热响应微凝胶非平衡溶胀动力学的溶剂通量理论
A solvent-flux theory for nonequilibrium swelling dynamics of thermoresponsive microgels
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中文总结 AI 辅助
本文建立溶剂通量理论描述热响应微凝胶非平衡溶胀动力学，可预测pNIPAM微凝胶非对称溶胀路径、类滞后环及尺寸涨落，关联其溶剂输运与非平衡行为。
中文摘要 AI 辅助
热响应微凝胶会随温度改变溶剂品质而发生大的可逆尺寸变化。预测其非平衡溶胀与退溶胀动力学颇具挑战，因为在大体积变化过程中，聚合物体积分数、力学响应及溶剂输运均会发生演化。本文针对球形微凝胶的动力学建立了溶剂通量理论：半径变化速率由颗粒边界两侧的渗透压不平衡驱动，同时受到水通过聚合物网络输运的阻力，由此得到全局溶胀坐标的非线性方程，以及与状态和温度相关的溶胀扩散系数$D_{\text{SW}}(\boldsymbol{\rho},T)$。在线性响应区，该理论还原了Tanaka-Fillmore指数弛豫与标度关系$\tau_{\text{SW}}\backsim R_{\text{eq}}^2\boldsymbol{\rho}/K_{\text{eq}}$，同时给出了聚合物-溶剂摩擦系数$\boldsymbol{\rho}$的微观解释。超出该极限后，模型保留二次方尺寸标度，同时考虑状态依赖的输运与力学特性。对于pNIPAM微凝胶，它预测了非对称路径：在相同温度区间内，退溶胀速度快于溶胀。有限热化过程会产生从微凝胶控制到热化控制的转变，其中表观弛豫时间随外部热化时间线性增长，且在半径-温度平面出现类滞后环。基于Smoluchowski方程的随机扩展预测了坍缩过程中半径分布的瞬态展宽，在体积转变区域波动最大。该理论将响应微凝胶中的溶剂输运、非线性溶胀动力学、热化效应与非平衡尺寸涨落关联起来。
英文摘要
Thermoresponsive microgels undergo large reversible size changes as temperature alters solvent quality. Predicting their nonequilibrium swelling and deswelling kinetics is challenging because polymer volume fraction, mechanical response, and solvent transport evolve during large volume changes. Here we develop a solvent-flux theory for the dynamics of a spherical microgel. The radius-change rate is driven by the osmotic-pressure imbalance across the particle boundary and resisted by water transport through the polymer network, yielding a nonlinear equation for the global swelling coordinate and a state- and temperature-dependent swelling diffusion coefficient, $D_{\mathrm{SW}}(ϕ,T)$. In the linear-response regime, the theory recovers Tanaka--Fillmore exponential relaxation and the scaling $τ_\mathrm{SW}\sim R_{\mathrm{eq}}^2γ/K_{\mathrm{eq}}$, while providing a microscopic interpretation of the polymer--solvent friction coefficient $γ$. Beyond this limit, the model retains quadratic size scaling while accounting for state-dependent transport and mechanics. For pNIPAM microgels, it predicts asymmetric pathways, with deswelling faster than swelling over the same temperature interval. Finite thermalization produces a crossover from a microgel-controlled to a thermalization-controlled regime, in which the apparent relaxation time grows linearly with the external thermalization time and hysteresis-like loops emerge in the radius--temperature plane. A stochastic extension based on the Smoluchowski equation predicts transient broadening of the radius distribution during collapse, with maximal fluctuations in the volume-transition region. The theory links solvent transport, nonlinear swelling dynamics, thermalization effects, and nonequilibrium size fluctuations in responsive microgels.
