It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent appears to be related to the two-body interactions in the dilute-gas limit.
REFERENCES
1.
J. C.
Dyre
, “Perspective: Excess-entropy scaling
,” J. Chem. Phys.
149
, 210901
(2018
).2.
D.
Fragiadakis
and C. M.
Roland
, “Intermolecular distance and density scaling of dynamics in molecular liquids
,” J. Chem. Phys.
150
, 204501
(2019
).3.
I. H.
Bell
, “Probing the link between residual entropy and viscosity of molecular fluids and model potentials
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 4070
–4079
(2019
).4.
D.
Fragiadakis
and C. M.
Roland
, “Connection between dynamics and thermodynamics of liquids on the melting line
,” Phys. Rev. E
83
, 031504
(2011
).5.
Y.
Rosenfeld
, “Relation between the transport coefficients and the internal entropy of simple systems
,” Phys. Rev. A
15
, 2545
–2549
(1977
).6.
Y.
Rosenfeld
, “A quasi-universal scaling law for atomic transport in simple fluids
,” J. Phys.: Condens. Matter
11
, 5415
–5427
(1999
).7.
M.
Dzugutov
, “A universal scaling law for atomic diffusion in condensed matter
,” Nature
381
, 137
–139
(1996
).8.
I. H.
Bell
, R.
Hellmann
, and A. H.
Harvey
, “Zero-density limit of the residual entropy scaling of transport properties
,” J. Chem. Eng. Data
65
, 1038
–1050
(2019
).9.
I. H.
Bell
, R.
Messerly
, M.
Thol
, L.
Costigliola
, and J. C.
Dyre
, “Modified entropy scaling of the transport properties of the Lennard-Jones fluid
,” J. Phys. Chem. B
123
, 6345
–6363
(2019
).10.
X.
Yang
, D.
Kim
, E. F.
May
, and I. H.
Bell
, “Entropy scaling of thermal conductivity: Application to refrigerants and their mixtures
,” Ind. Eng. Chem. Res.
60
, 13052
–13070
(2021
).11.
X.
Yang
, X.
Xiao
, E. F.
May
, and I. H.
Bell
, “Entropy scaling of viscosity—III: Application to refrigerants and their mixtures
,” J. Chem. Eng. Data
66
, 1385
–1398
(2021
).12.
I. H.
Bell
, “Entropy scaling of viscosity—II: Predictive scheme for normal alkanes
,” J. Chem. Eng. Data
65
, 5606
–5616
(2020
).13.
I. H.
Bell
, “Entropy scaling of viscosity—I: A case study of propane
,” J. Chem. Eng. Data
65
, 3203
–3215
(2020
).14.
R.
Casalini
and T. C.
Ransom
, “On the experimental determination of the repulsive component of the potential from high pressure measurements: What is special about twelve?
,” J. Chem. Phys.
151
, 194504
(2019
).15.
F.
Hummel
, G.
Kresse
, J. C.
Dyre
, and U. R.
Pedersen
, “Hidden scale invariance of metals
,” Phys. Rev. B
92
, 174116
(2015
).16.
G.
Galliero
, C.
Boned
, and J.
Fernández
, “Scaling of the viscosity of the Lennard-Jones chain fluid model, argon, and some normal alkanes
,” J. Chem. Phys.
134
, 064505
(2011
).17.
C.
Alba-Simionesco
, D.
Kivelson
, and G.
Tarjus
, “Temperature, density, and pressure dependence of relaxation times in supercooled liquids
,” J. Chem. Phys.
116
, 5033
–5038
(2002
).18.
L.
Bøhling
, T. S.
Ingebrigtsen
, A.
Grzybowski
, M.
Paluch
, J. C.
Dyre
, and T. B.
Schrøder
, “Scaling of viscous dynamics in simple liquids: Theory, simulation and experiment
,” New J. Phys.
14
, 113035
(2012
).19.
A.
Sanz
, T.
Hecksher
, H. W.
Hansen
, J. C.
Dyre
, K.
Niss
, and U. R.
Pedersen
, “Experimental evidence for a state-point-dependent density-scaling exponent of liquid dynamics
,” Phys. Rev. Lett.
122
, 055501
(2019
).20.
T. C.
Ransom
, R.
Casalini
, D.
Fragiadakis
, and C. M.
Roland
, “The complex behavior of the ‘simplest’ liquid: Breakdown of density scaling in tetramethyl tetraphenyl trisiloxane
,” J. Chem. Phys.
151
, 174501
(2019
).21.
J. C.
Dyre
, “Simple liquids’ quasiuniversality and the hard-sphere paradigm
,” J. Phys.: Condens. Matter
28
, 323001
(2016
).22.
N.
Gnan
, T. B.
Schrøder
, U. R.
Pedersen
, N. P.
Bailey
, and J. C.
Dyre
, “Pressure-energy correlations in liquids. IV. ‘Isomorphs’ in liquid phase diagrams
,” J. Chem. Phys.
131
, 234504
(2009
).23.
N. P.
Bailey
, U. R.
Pedersen
, N.
Gnan
, T. B.
Schrøder
, and J. C.
Dyre
, “Pressure-energy correlations in liquids. I. Results from computer simulations
,” J. Chem. Phys.
129
, 184507
(2008
).24.
U. R.
Pedersen
, N. P.
Bailey
, T. B.
Schrøder
, and J. C.
Dyre
, “Strong pressure-energy correlations in van der Waals liquids
,” Phys. Rev. Lett.
100
, 015701
(2008
).25.
T. S.
Ingebrigtsen
, T. B.
Schrøder
, and J. C.
Dyre
, “What is a simple liquid?
,” Phys. Rev. X
2
, 011011
(2012
).26.
H. W.
Hansen
, A.
Sanz
, K.
Adrjanowicz
, B.
Frick
, and K.
Niss
, “Evidence of a one-dimensional thermodynamic phase diagram for simple glass-formers
,” Nat. Commun.
9
, 518
(2018
).27.
cv ≡ T(∂s/∂T)ρ, so we may write or . A similar starting identity of (∂s/∂v)T = (∂p/∂T)v with v = 1/ρ yields the transformation of the numerator.
28.
L.
Costigliola
, “Isomorph theory and extensions
,” Ph.D. thesis, Roskilde University
, Denmark
, 2016
.29.
R.
Lustig
, “Statistical analogues for fundamental equation of state derivatives
,” Mol. Phys.
110
, 3041
–3052
(2012
).30.
I. H.
Bell
, “Effective hardness of interaction from thermodynamics and viscosity in dilute gases
,” J. Chem. Phys.
152
, 164508
(2020
).31.
T.
Maimbourg
, J. C.
Dyre
, and L.
Costigliola
, “Density scaling of generalized Lennard-Jones fluids in different dimensions
,” SciPost Phys.
9
, 90
(2020
).32.
N.
Bailey
, T.
Ingebrigtsen
, J. S.
Hansen
, A.
Veldhorst
, L.
Bøhling
, C.
Lemarchand
, A.
Olsen
, A.
Bacher
, L.
Costigliola
, U.
Pedersen
, H.
Larsen
, J.
Dyre
, and T.
Schrøder
, “RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles
,” SciPost Phys.
3
, 038
(2017
).33.
S.
Deublein
, B.
Eckl
, J.
Stoll
, S. V.
Lishchuk
, G.
Guevara-Carrion
, C. W.
Glass
, T.
Merker
, M.
Bernreuther
, H.
Hasse
, and J.
Vrabec
, “ms2: A molecular simulation tool for thermodynamic properties
,” Comput. Phys. Commun.
182
, 2350
–2367
(2011
).34.
C. W.
Glass
, S.
Reiser
, G.
Rutkai
, S.
Deublein
, A.
Köster
, G.
Guevara-Carrion
, A.
Wafai
, M.
Horsch
, M.
Bernreuther
, T.
Windmann
, H.
Hasse
, and J.
Vrabec
, “ms2: A molecular simulation tool for thermodynamic properties, new version release
,” Comput. Phys. Commun.
185
, 3302
–3306
(2014
).35.
G.
Rutkai
, A.
Köster
, G.
Guevara-Carrion
, T.
Janzen
, M.
Schappals
, C. W.
Glass
, M.
Bernreuther
, A.
Wafai
, S.
Stephan
, M.
Kohns
, S.
Reiser
, S.
Deublein
, M.
Horsch
, H.
Hasse
, and J.
Vrabec
, “ms2: A molecular simulation tool for thermodynamic properties, release 3.0
,” Comput. Phys. Commun.
221
, 343
–351
(2017
).36.
R.
Fingerhut
, G.
Guevara-Carrion
, I.
Nitzke
, D.
Saric
, J.
Marx
, K.
Langenbach
, S.
Prokopev
, D.
Celný
, M.
Bernreuther
, S.
Stephan
, M.
Kohns
, H.
Hasse
, and J.
Vrabec
, “ms2: A molecular simulation tool for thermodynamic properties, release 4.0
,” Comput. Phys. Commun.
262
, 107860
(2021
).37.
B.
Widom
, “Some topics in the theory of fluids
,” J. Chem. Phys.
39
, 2808
–2812
(1963
).38.
M. S.
Green
, “Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids
,” J. Chem. Phys.
22
, 398
–413
(1954
).39.
R.
Kubo
, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems
,” J. Phys. Soc. Jpn.
12
, 570
–586
(1957
).40.
Z.
Zhang
and Z.
Duan
, “An optimized molecular potential for carbon dioxide
,” J. Chem. Phys.
122
, 214507
(2005
).41.
J. G.
Harris
and K. H.
Yung
, “Carbon dioxide’s liquid-vapor coexistence curve and critical properties as predicted by a simple molecular model
,” J. Phys. Chem.
99
, 12021
–12024
(1995
).42.
J.
Vrabec
, J.
Stoll
, and H.
Hasse
, “A set of molecular models for symmetric quadrupolar fluids
,” J. Phys. Chem. B
105
, 12126
–12133
(2001
).43.
T.
Merker
, C.
Engin
, J.
Vrabec
, and H.
Hasse
, “Molecular model for carbon dioxide optimized to vapor-liquid equilibria
,” J. Chem. Phys.
132
, 234512
(2010
).44.
J.
Errington
, “The development of novel simulation methodologies and intermolecular potential models for real fluids
,” Ph.D. thesis, Cornell University
, 1999
.45.
R.
Hellmann
, “Ab initio potential energy surface for the carbon dioxide molecule pair and thermophysical properties of dilute carbon dioxide gas
,” Chem. Phys. Lett.
613
, 133
–138
(2014
).46.
P.
Mausbach
, A.
Köster
, and J.
Vrabec
, “Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry
,” Phys. Rev. E
97
, 052149
(2018
).47.
C. S.
Murthy
, K.
Singer
, and I. R.
McDonald
, “Interaction site models for carbon dioxide
,” Mol. Phys.
44
, 135
–143
(1981
).48.
J. J.
Potoff
and J. I.
Siepmann
, “Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen
,” AIChE J.
47
, 1676
–1682
(2001
).49.
D.
Möller
and J.
Fischer
, “Determination of an effective intermolecular potential for carbon dioxide using vapour-liquid phase equilibria from NpT + test particle simulations
,” Fluid Phase Equilib.
100
, 35
–61
(1994
).50.
J. J.
Potoff
, J. R.
Errington
, and A. Z.
Panagiotopoulos
, “Molecular simulation of phase equilibria for mixtures of polar and non-polar components
,” Mol. Phys.
97
, 1073
–1083
(1999
).51.
N.
Chetty
and V. W.
Couling
, “Measurement of the electric quadrupole moments of CO2 and OCS
,” Mol. Phys.
109
, 655
–666
(2011
).52.
R. L.
Beil
and R. J.
Hinde
, “Ab initio electrical properties of CO2: Polarizabilities, hyperpolarizabilities, and multipole moments
,” Theor. Chem. Acc.
140
, 120
(2021
).53.
54.
I. H.
Bell
, J. C.
Dyre
, and T. S.
Ingebrigtsen
, “Excess-entropy scaling in supercooled binary mixtures
,” Nat. Commun.
11
, 4300
(2020
).55.
M.
Thol
, G.
Rutkai
, A.
Köster
, R.
Lustig
, R.
Span
, and J.
Vrabec
, “Equation of state for the Lennard-Jones fluid
,” J. Phys. Chem. Ref. Data
45
, 023101
(2016
).56.
R.
Span
and W.
Wagner
, “A new equation of state for carbon dioxide covering the fluid region from the triple point temperature to 1100 K at pressures up to 800 MPa
,” J. Phys. Chem. Ref. Data
25
, 1509
–1596
(1996
).57.
E. W.
Lemmon
, I. H.
Bell
, M. L.
Huber
, and M. O.
McLinden
, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0, National Institute of Standards and Technology, http://www.nist.gov/srd/nist23.cfm, 2018
.58.
T. L.
Hill
, An Introduction to Statistical Thermodynamics
(Dover Publications, Inc.
, New York
, 1986
).59.
N. P.
Bailey
, U. R.
Pedersen
, N.
Gnan
, T. B.
Schrøder
, and J. C.
Dyre
, “Pressure-energy correlations in liquids. II. Analysis and consequences
,” J. Chem. Phys.
129
, 184508
(2008
).60.
R. J.
Sadus
, “Second virial coefficient properties of the n-m Lennard-Jones/Mie potential
,” J. Chem. Phys.
149
, 074504
(2018
).61.
R. J.
Sadus
, “Erratum: ‘Second virial coefficient properties of the n-m Lennard-Jones/Mie potential’ [J. Chem. Phys. 149, 074504 (2018)]
,” J. Chem. Phys.
150
, 079902
(2019
).62.
S.
Polychroniadou
, K. D.
Antoniadis
, M. J.
Assael
, and I. H.
Bell
, “A reference correlation for the viscosity of krypton from entropy scaling
,” Int. J. Thermophys.
43
, 6
(2021
).Published by AIP Publishing.
2022
Public Domain
You do not currently have access to this content.