Penetrable Square-Well fluids: Exact results in one dimension

Abstract

We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well defined thermodynamic limit is identified.

20 pages, 7 figures, to appear in Physical Review E (2008)

References in corpus (8)

• Mean Field Fluid Behavior of the Gaussian Core Model
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• Patchy sticky hard spheres: analytical study and Monte Carlo simulations
• Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures
• Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
• The penetrable-sphere fluid in the high-temperature, high-density limit
• Are the energy and virial routes to thermodynamics equivalent for hard spheres?
• Radial distribution function of penetrable sphere fluids to second order in density

Cited by in corpus (18)

• Freezing of soft-core bosons at zero temperature: A variational theory
• Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution
• Probing the existence of phase transitions in one-dimensional fluids of penetrable particles
• Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
• Phase diagram of the penetrable square well-model
• Thermodynamic and structural anomalies of the Gaussian-core model in one dimension
• A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
• Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-Hückel theory
• One-dimensional fluids with second nearest-neighbor interactions
• The penetrable square-well model: extensive versus non-extensive phase
• Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids
• Non existence of a phase transition for the Penetrable Square Wells in one dimension
• Interacting hard rods on a lattice: Distribution of microstates and density functionals
• Monte Carlo simulation of Hard-, Square-Well, and Square-Shoulder Disks in narrow channels
• Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient
• Kinetic Theory of Soft Matter. The Penetrable-Square-Well Model
• From the Liouville to the Smoluchowski equation for a colloidal solute particle in a solvent
• Finite-size effects and thermodynamic limit in one-dimensional Janus fluids