Frenkel line in a dipolar fluid: decoupling of sound dispersion and transverse waves

The Frenkel line, which marks the crossover from gas-like to solid-like dynamics in fluids, has been extensively studied in simple and molecular systems but remains unexplored for dipolar fluids. Using molecular dynamics simulations of a model diatomic dipolar fluid (parametrized after CO), we locate the Frenkel line along the supercritical isotherm $T=800$ K using two criteria: the isochoric heat capacity $c_V/k_{\mathrm{B}} = 3.0$
 and the disappearance of oscillations in the velocity autocorrelation function. Both criteria consistently place the Frenkel line at a density of $\rho \approx 1.1$ g/ml. Analysis of the excitation spectra reveals an unusual decoupling: positive sound dispersion already appears at $\rho=0.9$ g/ml, whereas transverse (shear) waves emerge only at the Frenkel line density of $\rho=1.1$ g/ml. The magnitude of the positive sound dispersion is about $20 \%$, similar to that in simple monatomic melts. For the first time, we investigate rotational dynamics across the Frenkel line using the autocorrelation functions $C_1(t)$ and $C_2(t)$. The corresponding correlation times $\tau_1$ and $\tau_2$ increase monotonically with density and show no detectable anomaly upon crossing the Frenkel line. Our results suggest that although translational dynamics exhibit a clear crossover at the Frenkel line, rotational motion in dipolar fluids is not significantly affected.