Comments on article

Comments on article OBSERVATION OF LIQUID-LIQUID PHASE TRANSITIONS IN ETHANE AT 300 K

THE AIM OF OUR COMMENTS The aim of our comments is to explain the experiments published in [1] by supramolecular structure of fluids derived on the base of Roger Boscovich’s (1711-1778) comprehensions [2,3]. Hence, we extracted from [1] some important issues, i.e. proposals, findings, conclusions, empirical facts and comment them.

EXTRACT FROM [1] Authors [1] conducted Raman spectroscopy experiments on liquid ethane at 300 K and high pressures. They recognized several transitions: (a) Nonrigid to rigid liquid-like behavior at a density of ca. 10 molecules nm-3 at pressure of about 70 MPa. (b) Transition between rigid and nonrigid liquid states at ca. 250 MPs (fig. 3a) corresponding to the recently proposed Frenkel line, a dynamic transition between rigid liquid (liquid-like) and nonrigid liquid (gas-like) states beginning in the subcritical region and extending to arbitrarily high pressure and temperature.

Figure 3a Variation of 11 peak position and width as a function of pressure. The peak shifts to lower frequency upon pressure increase at extremely low pressures below ca. 250 MPa (shaded region). Lines are guides to the eye only and have no physical significance [1].

(c) Narrow transition at ca. 1000 MPa to a second rigid liquid state (figs. 2a and 4a) Authors [1] proposed that this corresponds to a state in which orientational order must exist to achieve the expected density.

Figure 2a. Variation of 3 peak width and normalized intensity as a function of pressure, showing transition at ca. 1000 MPa (shaded). Lines are guides to the eye only and have no physical significance [1].

Figure 4a. Plot of 26 peak position and width as a function of pressure, demonstrating transition at ca. 1000 MPa (shaded). Lines are guides to the eye only and have no physical significance [1].

SUPRAMOLECULAR STRUCTURES OF FLUIDS DERIVED BY BOSCOVICH’S COMPREHENSIONS [3]

Our model of liquid and  phase: 3D rotating bimolecules are in bubbles (discontinuous disordered non-rigid “gas-like” micro-phase) which are dispersed in continuous ordered rigid phase of 1D rotating oligomolecules /3,17/

Figure A. Phase states and supramolecular structure of ethylene [3,4]. The distances between the molecules in supramolecular particles correspond to the positions at which attractive and repulsive forces are in equilibrium, i.e. the total force is zero (fig. B). These equilibrium positions represent some definite characteristic states of matter. There are universal and very simple mathematical relations between their volumes (fig. C).

Figure B.

Boscovich's curve for fluids. We completed it with supermolecular particles, characteristic volumes of matter and phase states [3]

2

Figure C. Correlation between critical volume Vc and characteristic volumes of matter and corresponding particles [3,5,6]. (Confirmed by empirical data (175 sets of data for 144 substances) taken from literature: 6 sets of metals, 13 sets for inert gases, 25 elements, 6 unsaturated and 19 saturated hydrocarbons, 12 aromatics, and several dozen organic compounds of oxygen, nitrogen, sulfur and halogens.)

Transition of nonrigid to rigid liquid-like behavior occurs above critical point at critical isentrope conditions (S/Sc = 1, i.e.  to  phase transition) and condensation-boiling conditions below critical point. By cooling, bimolecules which rotate about three axes (3D rotation) are transformed to oligomolecules which molecules rotate about one axis (1D rotation). Liquid and  phases consist of bimolecular and oligomolecular microphases [3].

ETHANE PHASE TRANSITION AT 70 MPa Finding (a) in [1]: For ethane, transition of nonrigid to rigid liquid-like behavior occurs at a density of ca. 10 molecules nm-3; this corresponds to a pressure of about 70 MPa [1]. Our comments: We calculated that this density corresponds to molar volume V70 = 60.22 cm3/mol. The value of V70 is very close to van der Waals constant b = 63.8 cm3/mol (experimental value [7]), i.e. volume of rotating bimolecule of ethane.

ETHANE PHASE TRANSITION AT 250 MPa Our comments and prediction: With the increase of pressure, i.e. decrease of volume, more and more 3D rotating bimolecules are transformed to 1D rotating oligomolecules. Having Vc = 148 cm3/mol, molar volume of ethane oligomolecule can be calculated by relation in fig. C: Vom = (21/3/4) Vc = 46.6 cm3/mol. When this volume is achieved by compression, there is no enough space for 3D rotation of bimolecules; all 3D rotating bimolecules are completely transformed to 1D rotating oligomolecules. At V = Vom only oligomolecules are present. This volume Vom is achieved at  400 MPa (fig. 1) [1] Finding (b) in [1]: There is transition at 250 MPa: it started at 125 MPa and finished at 375 MPa (figs. 3a and 5a in [1]). Corresponding volumes are V250  50 and V375  47 cm3/mol (roughly estimated from fig. 1).

Figure 1. Experimental EOS data for ethane from NIST20 (circles), EOS calculated using ThermoC software22 (lines) and volume of ethane in the solid phase IV following crystallization [1]

OUR PROPOSAL OF OLIGOMOLECULE STRUCTURE Authors [1] accepted that ethane molecule can be considered as a rigid rod with dimensions 4.755 Å x 3.988 Å (fig. D). We propose that 3D rotating ethane bimolecule has cross structure (fig. E) as it was proposed for ethylene bimolecule (fig. G) [4].

Figure D. Ethane molecule as rigid rod.

Figure E. Proposed cross structure of 3D rotating ethane bimolecule

Figure G. Cross structure of 3 D rotting ethylene bimolecule [4]

We propose that 1D rotating ethane oligomolecule has cross structure (fig. H), as it was proposed for ethylene oligomolecules [4], since both originate by cooling and merging the cross bimolecules. In a cross oligomolecule (OMC), all molecules rotate around their transversal axes.

Figure H. 1D rotating cross oligomolecule (OMC) of ethane Rc = 4.755/2 Å, Lc = 3.988 Å Vomc = π Rc2 Lc N = 42.64 cm3/mol. (N is Avogadro’s number, N = 6.022 1023 molecules/mole.)

Molar volume of OMC is Vomc = 42.64 cm3/mol calculated only by the dimensions of ethane molecule, but the distance between molecules was not taken into account. To calculate the volume of compressed liquid ethane (V liq,omc) that contains only OMCs, it is necessary to take into account the voids between them. For close packed cylinders, fraction of filled space is 0.9 [10]. Hence Vliq,omc = Vomc/0.9 = 42.64 / 0.9 = 47.4 cm3/mol. SUMMARY. There is very good agreement for the volumes of at the end of phase transition in the range 125-375 MPa: - Experimental value: V375  47 cm3/mol 1/3 - Calculated by critical volume, i.e. Vom = (2 /4) Vc: Vom = = 46.6 cm3/mol - Calculated by dimensions of ethane molecules in OMC: Vliq,omc = 47.4 cm3/mol

ETHANE PHASE TRANSITION AT 1000 MPa Our proposal: Liquid ethane, however, can be compressed to volume V lower than Vliq,omc. It means that some new kind of supramolecular particles are formed with the molecules which need less space for rotation. It is reasonable to assume that there is a gradual restructuring of rotating crosswise (fig. H) to 1D rotating linear oligomolecules (OML) (fig. I). Molar volume of 1D rotating linear oligomolecule, calculated by the dimensions of ethane molecule, is VomL = 35.75 cm3/mol. 4

To calculate the volume of compressed liquid ethane (Vliq,omL) that contains only OMLs, it is necessary to take into account the voids between them. For close packed cylinders, fraction of filled space is 0.9 [10]. Hence Vliq,omL = VomL/0.9 = 35.75 / 0.9 = 39.72 cm3/mol. Figure I. Linear 1D rotating ethane oligomolecule (OML); RL = 3.988/2 Å, LL = 4.755 Å VomL = π Rl2 Ll N = 35.75 cm3/mol. Finding in [1]: Some transition was noticed in the range 900 to 1100 MPa (figs. 2a and 4a in [1]). The highest intensity is at 1000 MPa at V1000  42 cm3/mol (fig. 1). If the volume Vliq of ethane is Vliq,omc