A critical comparison of equilibrium, non-equilibrium and boundary-driven molecular dynamics techniques for studying transport in microporous materials

Non-equilibrium molecular dynamics of steady-state fluid transport through a 2D membrane driven by a concentration gradient

We use a novel non-equilibrium algorithm to simulate steady-state fluid transport through a two-dimensional (2D) membrane due to a concentration gradient by molecular dynamics (MD) for the first time. We confirm that, as required by the Onsager reciprocal relations in the linear-response regime, the solution flux obtained using this algorithm agrees with the excess solute flux obtained from an established non-equilibrium MD algorithm for pressure-driven flow. In addition, we show that the concentration-gradient-driven solution flux in this regime is quantified far more efficiently by explicitly applying a transmembrane concentration difference using our algorithm than by applying Onsager reciprocity to pressure-driven flow. The simulated fluid fluxes are captured with reasonable quantitative accuracy by our previously derived continuum theory of concentration-gradient-driven fluid transport through a 2D membrane [D. J. Rankin, L. Bocquet, and D. M. Huang, J. Chem. Phys. 151, 044705 (2019)] for a wide range of solution and membrane parameters, even though the simulated pore sizes are only several times the size of the fluid particles. The simulations deviate from the theory for strong solute-membrane interactions relative to thermal energy, for which the theoretical approximations breakdown. Our findings will be beneficial for a molecular-level understanding of fluid transport driven by concentration gradients through membranes made from 2D materials, which have diverse applications in energy harvesting, molecular separations, and biosensing.

Non-Equilibrium Modeling of Concentration-Driven processes with Constant Chemical Potential Molecular Dynamics Simulations

ConspectusConcentration-driven processes in solution, i.e., phenomena that are sustained by persistent concentration gradients, such as crystallization and surface adsorption, are fundamental chemical processes. Understanding such phenomena is crucial for countless applications, from pharmaceuticals to biotechnology. Molecular dynamics (MD), both in- and out-of-equilibrium, plays an essential role in the current understanding of concentration-driven processes. Computational costs, however, impose drastic limitations on the accessible scale of simulated systems, hampering the effective study of such phenomena. In particular, due to these size limitations, closed system MD of concentration-driven processes is affected by solution depletion/enrichment that unavoidably impacts the dynamics of the chemical phenomena under study. As a notable example, in simulations of crystallization from solution, the transfer of monomers between the liquid and crystal phases results in a gradual depletion/enrichment of solution concentration, altering the driving force for phase transition. In contrast, this effect is negligible in experiments, given the macroscopic size of the solution volume. Because of these limitations, accurate MD characterization of concentration-driven phenomena has proven to be a long-standing simulation challenge. While disparate equilibrium and nonequilibrium simulation strategies have been proposed to address the study of such processes, the methodologies are in continuous development.In this context, a novel simulation technique named constant chemical potential molecular dynamics (CμMD) was recently proposed. CμMD employs properly designed, concentration-dependent external forces that regulate the flux of solute species between selected subregions of the simulation volume. This enables simulations of systems under a constant chemical drive in an efficient and straightforward way. The CμMD scheme was originally applied to the case of crystal growth from solution and then extended to the simulation of various physicochemical processes, resulting in new variants of the method. This Account illustrates the CμMD method and the key advances enabled by it in the framework of in silico chemistry. We review results obtained in crystallization studies, where CμMD allows growth rate calculations and equilibrium shape predictions, and in adsorption studies, where adsorption thermodynamics on porous or solid surfaces was correctly characterized via CμMD. Furthermore, we will discuss the application of CμMD variants to simulate permeation through porous materials, solution separation, and nucleation upon fixed concentration gradients. While presenting the numerous applications of the method, we provide an original and comprehensive assessment of concentration-driven simulations using CμMD. To this end, we also shed light on the theoretical and technical foundations of CμMD, underlining the novelty and specificity of the method with respect to existing techniques while stressing its current limitations. Overall, the application of CμMD to a diverse range of fields provides new insight into many physicochemical processes, the in silico study of which has been hitherto limited by finite-size effects. In this context, CμMD stands out as a general-purpose method that promises to be an invaluable simulation tool for studying molecular-scale concentration-driven phenomena.

Mass Transfer through Vapor-Liquid Interfaces Studied by Non-Stationary Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are highly attractive for studying the influence of interfacial effects, such as the enrichment of components, on the mass transfer through the interface. In a recent work, we have presented a steady-state MD simulation method for investigating this phenomenon and tested it using model mixtures with and without interfacial enrichment. The present study extends this work by introducing a non-stationary MD simulation method. A rectangular simulation box that contains a mixture of two components 1 + 2 with a vapor phase in the middle and two liquid phases on both sides is used. Starting from a vapor-liquid equilibrium state, a non-stationary molar flux of component 2 is induced by inserting particles of component 2 into the center of the vapor phase in a pulse-like manner. During the isothermal relaxation process, particles of component 2 pass through the vapor phase, cross the vapor-liquid interface, and enter the liquid phase. The system thereby relaxes into a new vapor-liquid equilibrium state. During the relaxation process, spatially resolved responses for the component densities, fluxes, and pressure are sampled. To reduce the noise and provide measures for the uncertainty of the observables, a set of replicas of simulations is carried out. The new simulation method was applied to study mass transfer in two binary Lennard-Jones mixtures: one that exhibits a strong enrichment of the low-boiling component 2 at the vapor-liquid interface and one that shows no enrichment. Even though both mixtures have similar transport coefficients in the bulk phases, the results for mass transfer differ significantly, indicating that the interfacial enrichment influences the mass transfer.

High Efficient CO2 Separation at High Pressure by Grain-Boundary-Controlled CHA Zeolite Membrane Investigated by Non-Equilibrium Molecular Dynamics

The CO₂ permeability and selectivity of CHA-type zeolite membranes in the separation of a CO₂/CH₄ mixture gas at high pressure were evaluated using non-equilibrium molecular dynamics (NEMD). It was found that in a perfectly crystalline, defect-free CHA membrane, the adsorption of CH₄, which diffuses slowly in the pores, hinders CO₂ permeation. Therefore, an increase in the amount of CH₄ adsorbed at high pressure decreases the CO₂ permeability and significantly reduces the CO₂ selectivity of the CHA membrane. CHA membranes with grain boundaries parallel to the permeation direction were found to show higher CO₂ selectivity than perfectly crystalline CHA membranes at high pressure, as the blocking effect of CH₄ on CO₂ permeation occurring within the grain boundary is not significant. This paper is the first to show that the CO₂ permeability of CHA membranes with controlled grain boundaries can exceed the intrinsic performance of fully crystalline zeolite membranes at high pressure.

Numerical Test of the Onsager Relations in a Driven System

The Onsager reciprocity relations were formulated in the context of irreversible thermodynamics, but they are based on assumptions that have a wider applicability. Here, we present simulations testing the Onsager relations between surface-coupled diffusive and bulk fluxes in a system prepared in a nonequilibrium steady state. The system consists of a mixture of two identical species maintained at different temperatures inside a channel. In order to tune the friction of the two species with the walls independently, while keeping the particle-wall interaction potentials the same, we allow the kinematics of particle-wall collisions to be different: "bounce-back" (B) or "specular" (S). In the BB case, diffusio-capillary transport can only take place if the two species have different temperatures. We find that the Onsager reciprocity relations are obeyed in the linear regime, even in the BB case where all fluxes are the result of perturbing the system from a nonequilibrium steady state in a way that does not satisfy time-reversal symmetry. Our Letter provides a direct, numerical illustration of the validity of the Onsager relations outside their original range of application, and suggests their relevance for transport in driven or active systems.

Flow Reduction in Pore Networks of Packed Silica Nanoparticles: Insights from Mesoscopic Fluid Models

A modified many-body dissipative particle dynamics (mDPD) model is rigorously calibrated to achieve realistic fluid-fluid/solid interphase properties and applied for mesoscale flow simulations to elucidate the transport mechanisms of heptane liquid and water, respectively, through pore networks formed by packed silica nanoparticles with a uniform diameter of 30 nm. Two million CPU core hours were used to complete the simulation studies. Results show reduction of permeability by 54-64% in heptane flow and by 88-91% in water flow, respectively, compared to the Kozeny-Carman equation. In these nanopores, a large portion of the fluids are in the near-wall regions and thus not mobile due to the confinement effect, resulting in reduced hydraulic conductivity. Moreover, intense oscillations in the calculated flow velocities also indicate the confinement effect that contests the external driven force to flow. The generic form of Darcy's law is considered valid for flow through homogeneous nanopore networks, while permeability depends collectively on pore size and surface wettability. This fluid-permeability dependency is unique to flow in nanopores. In addition, potential dependence of permeability on pore connectivity is observed when the porosity remains the same in different core specimens.

Use of Boundary-Driven Nonequilibrium Molecular Dynamics for Determining Transport Diffusivities of Multicomponent Mixtures in Nanoporous Materials

The boundary-driven molecular modeling strategy to evaluate mass transport coefficients of fluids in nanoconfined media is revisited and expanded to multicomponent mixtures. The method requires setting up a simulation with bulk fluid reservoirs upstream and downstream of a porous media. A fluid flow is induced by applying an external force at the periodic boundary between the upstream and downstream reservoirs. The relationship between the resulting flow and the density gradient of the adsorbed fluid at the entrance/exit of the porous media provides for a direct path for the calculation of the transport diffusivities. It is shown how the transport diffusivities found this way relate to the collective, Onsager, and self-diffusion coefficients, typically used in other contexts to describe fluid transport in porous media. Examples are provided by calculating the diffusion coefficients of a Lennard-Jones (LJ) fluid and mixtures of differently sized LJ particles in slit pores, a realistic model of methane in carbon-based slit pores, and binary mixtures of methane with hypothetical counterparts having different attractions to the solid. The method is seen to be robust and particularly suited for the study of study of transport of dense fluids and liquids in nanoconfined media.

Cassie-Baxter and Wenzel States and the Effect of Interfaces on Transport Properties across Membranes

Mass transfer across a liquid-repelling gas permeable membrane is influenced by the state(s) of the liquid-vapor interface(s) on the surface of the membrane, the pore geometry, and the solid-fluid interactions inside the membrane. By tuning the different local contributions, it is possible to enhance the temperature difference-driven mass flux across the membrane for a constant driving force. Non-equilibrium molecular dynamics simulations were used to simulate a temperature difference-driven mass flux through a gas permeable membrane with the evaporating liquid on one side and the condensing liquid on the other. Both sides were simulated for Wenzel- and Cassie-Baxter-like states. The interaction between the fluid and the solid inside the gas permeable membrane varied between the wetting angles of θ = 125° and θ = 103°. For a constant driving force, the Cassie-Baxter state led to an increased mass flux of almost 40% in comparison to the Wenzel state (given a small pore resistance). This difference was caused by an insufficient supply of vapor particles at the pore entrance in the Wenzel state. The difference between the Wenzel and Cassie-Baxter states decreased with increasing resistance of the pore. The condensing liquid-vapor interface area contributed in the same manner to the overall transport resistance as the evaporating liquid-vapor interface area. A higher repulsion between the fluid and the solid inside the membrane decreased the overall resistance.

Recent advances in simulating gas permeation through MOF membranes

In the last two decades, metal organic frameworks (MOFs) have gained increasing attention in membrane-based gas separations due to their tunable structural properties. Computational methods play a critical role in providing molecular-level information about the membrane properties and identifying the most promising MOF membranes for various gas separations. In this review, we discuss the current state-of-the-art in molecular modeling methods to simulate gas permeation through MOF membranes and review the recent advancements. We finally address current opportunities and challenges of simulating gas permeation through MOF membranes to guide the development of high-performance MOF membranes in the future.

Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane

We have investigated the transport of fluid through a vapor-gap membrane. The transport due to a membrane temperature difference was investigated under isobaric as well as non-isobaric conditions. Such a concept is relevant for water cleaning and power production purposes. A coarse-grained water model was used for modelling transport through pores of different diameters and lengths. The wall-fluid interactions were set so as to mimic hydrophobic interactions between water and membrane. The mass transport through the membrane scaled linearly with the applied temperature difference. Soret equilibria were obtained when the thermo-osmotic pressure was 18 bar K-1. The state of the Soret equilibrium did not depend on the pore size or pore length as expected. We show that the Soret equilibrium cannot be sustained by a gradient in vapor pressure. The fluxes of heat and mass were used to compute the total resistances to the transport of heat and mass.

Studying polymer diffusiophoresis with non-equilibrium molecular dynamics

We report a numerical study of the diffusiophoresis of short polymers using non-equilibrium molecular dynamics simulations. More precisely, we consider polymer chains in a fluid containing a solute that has a concentration gradient and examine the variation of the induced diffusiophoretic velocity of the polymer chains as the interaction between the monomer and the solute is varied. We find that there is a non-monotonic relation between the diffusiophoretic mobility and the strength of the monomer-solute interaction. In addition, we find a weak dependence of the mobility on the length of the polymer chain, which shows clear difference from the diffusiophoresis of a solid particle. Interestingly, the hydrodynamic flow through the polymer is much less screened than for pressure driven flows.

Simulation of H2/CH4 mixture permeation through MOF membranes using non-equilibrium molecular dynamics

Grand canonical Monte Carlo (GCMC) simulations are widely used with equilibrium molecular dynamics (EMD) to predict gas adsorption and diffusion in single-crystals of metal-organic frameworks (MOFs). Adsorption and diffusion data obtained from these simulations are then combined to predict gas permeabilities and selectivities of MOF membranes. This GCMC + EMD approach is highly useful to screen a large number of MOFs for a target membrane-based gas separation process. External field non-equilibrium molecular dynamics (NEMD) simulations, on the other hand, can directly compute gas permeation by providing an accurate representation of MOF membranes but they are computationally demanding and require long simulation times. In this work, we performed NEMD simulations to investigate H₂/CH₄ separation performances of MOF membranes. Both single-component and binary mixture permeabilities of H₂ and CH₄ were computed using the NEMD approach and results were compared with the predictions of the GCMC + EMD approach and experimental measurements reported in the literature. Our results showed that there is a good agreement between NEMD simulations and experiments for the permeability and selectivity of MOF membranes. NEMD simulations provided the direct observation of the mass transfer resistances on the pore mouth of MOF membranes, which is neglected in the GCMC + EMD approach. Our results suggested that once the very large numbers of MOF materials were screened using the GCMC + EMD approach, more detailed NEMD calculations can be performed for the best membrane candidates to unlock the actual gas transport mechanism before the experimental fabrication of MOF membranes.

Fluid-fluid interfacial mobility from random walks

Dual control volume grand canonical molecular dynamics is used to perform the first calculation of fluid-fluid interfacial mobilities. The mobility is calculated from one-dimensional random walks of the interface by relating the diffusion coefficient to the interfacial mobility. Three different calculation methods are employed: one using the interfacial position variance as a function of time, one using the mean-squared interfacial displacement, and one using the time-autocorrelation of the interfacial velocity. The mobility is calculated for two liquid-liquid interfaces and one liquid-vapor interface to examine the robustness of the methods. Excellent agreement between the three calculation methods is shown for all the three interfaces, indicating that any of them could be used to calculate the interfacial mobility.

Adsorption and Diffusion of C1 to C4 Alkanes in Dual-Porosity Zeolites by Molecular Simulations

We employ grand canonical Monte Carlo and molecular dynamics simulations to systematically study the adsorption and diffusion of C₁ to C₄ alkanes in hierarchical ZSM-5 zeolite with micropores (∼1 nm) and mesopores (>2 nm). The zeolite is characterized by a large surface area of active sites on the microporous scale with high permeability and access to the active sites, which arises from the enhanced transport at the mesoporous scale. We model this zeolite as a microporous Na⁺-exchanged alumino-sillicate zeolite ZSM-5/35 (Si/Al = 35) in which cylindrical mesopores with a diameter of 4 nm have been built by deleting atoms accordingly. We use the TraPPE and Vujić-Lyubartsev force fields along with the Lorentz-Berthelot combining rules to describe adsorbate-adsorbate and adsorbate-adsorbent interactions. The performance of the force fields is assessed by comparing against experimental single-component adsorption isotherms of methane and ethane in microporous ZSM-5/35, which we measured as part of this work. We compare the adsorption isotherms and diffusivities of the adsorbed alkanes in the dual-porosity zeolite with those in microporous ZSM-5/35 and discern the specific behavior at each porosity scale on the overall adsorption, self-diffusion, and transport behavior in zeolites with dual micro/mesoporosities.

Transport Diffusion of Light Gases in Polyethylene Using Atomistic Simulations

We explore the temperature dependence of the self-, corrected-, and transport-diffusivities of CO₂, CH₄, and N₂ in a polyethylene (PE) polymer membrane through equilibrium molecular dynamics simulations. We also investigate the morphology of the polymer membrane based on the intermolecular radial distribution function, free volume, and pore size distribution analysis. The results indicate the existence of 1.5-3 Å diameter pores in the PE membrane, and with the increase in the temperature, the polymer swells linearly with changing slope at 450 K in the absence of gas and exponentially in the presence of gas. The gas adsorption isotherms extracted via a two-step methodology, considering the dynamics and structural transitions in the polymer matrix upon gas adsorption, were fitted using a "two-mode sorption" model. Our results suggest that CO₂ adsorbs strongly, whereas N₂ shows weak adsorption in PE. The results demonstrate that CO₂ is more soluble, whereas N₂ is least soluble. Further, it is found that an increase in the temperature negatively impacts the solubility of CO₂ and CH₄ but positively for N₂; this reverse solubility behavior is due to increased availability of pores accessible to N₂, which are kinetically closed at the lowest temperatures. The reported self-diffusivities of the gases from our simulations are on the order of 10^-6 cm²/s, consistent with the experimental evidence, whereas transport-diffusivities are 2 orders of magnitude higher than self-diffusivities. Furthermore, the temperature dependence of the self-diffusivity follows Arrhenius behavior, whereas the transport-diffusivity follows non-Arrhenius behavior having different activation energies in low and high temperature regions. Also, it is seen that loading has little effect on the self- and corrected-diffusion coefficients of all gases in the PE membrane.

Mass-flow-rate-controlled fluid flow in nanochannels by particle insertion and deletion

A nonequilibrium molecular dynamics method to induce fluid flow in nanochannels, the insertion-deletion method (IDM), is introduced. IDM inserts and deletes particles within distinct regions in the domain, creating locally high and low pressures. The benefits of IDM are that it directly controls a physically meaningful quantity, the mass flow rate, allows for pressure and density gradients to develop in the direction of flow, and permits treatment of complex aperiodic geometries. Validation of IDM is performed, yielding good agreement with the analytical solution of Poiseuille flow in a planar channel. Comparison of IDM to existing methods indicates that it is best suited for gases, both because it intrinsically accounts for compressibility effects on the flow and because the computational cost of particle insertion is lowest for low-density fluids.

Computational study of pressure-driven methane transport in hierarchical nanostructured porous carbons

Using the reflecting particle method together with a perturbation-relaxation loop developed in our previous work, we studied pressure-driven methane transport in hierarchical nanostructured porous carbons (HNPCs) containing both mesopores and micropores in non-equilibrium molecular dynamics simulations. The surface morphology of the mesopore wall was systematically varied by tuning interaction strength between carbon atoms and the template in a mimetic nanocasting process. Effects of temperature and mesopore size on methane transport in HNPCs were also studied. Our study shows that increased mesopore wall surface roughness changes the character of the gas-wall interaction from specular to diffuse, while the gas-gas interaction is diminished due to the decrease of adsorption density. Effects of the mesopore wall surface morphology are the most significant at low temperatures and in small channels. Our systematic study provides a better understanding of the transport mechanisms of light gases through carbon nanotube composite membranes in experiments.

Impact of Adsorption on Gas Transport in Nanopores

Given the complex nature of the interaction between gas and solid atoms, the development of nanoscale science and technology has engendered a need for further understanding of gas transport behavior through nanopores and more tractable models for large-scale simulations. In the present paper, we utilize molecular dynamic simulations to demonstrate the behavior of gas flow under the influence of adsorption in nano-channels consisting of illite and graphene, respectively. The results indicate that velocity oscillation exists along the cross-section of the nano-channel, and the total mass flow could be either enhanced or reduced depending on variations in adsorption under different conditions. The mechanisms can be explained by the extra average perturbation stress arising from density oscillation via the novel perturbation model for micro-scale simulation, and approximated via the novel dual-region model for macro-scale simulation, which leads to a more accurate permeability correction model for industrial applications than is currently available.

Computational Study of Pressure-Driven Gas Transport in Nanostructured Carbons: An Alternative Approach

We demonstrated a computationally efficient method in nonequilibrium molecular dynamics (NEMD) simulations to study pressure-driven gas transport in porous media. The reflecting particle method (RPM)14 was used to establish a steady-state gas flow along the transport channel, and the gas density in the feed chamber was properly adjusted to allow a constant pressure drop under various conditions by using a perturbation-relaxation loop developed here. This method was validated for methane flow through carbon nanotubes over a wide range of temperatures, giving results comparable to those of the commonly used dual control volume grand canonical molecular dynamics (DCV-GCMD) method but at least 20 times more efficient, even though the transport condition tested is favorable for the latter. This made it possible to perform systematic studies on the effects of temperature, pressure, and channel size on the transport behaviors. Our study shows that adsorption density varies significantly with temperature, which dramatically influences the transport mechanisms, especially in small channels at low temperatures and under high pressures. This newly developed NEMD method can be readily extended to study gas transport through channels with more complex surface morphology.

Bottom-up model of adsorption and transport in multiscale porous media

We develop a model of transport in multiscale porous media which accounts for adsorption in the different porosity scales. This model employs statistical mechanics to upscale molecular simulation and describe adsorption and transport at larger time and length scales. Using atom-scale simulations, which capture the changes in adsorption and transport with temperature, pressure, pore size, etc., this approach does not assume any adsorption or flow type. Moreover, by relating the local chemical potential μ(r) and density ρ(r), the present model accounts for adsorption effects and possible changes in the confined fluid state upon transport. This model constitutes a bottom-up framework of adsorption and transport in multiscale materials as it (1) describes the adsorption-transport interplay, (2) accounts for the hydrodynamics breakdown at the nm scale, and (3) is multiscale.

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore

In this article, uncertainty quantification is applied to molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. We consider a silica pore model connecting two reservoirs containing a solution of sodium (Na(+)) and chloride (Cl(-)) ions in water. An ad hoc concentration control algorithm is developed to simulate a concentration driven counter flow of ions through the pore, with the ionic flux being the main observable extracted from the MD system. We explore the sensitivity of the system to two physical parameters of the pore, namely, the pore diameter and the gating charge. First we conduct a quantitative analysis of the impact of the pore diameter on the ionic flux, and interpret the results in terms of the interplay between size effects and ion mobility. Second, we analyze the effect of gating charge by treating the charge density over the pore surface as an uncertain parameter in a forward propagation study. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of intrinsic noise and quantify the impact of parametric uncertainty on the MD predictions. We highlight the challenges arising from the heterogeneous nature of the system, given the several components involved, and from the substantial effect of the intrinsic thermal noise.

Molecular simulation of adsorption and transport in hierarchical porous materials

Adsorption and transport in hierarchical porous solids with micro- (~1 nm) and mesoporosities (>2 nm) are investigated by molecular simulation. Two models of hierarchical solids are considered: microporous materials in which mesopores are carved out (model A) and mesoporous materials in which microporous nanoparticles are inserted (model B). Adsorption isotherms for model A can be described as a linear combination of the adsorption isotherms for pure mesoporous and microporous solids. In contrast, adsorption in model B departs from adsorption in pure microporous and mesoporous solids; the inserted microporous particles act as defects, which help nucleate the liquid phase within the mesopore and shift capillary condensation toward lower pressures. As far as transport under a pressure gradient is concerned, the flux in hierarchical materials consisting of microporous solids in which mesopores are carved out obeys the Navier-Stokes equation so that Darcy's law is verified within the mesopore. Moreover, the flow in such materials is larger than in a single mesopore, due to the transfer between micropores and mesopores. This nonzero velocity at the mesopore surface implies that transport in such hierarchical materials involves slippage at the mesopore surface, although the adsorbate has a strong affinity for the surface. In contrast to model A, flux in model B is smaller than in a single mesopore, as the nanoparticles act as constrictions that hinder transport. By a subtle effect arising from fast transport in the mesopores, the presence of mesopores increases the number of molecules in the microporosity in hierarchical materials and, hence, decreases the flow in the micropores (due to mass conservation). As a result, we do not observe faster diffusion in the micropores of hierarchical materials upon flow but slower diffusion, which increases the contact time between the adsorbate and the surface of the microporosity.

Electric Field Controlled Self-Assembly of Hierarchically Ordered Membranes

Self-assembly in the presence of external forces is an adaptive, directed organization of molecular components under nonequilibrium conditions. While forces may be generated as a result of spontaneous interactions among components of a system, intervention with external forces can significantly alter the final outcome of self-assembly. Superimposing these intrinsic and extrinsic forces provides greater degrees of freedom to control the structure and function of self-assembling materials. In this work we investigate the role of electric fields during the dynamic self-assembly of a negatively charged polyelectrolyte and a positively charged peptide amphiphile in water leading to the formation of an ordered membrane. In the absence of electric fields, contact between the two solutions of oppositely charged molecules triggers the growth of closed membranes with vertically oriented fibrils that encapsulate the polyelectrolyte solution. This process of self-assembly is intrinsically driven by excess osmotic pressure of counterions, and the electric field is found to modify the kinetics of membrane formation, and also its morphology and properties. Depending on the strength and orientation of the field we observe a significant increase or decrease of up to nearly 100% in membrane thickness, as well as the controlled rotation of nanofiber growth direction by 90 degrees, resulting in a significant increase in mechanical stiffness. These results suggest the possibility of using electric fields to control structure in self-assembly processes involving diffusion of oppositely charged molecules.