Comment pubs.acs.org/JPCB
Comment on “New Zeno-like Liquid States” I. H. Umirzakov* Institute of Thermophysics, Lavrentev prospect, 1, 630090 Novosibirsk, Russia
J. Phys. Chem. B 2016, 120 (15), 3705−3712. DOI: 10.1021/acs.jpcb.6b01364
I
ρg* /ρc = 2/(1 − Tc/Tc*)
t was shown that saturated liquid densities are a linear function of temperature T in the normal liquid range for molecular, polymeric, inorganic, ionic, and metallic liquids and superpose to form a single master curve.1 We will show that the existence of master curve is the consequence of rectilinear diameter law (or Cailletet−Mathias law), which is one of the main tools to define a critical density and temperature.2,3 The law can be presented as (ρL + ρV )/2ρc = 1 + A ·(1 − T /Tc)
As one can see from Table 1 the values of ρ*g /ρc, obtained from eq 3, are very close to each other for 30 of 40 substances. Therefore, we conclude that the existence of a single master curve is the consequence of rectilinear diameter law and eqs 2 might be useful for estimating critical densities from the critical temperature.
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(1)
where ρL and ρV are densities of liquid and vapor coexisting in conditions of phase equilibrium, ρc and Tc are values of density and temperature at a critical point of first order phase transition, and A is approximately constant. We suppose that A = const at low temperatures. We have ρL = ρ0 and ρV = 0 at T = 0. Therefore, we obtain from (1) A = ρ0/2ρc − 1. The density of vapor is negligibly small in comparison with the density of liquid at temperatures corresponding to small pressure: ρV ≪ ρL. Therefore, eq 1 can be presented as ρL /ρ0 + T /T0c = 1
T0c = Tc/(1 − 2ρc /ρ0 )
(3)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The author declares no competing financial interest.
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REFERENCES
(1) Sanches, I. C.; O’Keefe, S.; Xu, J. F. New Zeno-like Liquid States. J. Phys. Chem. B 2016, 120, 3705−3712. (2) Partington, J. R. Treatise on Physical Chemistry; Longmans, Green and Co.: London, 1949; Vol. 1. (3) Hirschfelder, J. O.; Curtis, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; J. Wiley and Sons: New York, 1954.
(2)
If we put ρ0 = ρg* and T0c = Tc* in eqs 2, then we obtain the single master curve (6) of ref 1 and
Table 1. Comparison of the Values of ρ*g /ρc, Obtained from Eq 3 Using T*c /Tc from Tables 1 and 3 of ref 1, with Those of the Tables of Ref 1 (δ = ρg*(3)/ρg* − 1) substance
T*c /Tc
ρ*g /ρc
ρ*g /ρc (3)
δ
substance
T*c /Tc
ρ*g /ρc
ρ*g /ρc (3)
δ
argon krypton xenon methane oxigen nitrogen CO ethylene ethane propane butane pentane hexane decane dodecane C6H12 C6H6 C6H5CH3 C(CH3)4 H2S
2.08 2.09 2.10 2.18 2.19 2.10 2.04 2.19 2.17 2.14 2.11 2.10 2.03 1.96 1.90 2.00 1.98 2.05 2.00 2.06
3.60 3.66 3.66 3.55 3.58 3.64 3.73 3.70 3.65 3.73 3.80 3.85 3.95 4.12 4.33 3.89 3.86 3.91 3.77 3.79
3.85 3.83 3.82 3.69 3.68 3.82 3.92 3.68 3.71 3.75 3.80 3.82 3.94 4.08 4.22 4.00 4.04 3.90 4.00 3.89
0.07 0.05 0.04 0.04 0.03 0.05 0.05 −0.01 0.02 0.01 0.00 −0.01 0.00 −0.01 −0.02 0.03 0.05 0.00 0.06 0.03
CF4 CHF3 CH2F2 CH3F C2F5H C2F6 ammonia methanol aluminum magnesium lithium sodium potassium rubidium cesium sulfur SnCl4 TiCl4 SbCl3 AlCl3
2.09 2.02 2.00 1.96 1.99 1.95 2.07 2.09 1.69 3.00 1.74 1.65 1.67 1.72 1.76 2.70 1.95 2.00 1.90 1.50
3.70 4.02 4.18 4.05 3.96 3.97 4.26 3.90 4.6 4.4 4.7 4.9 4.7 5.5 5.3 3.7 4.0 3.9 3.9 5.0
3.83 3.96 4.00 4.08 4.02 4.11 3.87 3.83 4.90 3.00 4.70 5.08 4.99 4.78 4.63 3.18 4.11 4.00 4.22 6.00
0.04 −0.01 −0.04 0.01 0.02 0.03 −0.09 −0.02 0.06 −0.32 0.00 0.04 0.06 −0.13 −0.13 −0.14 0.03 0.03 0.08 0.20
Received: February 15, 2017 Revised: March 12, 2017 Published: April 21, 2017 © XXXX American Chemical Society
A
DOI: 10.1021/acs.jpcb.7b01515 J. Phys. Chem. B XXXX, XXX, XXX−XXX
