The permeability of a membrane to solute penetrants is well defined on the linear response level simply as the ratio of penetrants’ flux and concentration gradient at the membrane boundary layers. However, nonlinearities emerge in the flux–force relation j(f) for large driving forces f, in which the definition of permeability becomes ambiguous. Here, we study nonequilibrium membrane permeation orchestrated by a generic driving force using penetrant- and monomer-resolved computer simulations of transport in a polymer network, supported by exact solutions of the Smoluchowski (drift–diffusion) equation in the stationary state. In the simulations, we consider the transport across a finite polymer membrane immersed in a reservoir of penetrants, addressing one- and two-component penetrant systems. We calculate the f-dependent inhomogeneous steady-state density profiles, boundary layer concentrations, and fluxes of the penetrants. The Smoluchowski approach, using solely coarse-grained equilibrium partitioning and diffusion profiles as input, exhibits remarkable qualitative agreement with our nonequilibrium simulations, which serves for rationalization of the observations. We discuss possible definitions of nonequilibrium, f-dependent permeability, distinguishing between “system” and “membrane” permeabilities. In particular, we introduce the concept of differential permeability as a response to f. The latter turns out to be a highly nonmonotonic function of f for low-permeable systems, demonstrating how a differential permselectivity is substantially tunable by the driving force beyond linear response.

中文翻译：

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超越线性响应的聚合物膜的渗透性

膜对溶质渗透剂的渗透性在线性响应水平上很好地定义为渗透剂在膜边界层的通量和浓度梯度的比率。然而，对于大驱动力f，通量-力关系j ( f ) 中出现非线性，其中渗透率的定义变得模棱两可。在这里，我们研究了由通用驱动力协调的非平衡膜渗透，使用聚合物网络中传输的渗透剂和单体分辨计算机模拟，得到静止状态下 Smoluchowski（漂移-扩散）方程的精确解的支持。在模拟中，我们考虑了穿过浸入渗透剂库中的有限聚合物膜的传输，解决了单组分和双组分渗透剂系统的问题。我们计算f- 依赖的非均匀稳态密度分布、边界层浓度和渗透剂通量。Smoluchowski 方法仅使用粗粒度平衡分配和扩散曲线作为输入，与我们的非平衡模拟表现出显着的定性一致性，这有助于使观察结果合理化。我们讨论了非平衡的可能定义，f依赖性渗透率，区分“系统”和“膜”渗透率。特别是，我们引入了微分渗透率的概念作为对f的响应。后者原来是f的高度非单调函数对于低渗透系统，展示了差分渗透选择性如何通过超出线性响应的驱动力进行基本调节。