平均场极限，随机几何图能定量再现渗流阈值，确立其为描述拓扑转变的预测框架，可从单链构象信息推断凝胶化等。
中文摘要 AI 辅助
溶胶-凝胶转变在软物质和生物系统中普遍存在，但经典的Flory-Stockmayer理论常常无法准确捕捉其阈值，因为忽略了空间组织和环的形成。本文结合分子动力学模拟与随机图和随机几何图模型，以确定拓扑结构和几何形状在可逆缔合聚合物溶液中的各自作用。研究表明，无坐标随机图恢复了平均场Flory-Stockmayer极限，而当根据聚合物构象大小选择检测半径时，随机几何图定量再现了分子动力学模拟中观察到的移动渗流阈值。这种几何映射在广泛的链刚度范围内对具有规则间隔结合位点的线性链仍然有效。在微观层面，确定了在凝胶前阶段形成的初级环是偏离平均场预测的主要来源。接近凝胶点时，模拟和随机几何图得到的簇尺寸统计与三维渗流的普适类一致。这些结果将随机几何图确立为描述可逆缔合聚合物溶液中拓扑转变的最小预测框架，并表明凝胶化和网络形成可直接从单链构象信息推断出来。
英文摘要
Sol-gel transitions are ubiquitous in soft matter and biological systems, yet their thresholds are often poorly captured by classical Flory-Stockmayer theory because spatial organization and loop formation are neglected. Here, we combine molecular dynamics simulations with random graph and random geometric graph models to determine the respective roles of topology and geometry in reversible associative polymer solutions. We show that a coordinate-free random graph recovers the mean-field Flory-Stockmayer limit, whereas a random geometric graph quantitatively reproduces the shifted percolation thresholds observed in molecular dynamics simulations when the detection radius is chosen according to the polymer conformational size. This geometric mapping remains quantitatively valid for linear chains with regularly spaced binding sites over a broad range of chain stiffness. At the microscopic level, we identify primary loops formed already in the pre-gel regime as the dominant source of the deviation from mean-field predictions. Near the gel point, the cluster-size statistics obtained from simulations and random geometric graphs are consistent with the universality class of three-dimensional percolation. These results establish random geometric graphs as a minimal predictive framework for describing topological transitions in reversible associative polymer solutions and show that gelation and network formation can be inferred directly from single-chain conformational information.
