An Apparent Dissociation Transition in Anharmonically Bound 1D Systems

TL;DR

This paper derives analytical expressions for thermodynamic properties of anharmonically bound 1D systems, revealing a dissociation transition characterized by a smooth crossover without singularities at finite pressure.

Contribution

It provides the first analytical characterization of the dissociation transition in 1D anharmonic systems, including explicit formulas for key thermodynamic observables.

Findings

Thermodynamic observables are analytically derived across the dissociation transition.

The transition shows no singularities at finite pressure, indicating a smooth crossover.

Mean interatomic separation scales exponentially with inverse temperature in the low-temperature regime.

Abstract

For diatomic molecules and chains bound anharmonically by interactions such a the Lennard Jones and Morse potentials, we obtain analytical expressions for thermodynamic observables including the mean bond length, thermally averaged internal energy, and the coefficient of thermal expansion. These results are valid across the shift from condensed to gas-like phases, a dissociation transition marked by a crossover with no singularities in thermodynamic variables for finite pressures, though singular behavior appears in the low pressure limit. In the regime where the thermal energy $k_{\mathrm{B}} T$ is much smaller than the dissociation energy $D$, the mean interatomic separation scales as $\langle l \rangle = R_{e} + {\mathcal B} (P R_{e}/k_{\mathrm{B}} T)^{-2} e^{-D/k_{\mathrm{B}} T} \left( D/k_{\mathrm{B}} T \right )^{1/2}$ for both the Morse and Lennard Jones potentials where $p$ is a pressure term, $R_{e}$ is the $T = 0$ bond length, and ${\mathcal B}$ is a constant specific to the potential.