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Using computer simulations, we study a membrane of parallel narrow pores filled with one-dimensional wires of hydrogen-bonded water molecules. We show that such a membrane is equivalent to a system of effective charges located at opposite sides of the membrane offering a computationally efficient way to model correlation effects in water-filled nanopore membranes. Based on our simulations we predict that membranes with square pore lattices undergo a continuous order-disorder transition to an antiferroelectric low-temperature phase in which water wires in adjacent pores are oriented in opposite directions. Strong antiferroelectric correlations exist also in the disordered phase far above the critical temperature or in membranes with geometric frustration, leading to a dielectric constant that is reduced considerably with respect to the case of uncoupled water wires. These correlations are also expected to hinder proton translocation through the membrane.

Water molecules confined to pores with sub-nanometre diameters form single-file hydrogen-bonded chains. In such nanoscale confinement, water has unusual physical properties that are exploited in biology and hold promise for a wide range of biomimetic and nanotechnological applications. The latter can be realized by carbon and boron nitride nanotubes which confine water in a relatively non-specific way and lend themselves to the study of intrinsic properties of single-file water. As a consequence of strong water-water hydrogen bonds, many characteristics of single-file water are conserved in biological and synthetic pores despite differences in their atomistic structures. Charge transport and orientational order in water chains depend sensitively on and are mainly determined by electrostatic effects. Thus, mimicking functions of biological pores with apolar pores and corresponding external fields gives insight into the structure-function relation of biological pores and allows the development of technical applications beyond the molecular devices found in living systems. In this Perspective, we revisit results for single-file water in apolar pores, and examine the similarities and the differences between these simple systems and water in more complex pores., (This journal is © the Owner Societies 2011)

We present a recently developed one-dimensional dipole lattice model that accurately captures the key properties of water in narrow nanopores. For this model, we derive three equivalent representations of the Hamiltonian that together yield a transparent physical picture of the energetics of the water chain and permit efficient computer simulations. In the charge representation, the Hamiltonian consists of nearest-neighbor interactions and Coulomb-like interactions of effective charges at the ends of dipole ordered segments. Approximations based on the charge picture shed light on the influence of the Coulomb-like interactions on the structure of nanopore water. We use Monte Carlo simulations to study the system behavior of the full Hamiltonian and its approximations as a function of chemical potential and system size and investigate the bimodal character of the density distribution occurring at small system sizes.

Water confined into the interior channels of narrow carbon nanotubes or transmembrane proteins forms collectively oriented molecular wires held together by tight hydrogen bonds. Here, we explore the thermodynamic stability and dipolar orientation of such 1D water chains from nanoscopic to macroscopic dimensions. We show that a dipole lattice model accurately recovers key properties of 1D confined water when compared to atomically detailed simulations. In a major reduction in computational complexity, we represent the dipole model in terms of effective Coulombic charges, which allows us to study pores of macroscopic lengths in equilibrium with a water bath (or vapor). We find that at ambient conditions, the water chains filling the tube are essentially continuous up to macroscopic dimensions. At reduced water vapor pressure, we observe a 1D Ising-like filling/emptying transition without a true phase transition in the thermodynamic limit. In the filled state, the chains of water molecules in the tube remain dipole-ordered up to macroscopic lengths of approximately 0.1 mm, and the dipolar order is estimated to persist for times up to approximately 0.1 s. The observed dipolar order in continuous water chains is a precondition for the use of nanoconfined 1D water as mediator of fast long-range proton transport, e.g., in fuel cells. For water-filled nanotube bundles and membranes, we expect anti-ferroelectric behavior, resulting in a rich phase diagram similar to that of a 2D Coulomb gas.

Multistate empirical valence bond (EVB) models provide an accurate description of the energetics of proton transfer and solvation in complex molecular systems and can be efficiently used in molecular dynamics computer simulations. Within such models, the location of the moving protonic charge can be specified by the so-called center of charge, defined as a weighted average over the diabatic states of the EVB model. In this paper, we use first-order perturbation theory to calculate the molecular forces that arise if a bias potential is applied to the center of charge. Such bias potentials are often necessary when molecular dynamics simulations are used to determine free energies related to proton transfer and not all relevant proton positions are sampled with sufficient frequency during the available computing time. The force expressions we derive are easy to evaluate and do not create any significant computational cost compared with unbiased EVB simulations. As an illustration of the method, we study proton transfer in a small liquid water droplet consisting of 128 water molecules plus an excess proton. Contrary to predictions of continuum electrostatics, but in agreement with previous computer simulations of similar systems, we observe that the excess proton is predominantly located at the surface of the droplet. Using the formalism developed in this paper, we calculate the reversible work required to carry the protonic charge from the droplet surface to its core, finding a value of roughly 4 k(B)T.

Proton transfer along 1D chains of water molecules inside carbon nanotubes is studied by simulations. Ab initio molecular dynamics and an empirical valence bond model yield similar structures and time scales. The proton mobility along 1D water chains exceeds that in bulk water by a factor of 40, but is reduced if orientational defects are present. Excess protons interact with hydrogen-bonding defects through long-range electrostatics, resulting in coupled motion of protons and defects.