Confinement, topography, universality, and non-scaling effects in the specific heat and superfluid density of helium-4 near the superfluid transition
Mooney, Kevin P
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The properties of bulk systems at a second order phase transition, in particular the superfluid transition of liquid helium, have been very well studied both theoretically and experimentally. Additionally, theoretical predictions have been made as how a system deviates from the thermodynamic limit as one or more of its confining dimensions becomes small relative to the bulk system's correlation length. This work presents measurements of the specific heat of 4 He confined in long channels of 1 μm × 1 μm square cross-section, and in 2 μm "boxes." In the case of the channels, additional specific heat measurements were done on mixtures of 3 He- 4 He. The technique of adiabatic fountain resonance allows one to measure the superfluid fraction in the fill-channels of the cells. Results are presented for three different channel geometries. In analysis of previous experiments involving the superfluid fraction of 4 He confined in thin films, it was noted that the data do not scale as theory predicts. A possible explanation for the lack of scaling was that the theory did not include the effects of the van der Waals interaction between the helium and confining surfaces. It is possible to estimate the magnitude of this effect in the context of ψ-theory. Estimates are presented of the superfluid fraction of helium confined in thin films, cylindrical pores, and spherical shells both with and without the van der Waals interaction. Where possible, these results are compared with experiment.