Frenkel line and solubility maximum in supercritical fluids

Abstract

A new dynamic line, the Frenkel line, has recently been proposed to separate the supercritical state into rigid-liquid and non-rigid gas-like fluid. The location of Frenkel line on the phase diagram is unknown for real fluids. Here, we map the Frenkel line for three important systems: CO2, H2O and CH4. This provides an important demarcation on the phase diagram of these systems, the demarcation that separates two distinct physical states with liquid-like and gas-like properties. We find that the Frenkel line can have similar trend as the melting line above the critical pressure. Moreover, we discuss the relationship between unexplained solubility maxima and Frenkel line, and propose that the Frenkel line corresponds to the optimal conditions for solubility.Recently, there has been a dramatical increase of using supercritical fluids in extraction and purification applications, including in food, nuclear waste, petrochemical and pharmaceutical industries [1][2][3][4]. Supercritical fluids attract significant attention due to their extremely good dissolving power and "tunable" properties. The solubility of supercritical fluids depend on density and diffusivity. Supercritical fluids combine the best of both worlds: high density of liquids and large diffusion constants of gases. Moreover, both of those properties can be tuned over a wide range pressure and temperature above the critical point, optimizing their dissolving ability.Carbon dioxide, water and methane are three most commonly used supercritical fluids. In particular, H 2 O and CO 2 , are both abundant, non flammable and non toxic. They are also "non-polar" and "polar" solvent, respectively, so they can dissolve "polar" and "non-polar" solutes, respectively. The critical temperature (T c ) of CO 2 is at 304 K, which is near the room temperature, and the critical pressure (P c ) is 74 bar, which is also accessible. Additionally, CO 2 can be used with co-solvents to modify it into "polar" solvent.The solubility of variety of solutes have been measured in supercritical CO 2 near the T c as a function of pressure [1]. Interestingly, the experiment show intriguing solubility maxima above critical temperature: solubility first substantially increase with pressure, followed by its decrease at higher pressure [5][6][7][8][9][10][11][12]. This effect is not currently understood theoretically. Understanding it would lead to more efficiently use of supercritical fluids. More generally, it is often acknowledged that wider deployment of supercritical fluids and optimizing their use would benefit from a theoretical guidance [1,2].Until recently, supercritical state was believed to be physically homogeneous, which means that moving along any path on a pressure and temperature above the critical point does not involve marked or distinct changes. The Frenkel line has recently been proposed, which separates two dynamically distinct states: the gas-like regime where particle only have diffusive motion and the liquidlike regime where particle combine both solid-like quasiharmon...

Structure of liquid carbon dioxide at pressures up to 10 GPa

“…We observe that all the data points collected in the supercritical region are located on the right side of the Frenkel line reported in Ref. [17] [line (5) in Fig. 1] and thus correspond to liquidlike states.…”

“…Notably, the phase diagram of CO 2 at conditions of high pressure and temperature has been the subject of many investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], the main results of which are summarized in Fig. 1.…”

“…Line (5) is the Frenkel line reported in Ref. [17]. The red lines with crosses show the two isotherms investigated in the present paper.…”

Reply to “Comment on ‘Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants’ ”

“…However, the points of the minima of the speed of sound in our analysis terminate at 0.5 GPa, approxi mately up to the pressure where the experimental data [8] are available. Above 0.5 GPa and up to 50 GPa, the Frenkel line was located not on the basis of the minima of the speed of sound but using (a) the scaling argument of parallelism between the melting line and the Frenkel line, the parallelism confirmed by recent molecular-dynamics (MD) simulations in several supercritical fluids [9,10], and (b) our previous result from MD simulations that the Frenkel line starts not far from the critical point (around 0.87]-) [3,5,9,10]. This pressure range constitutes almost the entire range of the Frenkel line presented in our Ref.…”

Dynamical crossover in supercritical core-softened fluids

“…These regions differ by the microscopic dynamics of particles and are separated by a crossover line called Frenkel line. Later on the phenomenon of dynamical crossover was studied for a number of other fluids [4][5][6][7][8].Another topic attracting wide attention of researchers is related to anomalous behavior of liquids (see, for example, [9] for the list of anomalies of water). It was found that models with isotropic pair core-softened potentials can demonstrate anomalous behavior [10][11][12][13][14][15][16][17].…”