Ard Louis

Abstract:

The fact that ice oats because of the hydrogen bonding imposing a perfect tetrahedrally coordinated network, linking them into six-membered rings with much empty space between the molecules (Franzese and Stanley, p. 105), is perhaps the best known of what are widely seen as a long list of curiosities. Water’s maximum density at 4°C and its unusually high thermal capacity are also familiar anomalies. Many others, however, are less celebrated but are surely as noteworthy. Both the melting and boiling points of water are unexpectedly high when it is placed in the sequence of group VI hydrides. So Lyndell-Bell and Debenedetti remind us by this extrapolation, although not by this imagery, that ice placed in a gin and tonic would melt at -100°C and a cup of tea should be prepared at -80°C. Not only that, but the effect of supercooling is also remarkable, so that at ambient pressure it can reach -41°C, whereas at 2 kbar it may be as low as -92°C (Franzese and Stanley, p. 102). These authors also remind us that if the supercooling is very rapid the water fails to crystallize and becomes a glass. This is of more than passing interest because in its high density form it is “the most abundant ice in the universe, where it is found as a frost on interstellar grains” (Franzese and Stanley, p. 103). This is not the only regime in which water becomes amorphous. In the hydration layer associated with a peptide, the water again has glasslike properties “with a very rough potential-energy landscape and slow hopping between local potential minima” (Ball, p. 56).

Abstract:

The crossover from single-file diffusion, where the mean-square displacement scales as (x2) to approximately t(1/2), to normal Fickian diffusion, where (x2) to approximately t, is studied as a function of channel width for colloidal particles. By comparing Brownian dynamics to a hybrid molecular dynamics and mesoscopic simulation technique, we can study the effect of hydrodynamic interactions on the single file mobility and on the crossover to Fickian diffusion for wider channel widths. For disc-like particles with a steep interparticle repulsion, the single file mobilities for different particle densities are well described by the exactly solvable hard-rod model. This holds both for simulations that include hydrodynamics, as well as for those that do not. When the single file constraint is lifted, then for particles of diameter sigma and pipe of width L such that (L - 2sigma)/sigma = deltac << 1, the particles can be described as hopping past one-another in an average time t(hop). For shorter times t << t(hop) the particles still exhibit sub-diffusive behaviour, but at longer times t >> t(hop), normal Fickian diffusion sets in with an effective diffusion constant Dhop to approximately 1/ mean square root of t(hop). For the Brownian particles, t(hop) to approximately deltac(-2) when deltac << 1, but when hydrodynamic interactions are included, we find a stronger dependence than deltac(-2). We attribute this difference to short-range lubrication forces that make it more difficult for particles to hop past each other in very narrow channels.