  When a fluid that undergoes a vapor to liquid transition in the bulk is
confined to a long cylindrical pore, the phase transition is shifted (mostly
due to surface effects at the walls of the pore) and rounded (due to finite
size effects). The nature of the phase coexistence at the transition depends on
the length of the pore: For very long pores the system is axially homogeneous
at low temperatures. At the chemical potential where the transition takes place
fluctuations occur between vapor-like and liquid-like states of the cylinder as
a whole. At somewhat higher temperatures (but still far below bulk criticality)
the system at phase coexistence is in an axially inhomogeneous multi-domain
state, where long cylindrical liquid-like and vapor-like domains alternate.
Using Monte Carlo simulations for the Ising/lattice gas model and the
Asakura-Oosawa model of colloid-polymer mixtures the transition between these
two different scenarios is characterized. It is shown that the density
distribution changes gradually from a double-peak structure to a triple-peak
shape, and the correlation length in axial direction (measuring the equilibrium
domain length) becomes much smaller than the cylinder length. The (rounded)
transition to the disordered phase of the fluid occurs when the axial
correlation length has decreased to a value comparable to the cylinder
diameter. It is also suggested that adsorption hysteresis vanishes when the
transition from the simple domain state to the multi-domain state of the
cylindrical pore occurs. We predict that the difference between the pore
critical temperature and the hysteresis critical emperature should increase
logarithmically with the length of the pore.
