Crossover between liquidlike and gaslike behavior in $\mathrm{C}{\mathrm{H}}_4$ at 400 K

We report experimental evidence for a crossover between a liquidlike state and a gaslike state in fluid methane ($\mathrm{C}{\mathrm{H}}_4$). This crossover is observed in all of our experiments, up to a temperature of 397 K, 2.1 times the critical temperature of methane. The crossover has been characterized with both Raman spectroscopy and x-ray diffraction in a number of separate experiments, and confirmed to be reversible. We associate this crossover with the Frenkel line—a recently hypothesized crossover in dynamic properties of fluids extending to arbitrarily high pressure and temperature, dividing the phase diagram into separate regions where the fluid possesses liquidlike and gaslike properties. On the liquidlike side the Raman-active vibration increases in frequency linearly as pressure is increased, as expected due to the repulsive interaction between adjacent molecules. On the gaslike side this competes with the attractive van der Waals potential leading the vibration frequency to decrease as pressure is increased.

Figure 1

Background correction of integrated diffraction patterns. (a) Diffraction pattern of fluid $\mathrm{C}{\mathrm{H}}_4$ at 0.69 GPa (black, upper) and background from empty DAC (red, lower). (b) Static structure factor $S\left(\mathit{q}\right)$ of $\mathrm{C}{\mathrm{H}}_4$ at 0.69 GPa obtained by subtracting background and normalizing in the high-$\mathit{q}$ limit.

Figure 2

(a) Equation of state (EOS) of fluid $\mathrm{C}{\mathrm{H}}_4$ at 298 K. Circles: experimental data. Solid line: Fit of ideal gas EOS modified with van der Waals correction [Eq. (4)]. Dotted line: Fit of Murnaghan EOS [Eq. (1)]. (b) HWHM of first peak in $S\left(\mathit{q}\right)$ plotted as a function of pressure at 298 K.

Figure 3

Plot of reduced frequency of $\mathrm{C}{\mathrm{H}}_4$ Raman-active vibration as a function of pressure at (a) 298 K, (b) 345 K, (c) 374 K, and (d) 397 K. Solid lines following the data are fits performed using Eq. (6) and arrows signify the minimum of this fit. Dotted lines are linear fits to data collected above 0.6 GPa [Eq. (5)]. Vertical solid lines are expected positions of the Joule-Thomson line and Frenkel line.

Figure 4

(a) Plot of Raman peak area (integrated intensity, blue circles) and HWHM (red squares) as a function of pressure at 298 K, showing discontinuous decrease in both area and HWHM when the gaslike side of the Frenkel line is reached. The green shaded region is the area in which the minimum in vibration frequency [fitted using Eq. (6)] lies, which we associate with the Frenkel line and the green line marks the experimentally measured melting line [32]. (b) Waterfall plot of spectra collected at 298 K in order collected, demonstrating the reversible nature of the crossover. Red spectra (marked with asterisks) are those on the gaslike side of the Frenkel line.

Figure 5

Phase diagram of $\mathrm{C}{\mathrm{H}}_4$. (a) The theoretically predicted Frenkel line in $\mathrm{C}{\mathrm{H}}_4$ [16] is marked along with the experimentally observed melting curve [32]. The data points are the crossovers we observe experimentally and attribute to the Frenkel line. (b) The position of the theoretically predicted Frenkel line compared to the Boyle curve, Joule-Thomson curve, and Amagat curve. Open squares are our Frenkel line data points and the red closed square is the critical point (c.p.).