Tuning the permeability of regular polymeric networks by the cross-link ratio

Abstract

The amount of cross-linking in the design of polymer materials is a key parameter for the modification of numerous physical properties, importantly, the permeability to molecular solutes. We consider networks with a diamond-like architecture and different cross-link ratios, concurring with a wide range of the polymer volume fraction. We particularly focus on the effect and the competition of two independent component-specific solute–polymer interactions, i.e., we distinguish between chain-monomers and cross-linkers, which individually act on the solutes and are altered to cover attractive and repulsive regimes. For this purpose, we employ coarse-grained, Langevin computer simulations to study how the cross-link ratio of polymer networks controls the solute partitioning, diffusion, and permeability. We observe different qualitative behaviors as a function of the cross-link ratio and interaction strengths. The permeability can be tuned ranging over two orders of magnitude relative to the reference bulk permeability. Finally, we provide scaling theories for the partitioning and diffusion that explicitly account for the component-specific interactions as well as the cross-link ratio and the polymer volume fraction. These are in overall good agreement with the simulation results and grant insight into the underlying physics, rationalizing how the cross-link ratio can be exploited to tune the solute permeability of polymeric networks.

Permeability of Polymer Membranes beyond Linear Response

“…In our previous work, we have obtained G ( z ) from simulations in equilibrium via where c eq ( z ) and are the penetrant’s equilibrium concentration profile and the bulk concentration, respectively. − We observed that G ( z ) can be conveniently mapped on a piecewise step function given in eq . The mean plateau value of G ( z ) in the membrane, Δ G , defines our partition ratio (see Table ) via …”

“…The potential field G ( z ) constitutes the membrane as a finite energy barrier (or attractive well) in the system and originates from the microscopic interactions between penetrants and the membrane. We consider G ( z ) as an average potential field, which can be obtained from molecular simulations by Boltzmann-inverting the average equilibrium partitioning profile. − The equilibrium diffusivity field D ( z ) also depends on the membrane and penetrant properties. Our system comprises two local diffusivities, D ( z ) = D 0 in the bulk and D ( z ) = D in in the membrane (see eq ).…”

“…Our system comprises two local diffusivities, D ( z ) = D 0 in the bulk and D ( z ) = D in in the membrane (see eq ). The latter depends on the penetrant–membrane interactions and membrane density. − The corresponding drift–diffusion scenario is depicted in Figure (d). Since we compare theoretical results with implicit-solvent computer simulations where no explicit solvent flow and drag are included (i.e., no hydrodynamics) and permeation is dominated by interaction potentials, the Smoluchowski equation given in eq is the appropriate coarse-grained transport equation.…”

Transport in polymer membranes beyond linear response: Controlling permselectivity by the driving force

“…Thus the membrane center of mass was tightly bound to the center of the simulation box (r center ), with the spring constant k com = 100 k B T /σ per membrane particles. The membrane thickness d(f ) is computed based on the full width at half maximum [99], which varies slightly with the force only for large P eq [see Fig. 3(c)], otherwise it is nearly constant (see Table I for the equilibrium d).…”

Coarse-Grained Simulations of Solute Diffusion in Crosslinked Flexible Hydrogels

“…The bead-spring model of the polymeric network has also been used to simulate solute diffusion in gels. This coarse-grained model, employed to study gel swelling and solute partitioning from the early 2000s, − allows us to explicitly consider crosslinked flexible polymer chains. ,, The model is particularly appropriate to explicitly consider solute–monomer and solute–crosslinker interactions or to simulate tightly meshed networks. ,− In addition, polydispersity or entanglements can also be implemented. , …”