The slow Arrhenius process (SAP) is a dielectric mode connected to thermally activated equilibration mechanisms, allowing for a fast reduction in free energy in liquids and glasses. The SAP, however, is still poorly understood, and so far, this process has mainly been investigated at temperatures above the glass transition. By employing a combination of methods to analyze dielectric measurements under both isochronal and isothermal conditions, we were able to quantitatively reproduce the dielectric response of the SAP of different polymers and to expand the experimental regime over which this process can be observed down to lower temperatures, up to 70 K below the glass transition. Employing thin films of thicknesses varying between 10 and 800 nm, we further verified that the peak shape and activation energy of the SAP of poly(4-bromostyrene) are not sensitive to temperature, nor do they vary upon confinement at the nanoscale level. These observations confirm the preliminary trends reported for other polymers. We find that one single set of parameters—meaning the activation barrier and the pre-exponential factor, respectively, linked to the enthalpic and entropic components of the process—can describe the dynamics of the SAP in both the supercooled liquid and glassy states, in bulk and thin films. These results are discussed in terms of possible molecular origins of the slow Arrhenius process in polymers.

1.
Z.
Song
,
C.
Rodríguez-Tinoco
,
A.
Mathew
, and
S.
Napolitano
, “
Fast equilibration mechanisms in disordered materials mediated by slow liquid dynamics
,”
Sci. Adv.
8
,
eabm7154
(
2022
).
2.
J. H.
Magill
and
D. J.
Plazek
, “
Crystallization kinetics of 1:3:5 tri-α-naphthyl benzene
,”
Nature
209
,
70
71
(
1966
).
3.
P. G.
de Gennes
, “
Reptation of a polymer chain in the presence of fixed obstacles
,”
J. Chem. Phys.
55
,
572
579
(
1971
).
4.
E.
Fischer
, “
Light scattering and dielectric studies on glass forming liquids
,”
Physica A
201
,
183
206
(
1993
).
5.
S.
Napolitano
and
M.
Wübbenhorst
, “
The lifetime of the deviations from bulk behaviour in polymers confined at the nanoscale
,”
Nat. Commun.
2
,
260
(
2011
).
6.
D.
Cangialosi
,
V. M.
Boucher
,
A.
Alegría
, and
J.
Colmenero
, “
Direct evidence of two equilibration mechanisms in glassy polymers
,”
Phys. Rev. Lett.
111
,
095701
(
2013
).
7.
D.
Roy
and
C. M.
Roland
, “
Reentanglement kinetics in polyisobutylene
,”
Macromolecules
46
,
9403
9408
(
2013
).
8.
S.
Chandran
,
R.
Handa
,
M.
Kchaou
,
S.
Al Akhrass
,
A. N.
Semenov
, and
G.
Reiter
, “
Time allowed for equilibration quantifies the preparation induced nonequilibrium behavior of polymer films
,”
ACS Macro Lett.
6
,
1296
1300
(
2017
).
9.
X.
Monnier
and
D.
Cangialosi
, “
Thermodynamic ultrastability of a polymer glass confined at the micrometer length scale
,”
Phys. Rev. Lett.
121
,
137801
(
2018
).
10.
S.
Chandran
and
G.
Reiter
, “
Segmental rearrangements relax stresses in nonequilibrated polymer films
,”
ACS Macro Lett.
8
,
646
650
(
2019
).
11.
E.
Thoms
and
S.
Napolitano
, “
Enthalpy-entropy compensation in the slow Arrhenius process
,”
J. Chem. Phys.
159
,
064505
(
2023
).
12.
B.
Wang
,
M.
Sanviti
,
A.
Alegría
, and
S.
Napolitano
, “
Molecular mobility of polymers at the melting transition
,”
ACS Macro Lett.
12
,
389
394
(
2023
).
13.
F.
Kremer
and
A.
Schönhals
,
Broadband Dielectric Spectroscopy
(
Springer Science & Business Media
,
2002
).
14.

While measurements at lower field frequencies would be technically possible, the associated longer measurement times might induce larger errors, due to the temperature and sample instabilities upon prolonged annealing.

15.
S.
Napolitano
,
S.
Capponi
, and
B.
Vanroy
, “
Glassy dynamics of soft matter under 1D confinement: How irreversible adsorption affects molecular packing, mobility gradients and orientational polarization in thin films
,”
Eur. Phys. J. E
36
,
61
(
2013
).
16.
S.
Havriliak
and
S.
Negami
, “
A complex plane representation of dielectric and mechanical relaxation processes in some polymers
,”
Polymer
8
,
161
210
(
1967
).
17.
G.
Floudas
,
M.
Paluch
,
A.
Grzybowski
, and
K.
Ngai
,
Molecular Dynamics of Glass-Forming Systems
(
Springer
,
Berlin, Heidelberg
,
2011
).
18.
A.
Panagopoulou
and
S.
Napolitano
, “
Irreversible adsorption governs the equilibration of thin polymer films
,”
Phys. Rev. Lett.
119
,
097801
(
2017
).
19.
Dynamics in Geometrical Confinement
, edited by
F.
Kremer
(
Springer International Publishing
,
2014
).
20.
Nonlinear Dielectric Spectroscopy
, edited by
R.
Richert
(
Springer International Publishing
,
2018
).
21.
The Scaling of Relaxation Processes
, edited by
F.
Kremer
and
A.
Loidl
(
Springer International Publishing
,
2018
).
22.
K.
Fukao
and
Y.
Miyamoto
, “
Glass transitions and dynamics in thin polymer films: Dielectric relaxation of thin films of polystyrene
,”
Phys. Rev. E
61
,
1743
1754
(
2000
).
23.
S.
Napolitano
and
M.
Wübbenhorst
, “
Structural relaxation and dynamic fragility of freely standing polymer films
,”
Polymer
51
,
5309
5312
(
2010
).
24.
S. L.
Malhotra
,
P.
Lessard
, and
L. P.
Blanchard
, “
A thermal decomposition and glass transition temperature study of poly(p-bromostyrene)
,”
J. Macromol. Sci., Part A: Chem.
15
,
1577
1599
(
1981
).
25.
A.
Rincon
and
I.
McNeill
, “
Thermal degradation of poly(methyl methacrylate)-poly-4-bromostyrene blends and methyl methacrylate-4-bromostyrene copolymers
,”
Polym. Degrad. Stab.
40
,
125
135
(
1993
).
26.
M.
Paluch
,
C. M.
Roland
,
S.
Pawlus
,
J.
Zioło
, and
K. L.
Ngai
, “
Does the Arrhenius temperature dependence of the Johari-Goldstein relaxation persist above Tg?
,”
Phys. Rev. Lett.
91
,
115701
(
2003
).
27.
F.
Caporaletti
,
S.
Capaccioli
,
S.
Valenti
,
M.
Mikolasek
,
A. I.
Chumakov
, and
G.
Monaco
, “
Experimental evidence of mosaic structure in strongly supercooled molecular liquids
,”
Nat. Commun.
12
,
1867
(
2021
).
28.
J. C.
Dyre
and
N. B.
Olsen
, “
Minimal model for beta relaxation in viscous liquids
,”
Phys. Rev. Lett.
91
,
155703
(
2003
).
29.
D.
Nieto Simavilla
,
A. A.
Abate
,
J.
Liu
,
Y. H.
Geerts
,
P.
Losada-Peréz
, and
S.
Napolitano
, “
1D-confinement inhibits the anomaly in secondary relaxation of a fluorinated polymer
,”
ACS Macro Lett.
10
,
649
653
(
2021
).
30.
O.
van den Berg
,
M.
Wübbenhorst
,
S. J.
Picken
, and
W. F.
Jager
, “
Characteristic size of molecular dynamics in polymers probed by dielectric probes of variable length
,”
J. Non-Cryst. Solids
351
,
2694
2702
(
2005
).
31.
D.
Labahn
,
R.
Mix
, and
A.
Schönhals
, “
Dielectric relaxation of ultrathin films of supported polysulfone
,”
Phys. Rev. E
79
,
011801
(
2009
).
32.
M.
Tress
,
M.
Erber
,
E. U.
Mapesa
,
H.
Huth
,
J.
Müller
,
A.
Serghei
,
C.
Schick
,
K.-J.
Eichhorn
,
B.
Voit
, and
F.
Kremer
, “
Glassy dynamics and glass transition in nanometric thin layers of polystyrene
,”
Macromolecules
43
,
9937
9944
(
2010
).
33.
K.
Adrjanowicz
,
R.
Winkler
,
A.
Dzienia
,
M.
Paluch
, and
S.
Napolitano
, “
Connecting 1D and 2D confined polymer dynamics to its bulk behavior via density scaling
,”
ACS Macro Lett.
8
,
304
309
(
2019
).
34.
C.-H.
Tu
,
J.
Zhou
,
M.
Doi
,
H.-J.
Butt
, and
G.
Floudas
, “
Interfacial interactions during in situ polymer imbibition in nanopores
,”
Phys. Rev. Lett.
125
,
127802
(
2020
).
35.
J.
Martín
,
C.
Mijangos
,
A.
Sanz
,
T. A.
Ezquerra
, and
A.
Nogales
, “
Segmental dynamics of semicrystalline poly(vinylidene fluoride) nanorods
,”
Macromolecules
42
,
5395
5401
(
2009
).
36.
C.
Zhang
,
V. M.
Boucher
,
D.
Cangialosi
, and
R. D.
Priestley
, “
Mobility and glass transition temperature of polymer nanospheres
,”
Polymer
54
,
230
235
(
2013
).
37.
D. E.
Martínez-Tong
,
M.
Soccio
,
A.
Sanz
,
C.
García
,
T. A.
Ezquerra
, and
A.
Nogales
, “
Chain arrangement and glass transition temperature variations in polymer nanoparticles under 3D-confinement
,”
Macromolecules
46
,
4698
4705
(
2013
).
38.
C.
Rotella
,
S.
Napolitano
,
L.
De Cremer
,
G.
Koeckelberghs
, and
M.
Wübbenhorst
, “
Distribution of segmental mobility in ultrathin polymer films
,”
Macromolecules
43
,
8686
8691
(
2010
).
39.
S.
Napolitano
, “
Irreversible adsorption of polymer melts and nanoconfinement effects
,”
Soft Matter
16
,
5348
5365
(
2020
).
40.
R. P.
White
and
J. E.
Lipson
, “
To understand film dynamics look to the bulk
,”
Phys. Rev. Lett.
125
,
058002
(
2020
).
41.
Z.
Fakhraai
and
J. A.
Forrest
, “
Probing slow dynamics in supported thin polymer films
,”
Phys. Rev. Lett.
95
,
025701
(
2005
).
42.
S.
Napolitano
,
E.
Glynos
, and
N. B.
Tito
, “
Glass transition of polymers in bulk, confined geometries, and near interfaces
,”
Rep. Prog. Phys.
80
,
036602
(
2017
).
43.
J. E. K.
Schawe
, “
Vitrification in a wide cooling rate range: The relations between cooling rate, relaxation time, transition width, and fragility
,”
J. Chem. Phys.
141
,
184905
(
2014
).
44.
E.-J.
Donth
,
The Glass Transition
(
Springer
,
Berlin, Heidelberg
,
2001
).
45.
I. S.
Gutzow
and
J. W.
Schmelzer
,
The Vitreous State
(
Springer
,
Berlin, Heidelberg
,
2013
).
46.
R. D.
Priestley
,
D.
Cangialosi
, and
S.
Napolitano
, “
On the equivalence between the thermodynamic and dynamic measurements of the glass transition in confined polymers
,”
J. Non-Cryst. Solids
407
,
288
295
(
2015
).
47.
A.
Debot
,
R. P.
White
,
J. E. G.
Lipson
, and
S.
Napolitano
, “
Experimental test of the cooperative free volume rate model under 1D confinement: The interplay of free volume, temperature, and polymer film thickness in driving segmental mobility
,”
ACS Macro Lett.
8
,
41
45
(
2018
).
48.
A.
Yelon
and
B.
Movaghar
, “
Microscopic explanation of the compensation (Meyer-Neldel) rule
,”
Phys. Rev. Lett.
65
,
618
620
(
1990
).
49.
A.
Yelon
,
B.
Movaghar
, and
R. S.
Crandall
, “
Multi-excitation entropy: Its role in thermodynamics and kinetics
,”
Rep. Prog. Phys.
69
,
1145
1194
(
2006
).

Supplementary Material

You do not currently have access to this content.