Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

Abstract

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the trianglewell and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function g(r) was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of g(r) up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus-Yevick, and Martynov-Sarkisov closures. Finally, the Fisher-Widom and Widom lines are obtained in the case of the triangle-well model.

On the decay of the pair correlation function and the line of vanishing excess isothermal compressibility in simple fluids

“…It is also interesting to note that the W lines shown in Ref. 49 have a similar shape as those in the three-dimensional SW and AO models, though these extend down to zero temperature as there is no critical point in d = 1.…”

“…Indeed, the original FW paper [10] was based on exact results for one-dimensional (d = 1) models. Recent studies for SW [48] and for triangle-well potentials [49] in d = 1 provide exact results for the FW line. It would be instructive to compare these with those based on our new criterion χ T = χ id T .…”

One-dimensional Janus fluids. Exact solution and mapping from the quenched to the annealed system

“…An analysis of the numerical solutions of the set of equations (4.20a) and (4.20b) shows that the zeroes of D(s) with a real part closest to the origin are always complex numbers (i.e., ω = 0). Therefore, no Fisher-Widom line [12] separating the oscillatory and monotonic large-distance behaviors exists in a one-dimensional Janus fluid, in contrast to what happens in the case of one-dimensional isotropic fluids [12,18,25]. Therefore, the restriction of attractive interactions to only the 1-2 pair frustrates the possibility of monotonic decay of correlations, even at low temperature.…”

“…Let us now use arguments similar to those conventionally used for isotropic potentials [13,14,15,16,17,18] to derive the structural properties of the mixture. Given a reference particle of species i, we focus on those particles to its right and denote by p (ℓ,+) ij (r)dr the (conditional) probability that its ℓth right neighbor belongs to species j and is located at a distance between r and r + dr.…”

Simulaciones moleculares con potenciales discontinuos

“…El potencial consta de seis parámetros moleculares; σ representa el diámetro de la partícula esférica, λ 1 y λ 2 son las longitudes características, 1 es la altura de energía para la parte repulsiva del potencial y 2 es la energía mínima del potencial. El parámetro n, controla la suavidad o dureza del potencial, es decir; para valores númericamente grandes de n este modelo de potencial adquiere la forma similar de los potenciales de Jagla [24,26], pozo cuadrado [21][22][23], y triangular [16,17,31], en tanto que para valores pequeños de n, esta interacción adquiere la forma de potencial de Lennard-Jones [32].…”