Phase transitions of CO₂confined in nanometer pores as revealed by positronium annihilation

Abstract

The results of a comprehensive positronium annihilation study of the phase behaviour of carbon dioxide in porous Vycor glass are presented. Isobaric measurements of the 3 gamma :2 gamma annihilation ratio show that on cooling, the gas-liquid phase boundary is raised by ~5 K while the liquid-solid transition is depressed by ~12 K relative to the bulk. The resulting phase diagram suggests the existence of a `triple point` of the confined fluid at a temperature ~10 K and a pressure ~2 bar below the bulk triple point.

The physics of premelted ice and its geophysical consequences

“…The shift, now known as the Gibbs-Thomson effect, has been studied with a variety of substances dispersed on inert substrates or confined in porous media. A sampling is given in the references in four groups: weakly interacting molecular species such as rare gas atoms in porous media ͑Brewer et Tell and Maris, 1983;Liezhao et al, 1986;Shimoda et al, 1986;Kondo et al, 1987;Brown et al, 1988;Bruschi et al, 1988;Hiroi et al, 1989;Jackson and McKenna, 1990;Rall et al, 1991;Duffy et al, 1995;Beaudoin et al, 1996͒, ice in porous media ͑Blachere andYoung, 1972;Gay et al, 1992;Maruyama et al, 1992;Ishizaki et al, 1996;Mori et al, 1996͒, dispersed metal particles ͑Takagi, 1954Gladkich et al, 1966;Wronski, 1967;Coombes, 1972;Peppiatt and Sambles, 1975;Buffat andBorel, 1976͒, andice in soils ͑Hoekstra andDelaney, 1974;Konrad and Morgenstern, 1981;Smith and Tice, 1988͒. The typical behavior of the first group is that melting begins appreciably below the bulk transition when the pores are filled. Although the first one or two adsorbed layers prefreeze, due to substrate attractive forces stronger than the interactions within the material.…”

Fluids in Model Pores or Cavities: The Influence of Confinement on Structure and Phase Behaviour

“…Although studies for single idealised pores cannot address the wealth of issues raised by the experiments one might hope to understand why freezing point depression is generally observed and what basic physical factors determine a phase diagram such as that reported in [27] for CO2 in Vycor where we see that the ratio of the depression to the bulk freezing temperature, (Tf -T fb) / T fb,iS about -0.05 for pressures near that of the bulk triple point. (The melting temperature is depressed by about half of this amount.…”

“…The effects of pore size distributions, interconnectivity and geometry of the pores must also play an important part in determining the nature of freezing of fluids in porous solids such as Vycor and other silica glasses. The hystereSiS which is observed [27] is complex and occurs over a wider temperature range than is found for capillary condensation. When crystallites form, their lateral extent, as estimated from the widths of diffraction peaks, is often much larger than a typical pore length, implying interconnection of crystallites in neighbouring pores.…”

“…Caution must be exercised in the interpretation of these results. As mentioned earlier, since Pz cannot be identified with the pressure of a bulk reservoir it is not straightforward to make direct comparisons of the results of Figures 5 and 6 with experimental studies such as those described in [27] or with simulation studies based on other ensembles. One obvious complication is that the average wall separation < f > varies along the coexistence lines calculated at fixed N. Nevertheless, one can make qualitative comparisons with other studies.…”

“…These are summarised in [24][25][26] and we simply state that experiments usually find a depression of the freezing temperature below the bulk value accompanied by pronounced hysteresis between freezing and melting, with melting still occurring below the bulk transition temperature. Duffy et al [27] used a positronium annihilation technique to determine both the freezing and condensation phase boundaries for CO2 in Vycor glass with a mean pore radius Rm -20 A. They found that confinement shifts the liquid-gas transition to a considerably higher and the liquid-solid transition to a considerably lower temperature than in bulk and that the triple point appears to be reduced in both pressure and temperature.…”