Molecular dynamics simulations of PVP kinetic inhibitor in liquid water and hydrate/liquid water systems

The possible effects of PVP (poly(N-vinylpyrrolidone)) on the properties of liquid and water in clathrate hydrate has been investigated using NVT molecular dynamics simulations. A model for a monomer of the PVP polymer is immersed in three systems, liquid water, a unit cell of a hydrate in liquid water with a hydrate former and a third system where some of the liquid water molecules of this last system are replaced by a PVP monomer. Both molecular dynamics simulation and integral equation theory predict hydrogen bonding between the double bonded oxygen in the PVP ring and hydrogens in water. For the composite system, the PVP monomer has a preference for hydrogen bonding to hydrogens from the water molecules at the surface of the hydrate lattice. The simulations indicate that the PVP monomer tends to orient perpendicular to the hydrate surface. For the model systems in this study PVP may form hydrogen bonds with liquid water through the double bonded oxygen in the ring. When a hydrate crystal is immersed in the liquid water phase this hydrogen bonding is shifted towards the hydrate due to a more favourable Coulomb interaction involving hydrogens from more than one water molecule at the hydrate surface. The PVP monomer has a preference for perpendicular orientation with respect to the hydrate surface. A scheme is suggested for the characterization of kinetic hydrate inhibitors based on molecular dynamics simulations and on three basic properties. In addition to the energy between the active groups of the inhibitor and hydrate water another point of focus is the free energy changes in the interactions between the inhibitor and water as the charges are changed from zero to the original model charges. In particular the difference between this integral for the (hydrate water)–(PVP monomer) interaction and the (liquid water)–(PVP inhibitor) interaction should reflect the driving forces in freezing the inhibitor out from the liquid water phase and onto the hydrate surface. The third property in the characterization scheme is the diffusivities of groups connecting to the hydrate crystal, relative to the diffusivities of the hydrate crystal. Results are presented from simulations where a small cavity with a methane model as a guest is immersed in liquid water with free methane molecules at a temperature of 150K. Changes in structure, diffusivities and energy indicate a tendency towards a more solid–like structurde around the cavity.     

ON THE SUSTAINABLE PROGRAM IN SOLOW'S MODEL

ABSTRACT. We show that our general result (Withagen and Asheim [1998]) on the converse of Hartwick's rule also applies for the special case of Solow's model with one capital good and one exhaustible resource. Hence, the criticism by Cairns and Yang [2000] of our paper is unfounded.