Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks

• Published in: Journal of molecular liquids 2023-10, Vol.387, p.122572, Article 122572
• Main Authors: Pergamenshchik, V.M., Bryk, T., Trokhymchuk, A.
• Format: Article
• Language: English
• Subjects: Correlation functions; Hard-disk system; Partition function; Quasi-one-dimensional pore
• ISSN: 0167-7322; 1873-3166
• DOI: 10.1016/j.molliq.2023.122572

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks Pergamenshchik [19] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density Nd/L where d is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at Nd/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. Comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed. •Analytical formula for the pair correlation functions between two neighbor disks in a quasi-1D hard disk system (pore).•Analytical formula for the pair correlation function as a function of distance between two disks.•Presentation of both correlation functions and analysis of the ordering they describe.•Discussion of the theoretical vs simulation data in the context of the relation finite system vs infinite system.