Ordering of hard spheres inside hard cylindrical pores

Abstract

Isothermal-isobaric simulations on the ordering behavior of hard spheres upon confinement are presented. The radii of the confining cylinders go from 1.1 to 2 in units of the diameters of the hard spheres adsorbed. In all the range of pressures considered the spheres were located in concentric layers, as many as the radius of the hard cylinder would permit. When the pressure increases, the hard spheres go from being loosely arranged to the formation of ordered structures. This change is marked in all cases by a distinct break in the density of spheres in a narrow pressure range. When the tube radius is smaller than 1.5, the high-pressure ordering is determined by the number of coplanar spheres you can have within a circle of radius equal to that of the confining tube. For wider tubes, the change upon compression is determined by the formation of defected two-dimensional triangular lattices wrapped to fit inside the particular cylinder we are considering.

Structural properties of hard disks in a narrow tube

“…It is easy to show that equation (6) gives ψ 0 = 1/ √ W and λ 0 = exp(−βP xx W D)/(βP xx D) for the squares and the relation between the pressure and the Gibbs free energy gives back the Tonks equation for the pressure, which is βP xx W = ρ/(1 − ρD). From the equation of transverse pressure (9) we get that the squares behaves as an ideal gas between the two walls, i.e. βP yy = N/(LW ).…”

Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: Exact results from transfer-matrix method

“…1,2 For example, with reducing the pore-size, the first order thermodynamic fluid-solid phase transition may completely vanish. 3,4 The confined colloidal system can behave like the one-dimensional Tonks gas in the limit when the particles are not allowed to pass each other (single-file fluid condition). 5,6 Furthermore, the reduction of the spatial dimensions has substantial impact on the diffusion properties of the colloidal systems.…”

“…[26][27][28][29][30] In slightly wider pores, where the singlefile fluid condition is not satisfied, it was found that a densityjump occurs between fluid-and solid-like structures at the freezing. 3,4 In this work we apply the transfer-matrix method 30 to determine the longitudinal and transversal pair correlation functions of hard core-fluids in such a narrow pore that only nearest neighbor interactions are allowed. The results of the transfer-matrix method are compared with our Monte Carlo simulation data.…”

Direct determination of fluid-solid coexistence of square-well fluids confined in narrow cylindrical hard pores

“…This behavior is attributed to the entropic dominance on the system, that particles spontaneously move to the more accessible space to maximize the entropy of the system. In the narrow pore, which can hold only one layer of particles at a plane perpendicular to the z direction, the at- tractive force has little impact to the radial density profile and the behavior of ͑r͒ is similar to that of hard sphere systems confined in hard pores discussed by DuranOlivencia et al 16 Similar behavior was also observed in D = 2.5, as seen in the g͑z͒ function shown in Fig. 11, where three peaks are observed at z Ͻ 1.0 at = 0.80, 0.83, and 0.85 indicating a twisted helical structure, and disappear at = 0.90 and 0.95, where the structure is transformed to a square shape consisting of four particles sharing the same z against another nearest square layer by rotating an angle of / 4.…”

“…[16][17][18][19][20] The structure of the confined fluids is highly dependent on the pore diameter and it seems there is no simple and continuous dependence, which can be generalized. Here we especially focus on the narrow pores, which can only hold one cylindrical layer of particles, and those are of great theoretical and experimental interest, as in such systems the particles can be self-assembled to form single helical or twisted helical structure.…”