In this paper, we present an overview of results in the literature regarding the thermodynamical scaling of the dynamics of liquids and polymers as measured from high-pressure measurements. Specifically, we look at the scaling exponent γ and argue that it exhibits the limiting behavior γ → 4 in regimes for which molecular interactions are dominated by the repulsive part of the intermolecular potential. For repulsive potentials of the form U(r) ∝ rn, γ has been found to be related to the exponent n via the relation γ = n/3. Therefore, this limiting behavior for γ would suggest that a large number of molecular systems may be described by a common repulsive potential U(r) ∝ rn with n ≈ 12.

1.
R.
Casalini
and
C. M.
Roland
,
Phys. Rev. E
69
,
062501
(
2004
).
2.
C.
Dreyfus
,
A.
Le Grand
,
J.
Gapinski
,
W.
Steffen
, and
A.
Patkowski
,
Eur. J. Phys. B
42
,
309
(
2004
).
3.
C.
Alba-Simionesco
,
A.
Cailliaux
,
A.
Alegria
, and
G.
Tarjus
,
Europhys. Lett.
68
,
58
(
2004
).
4.
C.
Alba-Simionesco
,
D.
Kivelson
, and
G.
Tarjus
,
J. Chem. Phys.
116
,
5033
(
2002
).
5.
C.
Alba-Simionesco
and
G.
Tarjus
,
J. Non-Cryst. Solids
352
,
4888
(
2006
).
6.
C. M.
Roland
,
S.
Hensel-Bielowka
,
M.
Paluch
, and
R.
Casalini
,
Rep. Prog. Phys.
68
,
1405
(
2005
).
7.
R.
Casalini
and
C. M.
Roland
,
Phys. Rev. E
72
,
031503
(
2005
).
8.
D.
Fragiadakis
and
C. M.
Roland
,
Phys. Rev. E
83
,
031504
(
2011
).
9.
E. H.
Abramson
,
J. Phys. Chem. B
118
,
11792
(
2014
).
10.
D.
Fragiadakis
and
C. M.
Roland
,
J. Chem. Phys.
138
,
12A502
(
2013
).
11.
L.
Bøhling
,
T. S.
Ingebrigtsen
,
A.
Grzybowski
,
M.
Paluch
,
J. C.
Dyre
, and
T. B.
Schrøder
,
New J. Phys.
14
,
113035
(
2012
).
12.
K.
Niss
,
C.
Dalle-Ferrier
,
G.
Tarjus
, and
C.
Alba-Simionesco
,
J. Phys.: Condens. Mater.
19
,
076102
(
2007
).
13.
A.
Sanz
,
T.
Hecksher
,
H. W.
Hansen
,
J. C.
Dyre
,
K.
Niss
, and
U. R.
Pedersen
,
Phys. Rev. Lett.
122
,
055501
(
2019
).
14.
T. C.
Ransom
,
R.
Casalini
,
D.
Fragiadakis
,
A. P.
Holt
, and
C. M.
Roland
,
Phys. Rev. Lett.
123
,
189601
(
2019
).
15.
R.
Casalini
and
C. M.
Roland
,
J. Chem. Phys.
144
,
024502
(
2016
).
16.
R.
Casalini
,
S. S.
Bair
, and
C. M.
Roland
,
J. Chem. Phys.
145
,
064502
(
2016
).
17.
M.
Sekula
,
S.
Pawlus
,
S.
Hensel-Bielowka
,
J.
Ziolo
,
M.
Paluch
, and
C. M.
Roland
,
J. Phys. Chem. B
108
,
4997
(
2004
).
18.
R.
Casalini
and
C. M.
Roland
,
J. Chem. Phys.
119
,
11951
(
2003
).
19.
D.
Fragiadakis
,
C. M.
Roland
, and
R.
Casalini
,
J. Chem. Phys.
132
,
144505
(
2010
).
20.
R.
Casalini
,
M.
Paluch
, and
C. M.
Roland
,
J. Phys. Chem. A
107
,
2369
(
2003
).
21.
T. C.
Ransom
,
R.
Casalini
,
D.
Fragiadakis
, and
C. M.
Roland
,
J. Chem. Phys.
151
,
174501
(
2019
).
22.
D.
Gundermann
,
U. R.
Pedersen
,
T.
Hecksher
,
N. P.
Bailey
,
B.
Jakobsen
,
T.
Christensen
,
N. B.
Olsen
,
T. B.
Schrøder
,
D.
Fragiadakis
,
R.
Casalini
,
C. M.
Roland
,
J. C.
Dyre
, and
K.
Niss
,
Nat. Phys.
7
,
816
(
2011
).
23.
R.
Casalini
,
R. F.
Gamache
, and
C. M.
Roland
,
J. Chem. Phys.
135
,
224501
(
2011
).
24.
R.
Casalini
,
C. M.
Roland
, and
S.
Capaccioli
,
J. Chem. Phys.
126
,
184903
(
2007
).
25.
M.
Paluch
,
J.
Gapinski
,
A.
Patkowski
, and
E. W.
Fischer
,
J. Chem. Phys.
114
,
8048
(
2001
).
26.

Note that in Ref. 25, Eq. (3) is obtained considering that the isobaric fragility mt = Ep(RT ln(10)).

27.
R.
Casalini
and
C. M.
Roland
,
Colloid Polym. Sci.
283
,
107
(
2004
).
28.
C. M.
Roland
,
R.
Casalini
,
R.
Bergman
, and
J.
Mattsson
,
Phys. Rev. B
77
,
012201
(
2008
).
29.
C. M.
Roland
,
S.
Bair
, and
R.
Casalini
,
J. Chem. Phys.
125
,
124508
(
2006
).
30.
I.
Cibulka
,
L.
Hnědkovskỳ
, and
T.
Takagi
,
J. Chem. Eng. Data
42
,
415
(
1997
).
31.
P. W.
Bridgman
, in
Proceedings of the American Academy of Arts and Sciences
(
JSTOR
,
1926
), Vol. 61, pp.
57
99
.
32.
G. P.
Johari
and
E.
Whalley
, in
Faraday Symposia of the Chemical Society
(
Royal Society of Chemistry
,
1972
), Vol. 6, pp.
23
41
.
33.
D.
Coslovich
and
C. M.
Roland
,
J. Phys. Chem. B
112
,
1329
(
2008
).
34.
N. H.
March
and
M. P.
Tosi
,
Introduction to Liquid State Physics
(
World Scientific
,
Singapore
,
2002
).
35.
W. G.
Hoover
and
M.
Rossj
,
Contemp. Phys.
12
,
339
(
1971
).
36.
Y.
Hiwatari
,
H.
Matsuda
,
T.
Ogawa
,
N.
Ogita
, and
A.
Ueda
,
Prog. Theor. Phys.
52
,
1105
(
1974
).
37.
N. P.
Bailey
,
U. R.
Pedersen
,
N.
Gnan
,
T. B.
Schrøder
, and
J. C.
Dyre
,
J. Chem. Phys.
129
,
184507
(
2008
).
38.
G.
Tsolou
,
V. G.
Mavrantzas
, and
D. N.
Theodorou
,
Macromolecules
38
,
1478
(
2005
).
39.
L.
Bøhling
,
N. P.
Bailey
,
T. B.
Schrøder
, and
J. C.
Dyre
,
J. Chem. Phys.
140
,
124510
(
2014
).
40.
R. A.
Buckingham
,
Proc. R. Soc. London, Ser. A
168
,
264
(
1938
).
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