11/08/2026
Finite-Range Attractions Reveal Hidden Structure in a Simple One-Dimensional Fluid
A new study shows that even a seemingly simple one-dimensional model of particles that can stick together in pairs can display unexpectedly rich behavior - and reveals precisely where a widely used theory succeeds and fails. The particles are hard rods with attractive ends, which form reversible chains. The researchers exploit an exact solution of the corresponding one-dimensional fluid to test Wertheim's theory, a standard approach for describing how particles associate. They find that the theory is exact when the attractive interaction is infinitely short-ranged, but misses important effects when attraction extends over a finite distance. By reformulating the exact solution in terms of the quantities used by the theory, they identify how it can be corrected exactly in one dimension. The finite range of attraction also produces previously unseen structural behavior: correlations between particles can change from a smooth to an oscillatory decay, and the characteristic distance over which particles remain correlated can develop several distinct extrema. At very high pressure, the correlation length grows differently for finite-range and infinitely short-range attractions. These results provide an exact benchmark for association theories and show how subtle changes in the range of an interaction can profoundly alter collective behavior.
Link to the paper: https://doi.org/10.1063/5.0344388