The manuscript ignores Gibbs phase rule (see remark 2.1) that prevents any method of coexistence
calculation from imposing temperature and liquid density at the same time. Solving only for vapor
density is a necessary step but liquid density is also an unknown in coexistence calculations. As
applications provide consistent results (see remark 3.1) with earlier work it is likely that the liquid
densities have been either (i) taken from previous work cited in reference, or (ii) that ITIC contains some
undocumented process to evaluate liquid density and related uncertainties (see remark 2.5).
2.1 In equation (1) it would be appropriate to recall which variables can be imposed and which
variables must be determined when computing phase equilibrium for a pure compound. As a result of
Gibbs phase rule, you cannot impose two variables such as temperature and liquid density. This
fundamental point is completely ignored in the manuscript (see also remark 2.4 and 2.5).
2.2 In equation 6, the variable Aig should be clearly defined : it is of course the free energy of the
ideal gas state, but in which conditions : same temperature and volume ? For a dense phase, is this a
physical state or an imaginary state ? What about conformer changes when heating/cooling ?
2.3 In equation (11) the limitations involved when truncating the virial expansion for Zvap should be
mentioned. The larger the density, the higher the order of the virial expansion required for an accurate
representation of pressure‐volume relationship.
2.4 The explanations on the solution of equation (15) for vapor density is surprising. Indeed, the
properties of the liquid phase are considered to be known, while they are also unknown variables when computing a phase equilibrium. In the examples shown by the authors (ethane, dodecane, water), the
liquid density is known from previous work using GEMC and thermodynamic integration. However, this
will no more be the case when more complex compounds will be investigated. In this respect, it is worth
pointing out that on the schematic plot of figure 1, the saturated liquid points 11, 13, 15, 17 and 19 are
considered to be known state points. In the Supplementary information file, these points are not
provided, but they are bracketed by higher density and lower density liquid state points. The
determination of saturated liquid density is somewhat obscure in the manuscript.
2.5 It appears that the authors have forgotten to mention a key step that should be mentioned if
changing ITIC into a sound algorithm. When the vapor density is obtained by solving eq. (15) and vapor
pressure by equation (16), the vapor pressure is imposed to the liquid phase so that its properties
(density, free energy ) can be precised (this is the classical substitution method used to solve phase
equilibrium with equations of state far from the critical point) . The ITIC method would then allow phase
equilibrium to be solved far from the critical point, when liquid properties depend little on the output of
eq. (15) and (16). Schematically, the ITIC method would work with these improvements for low reduced
temperatures (below 0.65) because in these conditions the equilibrium pressure is between 0 and 1
atm, and liquid properties do not change much when pressure changes by less than 1 bar. For Tr> 0.65
higher vapor pressures are found, and the liquid properties are changed more significantly, requiring to
iterate several times until the liquid and vapor properties appearing in eq. (15) do not change any more.
Omitting the phase rule and its consequences in solving phase equilibrium is certainly a major
fundamental flaw of the manuscript.
2.6 The method relies on the compressibility factor Z = PV/RT , thus it relies on consistent
pressure/volume relations in a large range.
2.7 As presented, the ITIC method involves a thermodynamic path that involves (a) an isochoric
temperature increase of the liquid up to Tr~ 1.2, which raises its pressure to very high values (b) an
isothermal volume increase, during which pressure‐volume work is important, (c) an isochoric
temperature decrease to recover the initial temperature. It is surprising that most of the text is spent is
discussing the volumetric behavior of low density phases using empirical virial expansions to the 2nd or
3d order, and integration steps (a) and (b) are little discussed. It would have been interesting to indicate
the accuracy requirements on the external energy, which is probably the most important factor in step
(a) and the accuracy requirement on pressure of dense phases which is involved in the computation of
the compressibility factor Z.
The manuscript ignores Gibbs phase rule (see remark 2.1) that prevents any method of coexistence calculation from imposing temperature and liquid density at the same time. Solving only for vapor density is a necessary step but liquid density is also an unknown in coexistence calculations. As applications provide consistent results (see remark 3.1) with earlier work it is likely that the liquid densities have been either (i) taken from previous work cited in reference, or (ii) that ITIC contains some undocumented process to evaluate liquid density and related uncertainties (see remark 2.5).
2.1 In equation (1) it would be appropriate to recall which variables can be imposed and which variables must be determined when computing phase equilibrium for a pure compound. As a result of Gibbs phase rule, you cannot impose two variables such as temperature and liquid density. This fundamental point is completely ignored in the manuscript (see also remark 2.4 and 2.5).
2.2 In equation 6, the variable Aig should be clearly defined : it is of course the free energy of the ideal gas state, but in which conditions : same temperature and volume ? For a dense phase, is this a physical state or an imaginary state ? What about conformer changes when heating/cooling ?
2.3 In equation (11) the limitations involved when truncating the virial expansion for Zvap should be mentioned. The larger the density, the higher the order of the virial expansion required for an accurate representation of pressure‐volume relationship.
2.4 The explanations on the solution of equation (15) for vapor density is surprising. Indeed, the properties of the liquid phase are considered to be known, while they are also unknown variables when computing a phase equilibrium. In the examples shown by the authors (ethane, dodecane, water), the liquid density is known from previous work using GEMC and thermodynamic integration. However, this will no more be the case when more complex compounds will be investigated. In this respect, it is worth pointing out that on the schematic plot of figure 1, the saturated liquid points 11, 13, 15, 17 and 19 are considered to be known state points. In the Supplementary information file, these points are not provided, but they are bracketed by higher density and lower density liquid state points. The determination of saturated liquid density is somewhat obscure in the manuscript.
2.5 It appears that the authors have forgotten to mention a key step that should be mentioned if changing ITIC into a sound algorithm. When the vapor density is obtained by solving eq. (15) and vapor pressure by equation (16), the vapor pressure is imposed to the liquid phase so that its properties (density, free energy ) can be precised (this is the classical substitution method used to solve phase equilibrium with equations of state far from the critical point) . The ITIC method would then allow phase equilibrium to be solved far from the critical point, when liquid properties depend little on the output of eq. (15) and (16). Schematically, the ITIC method would work with these improvements for low reduced temperatures (below 0.65) because in these conditions the equilibrium pressure is between 0 and 1 atm, and liquid properties do not change much when pressure changes by less than 1 bar. For Tr> 0.65 higher vapor pressures are found, and the liquid properties are changed more significantly, requiring to iterate several times until the liquid and vapor properties appearing in eq. (15) do not change any more. Omitting the phase rule and its consequences in solving phase equilibrium is certainly a major fundamental flaw of the manuscript.
2.6 The method relies on the compressibility factor Z = PV/RT , thus it relies on consistent pressure/volume relations in a large range.
2.7 As presented, the ITIC method involves a thermodynamic path that involves (a) an isochoric temperature increase of the liquid up to Tr~ 1.2, which raises its pressure to very high values (b) an isothermal volume increase, during which pressure‐volume work is important, (c) an isochoric temperature decrease to recover the initial temperature. It is surprising that most of the text is spent is discussing the volumetric behavior of low density phases using empirical virial expansions to the 2nd or 3d order, and integration steps (a) and (b) are little discussed. It would have been interesting to indicate the accuracy requirements on the external energy, which is probably the most important factor in step (a) and the accuracy requirement on pressure of dense phases which is involved in the computation of the compressibility factor Z.