Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called \"space charge\" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)JCPSA60021-960610.1063/1.1669814]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate (\"uniform potential\" or \"fine capillary pore\" model), are close to results of the full model.

Analysis of electrolyte transport through charged nanopores

Pressure-modulated ion transport through single graphene nanopores reveals a nonlinear electrohydrodynamic coupling phenomenon.

https://www.science.org/doi/pdf/10.1126/sciadv.abj2510?download=true

Nonlinear electrohydrodynamic ion transport in graphene nanopores

Despite decades of dominance in separation technology, progress in the design and development of high-performance polymer-based membranes has been incremental. Recent advances in materials science and chemical synthesis provide opportunities for molecular-level design of next-generation membrane materials. Such designs necessitate a fundamental understanding of transport and separation mechanisms at the molecular scale. Molecular simulations are important tools that could lead to the development of fundamental structure-property-performance relationships for advancing membrane design. In this Perspective, we assess the application and capability of molecular simulations to understand the mechanisms of ion and water transport across polymeric membranes. Additionally, we discuss the reliability of molecular models in mimicking the structure and chemistry of nanochannels and transport pathways in polymeric membranes. We conclude by providing research directions for resolving key knowledge gaps related to transport phenomena in polymeric membranes and for the construction of structure-property-performance relationships for the design of next-generation membranes.

Molecular Simulations to Elucidate Transport Phenomena in Polymeric Membranes.

Osmotic transport in nanoconfined aqueous electrolytes provides alternative venues for water desalination and “blue energy” harvesting. The osmotic response of nanofluidic systems is controlled by the interfacial structure of water and electrolyte solutions in the so-called electrical double layer (EDL), but a molecular-level picture of the EDL is to a large extent still lacking. Particularly, the role of the electronic structure has not been considered in the description of electrolyte/surface interactions. Here, we report enhanced sampling simulations based on ab initio molecular dynamics, aiming at unravelling the free energy of prototypical ions adsorbed at the aqueous graphene and hBN interfaces, and its consequences on nanofluidic osmotic transport. Specifically, we predicted the zeta potential, the diffusio-osmotic mobility, and the diffusio-osmotic conductivity for a wide range of salt concentrations from the ab initio water and ion spatial distributions through an analytical framework based on Stokes equation and a modified Poisson–Boltzmann equation. We observed concentration-dependent scaling laws, together with dramatic differences in osmotic transport between the two interfaces, including diffusio-osmotic flow and current reversal on hBN but not on graphene. We could rationalize the results for the three osmotic responses with a simple model based on characteristic length scales for ion and water adsorption at the surface, which are quite different on graphene and on hBN. Our work provides fundamental insights into the structure and osmotic transport of aqueous electrolytes on 2D materials and explores alternative pathways for efficient water desalination and osmotic energy conversion.

Osmotic Transport at the Aqueous Graphene and hBN Interfaces: Scaling Laws from a Unified, First-Principles Description.

Ionic transport through a charged nanopore at low ion concentration is governed by the surface conductance. Several experiments have reported various power-law relations between the surface conductance and ion concentration, i.e., Gsurf ∝ c0α. However, the physical origin of the varying exponent, α, is not yet clearly understood. By performing extensive coarse-grained Molecular Dynamics simulations for various pore diameters, lengths, and surface charge densities, we observe varying power-law exponents even with a constant surface charge and show that α depends on how electrically "perfect" the nanopore is. Specifically, when the net charge of the solution in the pore is insufficient to ensure electroneutrality, the pore is electrically "imperfect" and such nanopores can exhibit varying α depending on the degree of "imperfectness". We present an ionic conductance theory for electrically "imperfect" nanopores that not only explains the various power-law relationships but also describes most of the experimental data available in the literature.

Ion Transport in Electrically Imperfect Nanopores.

The unique properties of aqueous electrolytes in ultrathin nanopores have drawn a great deal of attention in a variety of applications, such as power generation, water desalination, and disease diagnosis Inside the nanopore, at the interface, properties of ions differ from those predicted by the classical ionic layering models (eg, Gouy–Chapman electric double layer) when the thickness of the nanopore approaches the size of a single atom (eg, nanopores in a single-layer graphene membrane) Here, using extensive molecular dynamics simulations, the structure and dynamics of aqueous ions inside nanopores are studied for different thicknesses, diameters, and surface charge densities of carbon-based nanopores [ultrathin graphene and finite-thickness carbon nanotubes (CNTs)] The ion concentration and diffusion coefficient in ultrathin nanopores show no indication of the formation of a Stern layer (an immobile counter-ionic layer) as the counter-ions and nanopore atoms are weakly correlated in time compared to the strong correlation observed in thick nanopores The weak correlation observed in ultrathin nanopores is indicative of a weak adsorption of counter-ions onto the surface compared to that of thick pores The vanishing counter-ion adsorption (ion–wall correlation) in ultrathin nanopores leads to several orders of magnitude shorter ionic residence times (picoseconds) compared to the residence times in thick CNTs (seconds) The results of this study will help better understand the structure and dynamics of aqueous ions in ultrathin nanopores

yechan noh

Papers

Ion Transport in Electrically Imperfect Nanopores.

Dynamic and weak electric double layers in ultrathin nanopores.