We present a classical density functional theory (DFT) for fluid mixtures that is based on a third-order thermodynamic perturbation theory of Feynman-Hibbs-corrected Mie potentials. The DFT is developed to study the interfacial properties of hydrogen, helium, neon, deuterium, and their mixtures, i.e., fluids that are strongly influenced by quantum effects at low temperatures. White Bear fundamental measure theory is used for the hard-sphere contribution of the Helmholtz energy functional, and a weighted density approximation is used for the dispersion contribution. For mixtures, a contribution is included to account for non-additivity in the Lorentz–Berthelot combination rule. Predictions of the radial distribution function from DFT are in excellent agreement with results from molecular simulations, both for pure components and mixtures. Above the normal boiling point and 5% below the critical temperature, the DFT yields surface tensions of neon, hydrogen, and deuterium with average deviations from experiments of 7.5%, 4.4%, and 1.8%, respectively. The surface tensions of hydrogen/deuterium, para-hydrogen/helium, deuterium/helium, and hydrogen/neon mixtures are reproduced with a mean absolute error of 5.4%, 8.1%, 1.3%, and 7.5%, respectively. The surface tensions are predicted with an excellent accuracy at temperatures above 20 K. The poor accuracy below 20 K is due to the inability of Feynman–Hibbs-corrected Mie potentials to represent the real fluid behavior at these conditions, motivating the development of new intermolecular potentials. This DFT can be leveraged in the future to study confined fluids and assess the performance of porous materials for hydrogen storage and transport.

1.
H. L.
Frisch
and
P.
Nielaba
,
J. Chem. Phys.
105
,
7238
(
1996
).
2.
X.
Zhao
,
J. K.
Johnson
, and
C. E.
Rasmussen
,
J. Chem. Phys.
120
,
8707
(
2004
).
3.
A.
Ramiere
,
S.
Volz
, and
J.
Amrit
,
Nat. Mater.
15
,
512
(
2016
).
4.
A.
Bauer
,
T.
Mayer
,
M.
Semmel
,
M. A. G.
Morales
, and
J.
Wind
,
Int. J. Hydrogen Energy
44
,
6795
(
2019
).
5.
Ø.
Wilhelmsen
,
D.
Berstad
,
A.
Aasen
,
P.
Nekså
, and
G.
Skaugen
,
Int. J. Hydrogen Energy
43
,
5033
(
2018
).
6.
D.
Berstad
,
G.
Skaugen
, and
Ø.
Wilhelmsen
,
Int. J. Hydrogen Energy
46
,
8014
(
2021
).
7.
G.
Skaugen
,
D.
Berstad
, and
Ø.
Wilhelmsen
,
Int. J. Hydrogen Energy
45
,
6663
(
2020
).
8.
H.
Oh
,
I.
Savchenko
,
A.
Mavrandonakis
,
T.
Heine
, and
M.
Hirscher
,
ACS Nano
8
,
761
(
2014
).
9.
J. P.
Toennies
,
A. F.
Vilesov
, and
K. B.
Whaley
,
Phys. Today
54
(
2
),
31
(
2001
).
10.
J. M.
Salazar
,
S.
Lectez
,
C.
Gauvin
,
M.
Macaud
,
J. P.
Bellat
,
G.
Weber
,
I.
Bezverkhyy
, and
J. M.
Simon
,
Int. J. Hydrogen Energy
42
,
13099
(
2017
).
11.
J. M.
McMahon
,
M. A.
Morales
,
C.
Pierleoni
, and
D. M.
Ceperley
,
Rev. Mod. Phys.
84
,
1607
(
2012
).
12.
D. M.
Ceperley
,
Rev. Mod. Phys.
67
,
279
(
1995
).
13.
L. M.
Sesé
and
R.
Ledesma
,
J. Chem. Phys.
102
,
3776
(
1995
).
14.
L. M.
Sesé
and
L. E.
Bailey
,
J. Chem. Phys.
119
,
10256
(
2003
).
15.
Q.
Wang
and
J. K.
Johnson
,
Fluid Phase Equilib.
132
,
93
(
1997
).
16.
A.
Gil-Villegas
,
A.
Galindo
,
P. J.
Whitehead
,
S. J.
Mills
,
G.
Jackson
, and
A. N.
Burgess
,
J. Chem. Phys.
106
,
4168
(
1997
).
18.
J. G.
Kirkwood
,
Phys. Rev.
44
,
31
(
1933
).
19.
R. P.
Feynman
,
A. R.
Hibbs
, and
D. F.
Styer
,
Quantum Mechanics and Path Integrals
, Emended ed. (
McGraw-Hill
,
New York
,
2005
), p.
384
.
20.
A. V. A.
Kumar
,
H.
Jobic
, and
S. K.
Bhatia
,
J. Phys. Chem. B
110
,
16666
(
2006
).
21.
F.
Calvo
,
J. P. K.
Doye
, and
D. J.
Wales
,
J. Chem. Phys.
114
,
7312
(
2001
).
22.
R.
Rodríguez-Cantano
,
R.
Pérez de Tudela
,
M.
Bartolomei
,
M. I.
Hernández
,
J.
Campos-Martínez
,
T.
González-Lezana
,
P.
Villarreal
,
J.
Hernández-Rojas
, and
J.
Bretón
,
J. Phys. Chem. A
120
,
5370
(
2016
).
23.
P.
Kowalczyk
,
L.
Brualla
,
P. A.
Gauden
, and
A. P.
Terzyk
,
Phys. Chem. Chem. Phys.
11
,
9182
(
2009
).
24.
V. M.
Trejos
,
A.
Gil-Villegas
, and
A.
Martinez
,
J. Chem. Phys.
139
,
184505
(
2013
).
25.
A.
Aasen
,
M.
Hammer
,
Å.
Ervik
,
E. A.
Müller
, and
Ø.
Wilhelmsen
,
J. Chem. Phys.
151
,
064508
(
2019
).
26.
A.
Aasen
,
M.
Hammer
,
E. A.
Müller
, and
Ø.
Wilhelmsen
,
J. Chem. Phys.
152
,
074507
(
2020
).
27.
A.
Aasen
,
M.
Hammer
,
S.
Lasala
,
J.-N.
Jaubert
, and
Ø.
Wilhelmsen
,
Fluid Phase Equilib.
524
,
112790
(
2020
).
28.
J.
Navarro
,
F.
Ancilotto
,
M.
Barranco
, and
M.
Pi
,
J. Phys. Chem. A
115
,
6910
(
2011
).
29.
P.
Rehner
,
A.
Aasen
, and
Ø.
Wilhelmsen
,
J. Chem. Phys.
151
,
244710
(
2019
).
30.
A.
Aasen
,
D.
Reguera
, and
Ø.
Wilhelmsen
,
Phys. Rev. Lett.
124
,
045701
(
2020
).
31.
Ø.
Wilhelmsen
,
T. T.
Trinh
,
S.
Kjelstrup
, and
D.
Bedeaux
,
J. Phys. Chem. C
119
,
8160
(
2015
).
32.
C.
Klink
,
C.
Waibel
, and
J.
Gross
,
Ind. Eng. Chem. Res.
54
,
11483
(
2015
).
33.
R.
Stierle
,
C.
Waibel
,
J.
Gross
,
C.
Steinhausen
,
B.
Weigand
, and
G.
Lamanna
,
Int. J. Heat Mass Transfer
151
,
119450
(
2020
).
34.
J.
Eller
and
J.
Gross
,
Langmuir
37
,
3538
(
2021
).
35.
E.
Sauer
and
J.
Gross
,
Ind. Eng. Chem. Res.
56
,
4119
(
2017
).
36.
J.
Mairhofer
and
J.
Gross
,
Fluid Phase Equilib.
439
,
31
(
2017
).
37.
E.
Sauer
,
A.
Terzis
,
M.
Theiss
,
B.
Weigand
, and
J.
Gross
,
Langmuir
34
,
12519
(
2018
).
38.
P. J.
Leonard
,
D.
Henderson
, and
J. A.
Barker
,
Trans. Faraday Soc.
66
,
2439
(
1970
).
39.
M.
Hammer
,
A.
Aasen
,
Å.
Ervik
, and
Ø.
Wilhelmsen
,
J. Chem. Phys.
152
,
134106
(
2020
).
40.
T.
Lafitte
,
A.
Apostolakou
,
C.
Avendaño
,
A.
Galindo
,
C. S.
Adjiman
,
E. A.
Müller
, and
G.
Jackson
,
J. Chem. Phys.
139
,
154504
(
2013
).
41.
R.
Stierle
,
E.
Sauer
,
J.
Eller
,
M.
Theiss
,
P.
Rehner
,
P.
Ackermann
, and
J.
Gross
,
Fluid Phase Equilib.
504
,
112306
(
2020
).
42.
43.
R.
Roth
,
R.
Evans
,
A.
Lang
, and
G.
Kahl
,
J. Phys.: Condens. Matter
14
,
12063
(
2002
).
44.
T.
Boublík
,
J. Chem. Phys.
53
,
471
(
1970
).
45.
G. A.
Mansoori
,
N. F.
Carnahan
,
K. E.
Starling
, and
T. W.
Leland
,
J. Chem. Phys.
54
,
1523
(
1971
).
46.
Y.-X.
Yu
and
J.
Wu
,
J. Chem. Phys.
116
,
7094
(
2002
).
47.
M. G.
Knepley
,
D. A.
Karpeev
,
S.
Davidovits
,
R. S.
Eisenberg
, and
D.
Gillespie
,
J. Chem. Phys.
132
,
124101
(
2010
).
48.
R.
Stierle
and
J.
Gross
,
Fluid Phase Equilib.
511
,
112500
(
2020
).
49.
50.
D. G. M.
Anderson
,
Numer. Algorithms
80
,
135
(
2019
).
51.
52.
P.
Pulay
,
J. Comput. Chem.
3
,
556
(
1982
).
53.
A.
Kovalenko
,
S.
Ten-no
, and
F.
Hirata
,
J. Comput. Chem.
20
,
928
(
1999
).
54.
J.
Mairhofer
and
J.
Gross
,
Fluid Phase Equilib.
444
,
1
(
2017
).
55.
J.
Mairhofer
,
B.
Xiao
, and
J.
Gross
,
Fluid Phase Equilib.
472
,
117
(
2018
).
56.
J. K.
Percus
,
Phys. Rev. Lett.
8
,
462
(
1962
).
57.
J.
Eller
,
T.
Matzerath
,
T.
van Westen
, and
J.
Gross
,
J. Chem. Phys.
154
,
244106
(
2021
).
58.
A. P.
Thompson
,
H. M.
Aktulga
,
R.
Berger
,
D. S.
Bolintineanu
,
W. M.
Brown
,
P. S.
Crozier
,
P. J.
in ’t Veld
,
A.
Kohlmeyer
,
S. G.
Moore
,
T. D.
Nguyen
,
R.
Shan
,
M. J.
Stevens
,
J.
Tranchida
,
C.
Trott
, and
S. J.
Plimpton
,
Comput. Phys. Commun.
271
,
108171
(
2022
).
59.
P.
Rehner
and
G.
Bauer
,
Front. Chem. Eng.
3
,
758090
(
2021
).
60.
Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, FeOs—Framework for equations of state, https://github.com/feos-org,
2021
.
61.
Ø.
Wilhelmsen
,
A.
Aasen
,
G.
Skaugen
,
P.
Aursand
,
A.
Austegard
,
E.
Aursand
,
M. A.
Gjennestad
,
H.
Lund
,
G.
Linga
, and
M.
Hammer
,
Ind. Eng. Chem. Res.
56
,
3503
(
2017
).
62.
SINTEF Energy Research and NTNU, Thermopack open source thermodynamics library, https://github.com/thermotools/thermopack/,
2020
.
63.
A.
Mulero
,
I.
Cachadiña
, and
M. I.
Parra
,
J. Phys. Chem. Ref. Data
41
,
043105
(
2012
).
64.
J. W.
Leachman
,
R. T.
Jacobsen
,
S. G.
Penoncello
, and
E. W.
Lemmon
,
J. Phys. Chem. Ref. Data
38
,
721
(
2009
).
65.
I. A.
Richardson
,
J. W.
Leachman
, and
E. W.
Lemmon
,
J. Phys. Chem. Ref. Data
43
,
013103
(
2014
).
66.
R.
Katti
,
R. T.
Jacobsen
,
R. B.
Stewart
, and
M.
Jahangiri
, in
Advances in Cryogenic Engineering
, edited by
R. W.
Fast
(
Springer US
,
Boston, MA
,
1986
), Vol. 31, pp.
1189
1197
.
67.
G.
Baidakov
,
K. V.
Khvostov
, and
V. P.
Skripov
,
Fiz. Nizk. Temp.
7
,
957
(
1981
).
68.
V. G.
Baidakov
and
K. V.
Khvostov
,
Sov. J. Low Temp. Phys.
8
,
233
(
1982
).
69.
E. A.
Guggenheim
,
J. Chem. Phys.
13
,
253
(
1945
).
70.
V. G.
Baidakov
,
Fiz. Nizk. Temp.
10
,
677
(
1984
).
71.
V. N.
Grigorev
and
N. S.
Rudenko
,
Sov. Phys. JETP
20
(
1
),
63
66
(
1965
).
72.
C. G.
Paine
and
G. M.
Seidel
,
Phys. Rev. B
46
,
1043
(
1992
).
73.
C. G.
Paine
and
G. M.
Seidel
,
Phys. B: Condens. Matter
194-196
,
969
(
1994
).
74.
Y. P.
Blagoi
and
V. V.
Pashkov
,
Sov. Phys. JETP
28
(
1
),
31
33
(
1969
).
75.
C. G.
Paine
and
G. M.
Seidel
,
Phys. Rev. B
50
,
3134
(
1994
).
76.
P.
Rehner
, “
Interfacial properties using classical density functional theory: Curved interfaces and surfactants
,” Ph.D. thesis,
University of Stuttgart
,
2021
.

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