Correlating properties of a simple liquid at criticality in a reduced geometry

Abstract

Abstract We examine correlating properties in terms of the pair-correlation function of order-parameter fluctuations for a near-critical liquid in a reduced geometry system of cylindrical form, in which the geometrical factor set the characteristic of spatial limitation and defined by K = a/Rco with a being the cylinder radius, which is reduced to the order of 100 compared with the amplitude of the correlation length Rco. The pair-correlation function G2 of order- parameter fluctuations (e.g., density fluctuations for the one-component fluid) is obtained as a solution of equation for Helmholtz operator which is associated with Ornstein-Zernike (OZ) equation. Reduced geometry of the system leads to the dependence of correlation function G2 not only on thermodynamical variables but on the cylinder radius as well. The correlation length turns out to be dependent on the geometric factor as Rc/Rco ∼ 0.81K at the bulk critical temperature and anisotropy of correlating properties of the system gives rise to R|c/R⊥c ∼ 1.06, where R|c and R|c denote the components of Rc associated with the axis of the cylinder. Our results suggest that the critical growth behaviour of correlation length should remain only along the axis associated with the present geometry, i.e., in spatially unlimited direction, moreover not under the critical temperature of the bulk liquid, but under the new one.