No Arabic abstract
The permeability is one of the most fundamental transport properties in soft matter physics, material engineering, and nanofluidics. Here we report by means of Langevin simulations of ideal penetrants in a nanoscale membrane made of a fixed lattice of attractive interaction sites, how the permeability can be massively tuned, even minimized or maximized, by tailoring the potential energy landscape for the diffusing penetrants, depending on the membrane attraction, topology, and density. Supported by limiting scaling theories we demonstrate that the observed non-monotonic behavior and the occurrence of extreme values of the permeability is far from trivial and triggered by a strong anti-correlation and substantial (orders of magnitude) cancellation between penetrant partitioning and diffusivity, especially within dense and highly attractive membranes.
The permeability anisotropy that results from a shear displacement u between the complementary self-affine walls of a rough fracture is investigated. Experiments in which a dyed fluid displaces a transparent one as it is radially injected into a transparent fracture exhibit a clear anisotropy in the presence of shear displacements, and allow us to estimate the ratio of the permeabilities for flows parallel and perpendicular to u. A simple model which accounts for the development of channels perpendicular to u qualitatively explains these results, and predicts a permeability decreasing (increasing) linearly with the variance of the aperture field for flow parallel (perpendicular) to the shear displacement. These predictions are then compared to the results of numerical simulations performed using a lattice-Boltzmann technique and to the anisotropies measured in displacement experiments.
The uptake and sorption of charged molecules by responsive polymer membranes and hydrogels in aqueous solutions is of key importance for the development of soft functional materials. Here we investigate the partitioning of simple monoatomic (Na$^+$, K$^+$, Cs$^+$, Cl$^-$, I$^-$) and one molecular ion (4-nitrophenolate; NP$^-$) within a dense, electroneutral poly($N$-isopropylacrylamide) membrane using explicit-water molecular dynamics simulations. Inside the predominantly hydrophobic environment water distributes in a network of polydisperse water nanoclusters. The average cluster size determines the mean electrostatic self-energy of the simple ions, which preferably reside deeply inside them; we therefore find substantially larger partition ratios $Ksimeq>$10$^{-1}$ than expected from a simple Born picture using a uniform dielectric constant. Despite their irregular shapes we observe that the water clusters possess a universal negative electrostatic potential with respect to their surrounding, as is known for aqueous liquid-vapor interfaces. This potential, which we find concealed in cases of symmetric monoatomic salts, can dramatically impact the transfer free energies of larger charged molecules because of their weak hydration and increased affinity to interfaces. Consequently, and in stark contrast to the simple ions, the molecular ion NP$^-$ can have a partition ratio much larger than unity, $Ksimeq>$10-30 (depending on the cation type) or even $10^3$ in excess of monovalent salt, which explains recent observations of enhanced reaction kinetics of NP$^-$ reduction catalyzed within dense polymer networks. These results also suggest that ionizing a molecule can even enhance the partitioning in a collapsed, rather hydrophobic gel, which strongly challenges the traditional simplistic reasoning.
Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counter-posed coupling of the lips of the slit to twist in the intact regions of the ribbon.
For a wide range of modern soft functional materials the selective transport of sub-nanometer-sized molecules (`penetrants) through a stimuli-responsive polymeric membrane is key to the desired function. In this study, we investigate the diffusion properties of penetrants ranging from non-polar to polar molecules and ions in a matrix of collapsed Poly(N-isopropylacrylamide) (PNIPAM) polymers in water by means of extensive molecular dynamics simulations. We find that the water distributes heterogeneously in fractal-like cluster structures embedded in the nanometer-sized voids of the polymer matrix. The nano-clustered water acts as an important player in the penetrant diffusion, which proceeds via a hopping mechanism through `wet transition states: the penetrants hop from one void to another via transient water channels opened by rare but decisive polymer fluctuations. The diffusivities of the studied penetrants extend over almost five orders of magnitude and thus enable a formulation of an analytical scaling relation with a clear non-Stokesian, exponential dependence of the diffusion coefficient on the penetrants radius for the uncharged penetrants. Charged penetrants (ions) behave differently as they get captured in large isolated water clusters. Finally, we find large energetic activation barriers for hopping, which significantly depend on the hydration state and thereby challenge available transport theories.
In this paper, we study the effects of both the amount of open cell walls and their aperture sizes on solid foams permeability. FEM flow simulations are performed at both pore and macroscopic scales. For foams with fully interconnected pores, we obtain a robust power-law relationship between permeability and membrane aperture size. This result owns to the local pressure drop mechanism through the membrane aperture as described by Sampson for fluid flow through a circular orifice in a thin plate. Based on this local law, pore-network simulation of simple flow is used and is shown to reproduce successfully FEM results. This low computational cost method allowed to study in detail the effects of the open wall amount on percolation, percolating porosity and permeability. A model of effective permeability is proposed and shows ability to reproduce the results of network simulations. Finally, an experimental validation of the theoretical model on well controlled solid foam is presented.