Temperature and pressure dependence of secondary process in an epoxy system.

Abstract

Dielectric spectroscopy as a function of temperature and pressure was used to study the secondary relaxation in poly [(phenyl glycidyl ether)-co-formaldehyde] at hydrostatic pressure up to 600 MPa and at different temperatures between 315 and 243 K. From the analysis of the isothermal measurements, we observe that the activation volume of the secondary relaxation has nonmonotonic temperature dependence with a maximum at the temperature of the glass transition at ambient pressure. An interpretation in terms of mean hole volume dispersion is proposed based on literature data. Moreover, from isobaric data, we studied the effect of pressure on activation entropy and enthalpy of the secondary relaxation evidencing its local nature but also the presence of a certain complexity of the motion, which supports the idea that this process reflects the motion of a large part of the molecule.

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THE JOURNAL OF CHEMICAL PHYSICS 134, 044510 (2011)
Temperature and pressure dependence of secondary process
in an epoxy system
Soheil Sharifi,1Simone Capaccioli,1,2Mauro Lucchesi,1,2Pierangelo Rolla,1,2and
Daniele Prevosto1,2,a)
1Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, 1-56127 Pisa, Italy
2Istituto per i Processi Chimico-Fisici del CNR, c/o Dipartimento di Fisica Largo B. Pontecorvo 3,
1-56127 Pisa, Italy
(Received 21 July 2010; accepted 1 November 2010; published online 24 January 2011)
Dielectric spectroscopy as a function of temperature and pressure was used to study the secondary re-
laxation in poly [(phenyl glycidyl ether)-co-formaldehyde] at hydrostatic pressure up to 600 MPa and
at different temperatures between 315 and 243 K. From the analysis of the isothermal measurements,
we observe that the activation volume of the secondary relaxation has nonmonotonic temperature
dependence with a maximum at the temperature of the glass transition at ambient pressure. An in-
terpretation in terms of mean hole volume dispersion is proposed based on literature data. Moreover,
from isobaric data, we studied the effect of pressure on activation entropy and enthalpy of the sec-
ondary relaxation evidencing its local nature but also the presence of a certain complexity of the
motion, which supports the idea that this process reflects the motion of a large part of the molecule.
© 2011 American Institute of Physics. [doi:10.1063/1.3518972]
I. INTRODUCTION
The relaxation dynamics of glass forming liquids and
amorphous polymers, especially as they are cooled or com-
pressed near to the liquid glass transition and in the glassy
state, is still an intriguing problem in condensed matter
physics.1–3In recent years the attention was focused not only
onthestructuralprocess,traditionallyrelatedtotheglasstran-
sition, but also on the secondary processes.4–11The latter have
been shown to be (in some cases) related to the structural pro-
cess, and to be involved in the vitrification process.4,12–15In
such cases the secondary process is called Johari–Goldstein
(JG) (secondary) relaxation,16and it is expected to have dy-
namic properties similar to the structural one.4However, the
investigation of secondary processes is still limited because
of some intrinsic experimental limits. In fact, the secondary
process, in most cases, is detectable only in the glassy state
and the connection to the structural process is difficult to
demonstrate. In most of the glass forming systems, the sec-
ondary process is detectable only at very high pressure and/or
at very low temperature, thus limiting the range of its investi-
gation. Even though such experimental difficulties may exist,
it is universally accepted that the secondary process, being
JG or not JG, in the glassy state can be treated as an acti-
vated process, concerning the temperature and pressure of its
characteristic relaxation frequency. Accordingly, its tempera-
ture dependence can be described in terms of the Arrhenius
equation.17However, another useful equation is the so called
Eyring equation, also proposed to describe the isobaric tem-
perature dependence of the rate of activated processes
νβ
max(T)=kBT/(2πh)exp[?Sβ/(kB)]exp[−?Hβ/(kBT)], (1)
a)Author to whom correspondence should be addressed. Electronic mail:
prevosto@df.unipi.it.
where νβ
is the Boltzmann constant, T the temperature, h is the Planck
constant, ?Sβthe activation entropy and ?Hβthe activation
enthalpy of the β-process. Such equation has the same num-
ber of free parameters of the Arrhenius equation, but contains
the parameter ?Sβthat can be seen as a measure of the local
molecular reorganization induced by the relaxation.18–24To
the knowledge of the authors, Eq. (1) has been applied only
at ambient pressure and the pressure dependence of the acti-
vation entropy and enthalpy has never been obtained directly
from experimental data.
On the other hand, the isothermal pressure dependence
of the secondary process is usually described in terms of an
Arrhenius like equation
maxis the relaxation frequency of the loss peak, kB
υβ
max(P) = νP=0exp[−P?Vβ/(kBT)],
where νP = 0is the relaxation frequency at ambient pressure
and temperature corresponding to that of the isotherm of in-
vestigation, ?Vβ is the activation volume of the secondary
(for example the β-) process and P?Vβis the (linearly) pres-
sure dependent term of Gibbs free energy barrier over which
the relaxation occurs. Because of experimental difficulties in
working at low temperature and high pressure, the tempera-
ture dependence of ?Vβis rarely reported and, when it is, it
spans only a limited temperature interval.
Nevertheless, the investigation of the temperature depen-
dence of ?Vβis important to clarify the molecular motion of
the secondary process, and to qualitatively establish a connec-
tion to the structural process. Moreover, the pressure depen-
dence of ?Sβand ?Hβcan help in understanding the molec-
ular nature of the energy barrier governing the process.
In this work, we investigated the pressure and tem-
perature dependence of the relaxation dynamics in the
epoxy system poly [(phenyl glycidyl ether)-co-formaldehyde]
(2)
0021-9606/2011/134(4)/044510/6/$30.00© 2011 American Institute of Physics
134, 044510-1
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044510-2Sharifi et al.J. Chem. Phys. 134, 044510 (2011)
(PPGE),15,25,26with particular focus on the intermediate sec-
ondary process. Experimental results on such a process, in the
following named the β-process, have already been reported,
supporting its classification as a JG secondary process.15The
present work extends the previous investigation to a broader
interval of temperature and pressure, in particular to the dif-
ferent states obtained following different paths of isobaric and
isothermal vitrification. The new obtained information about
the temperature dependence of ?Vβand the pressure depen-
dence of ?Sβand ?Hβ, supports the conclusion of the previ-
ous work. Moreover, an unexpected temperature dependence
of ?Vβis found and it is qualitatively related with fluctuation
of free volume in the glassy state.
II. EXPERIMENT AND MATERIALS
Poly[(phenyl glycidyl ether)-co-formaldehyde] (PPGE),
with average molecular weight (MW) = 345g/mol, and Tg
around 258 ± 1 K,15was supplied by Aldrich Chemicals.
Dielectric measurements were carried out by a dielectric
spectrometer (Alpha-Novocontrol) in the frequency interval
10−2–107Hz. For measurements at ambient pressure, the
sample was placed in a parallel plate cell (diameter 30 mm,
gap 0.1 mm) and the temperature control was performed with
a precision better than 0.1 K by using a dry nitrogen stream
based system. For measurements at high pressure, the sam-
ple was placed in a parallel plate cell (diameter 20 mm, gap
0.05 mm), that properly insulated from the external environ-
ment, was located inside a pressure chamber. Pressure vari-
ations (0.1–600 MPa) were generated by a manual pump
and transmitted to the sample through silicon oil. A liquid
circulator connected to a jacket, wrapped around the pres-
sure room, allowed the control of temperature (353–233 K)
within 0.1 K.
III. RESULTS AND DISCUSSION
Dielectric loss spectra, ε(ω) = ε?−iε??, of PPGE were
measured from above to below the glass transition. At am-
bient pressure, a structural, α-, process is visible above the
glass transition temperature, Tg, and for temperatures below
Tgtwo secondary processes, β- and γ-, are present.25All the
observed relaxation processes move toward lower frequencies
on decreasing temperature, or increasing pressure, with the α-
process being the most temperature and pressure sensitive and
the γ-process the less.15One of the secondary processes, that
appearing at lower frequencies and being named β-relaxation,
has been previously recognized to be a secondary Johary–
Goldstein process.13,15,26
In the following study an extensive investigation of the
pressure and temperature dependence of the β-relaxation in
the glassy state is reported.
A. Temperature dependence of activation volume
The β-relaxation peak shifts towards lower frequencies
by increasing pressure in the glassy state in isothermal con-
dition Fig. 1. Its pressure dependence is larger than that of
FIG. 1. Frequency dependence of dielectric loss spectra in the glassy state
of PPGE in isothermal condition at 243.5 K at different pressures.
the faster secondary γ-process (the relaxation scenario from
our measurements is depicted in Ref. 15) and, consequently,
it can be separated from the γ-process at high pressures
Fig. 1. We herein report data on the pressure dependence of
the β-process at several isothermal conditions, as sketched in
Fig. 2. We would like to point out that all the measurements
on the β-process reported here have been performed in the
glassy state only. We can consider two different regions of in-
vestigation. In region I, the glassy state is reached by isother-
mal compression starting from a point in the liquid state at
ambient pressure, (for example, point A). In the so called re-
gion II, the system is vitrified by cooling to the measuring
temperature at ambient pressure, (for example, point D), and
measurements have been carried out by isothermal compres-
sion. Variations of temperature have been typically applied
with rates of about 1 K/min and pressure variations have been
applied at about 10 MPa/min.
Relaxation spectra have been analyzed in terms of the
Cole–Cole equation
ε(ω) = ε∞+
?ε
1 +?iωτβ
?1−α,
(3)
FIG. 2. Scheme of the thermodynamic paths used in this paper. Dot points
(experimental data in Ref. 15) with the interpolating line represent Tg(P),
AC and DE lines represent two examples of isothermal paths followed for
the measurements.
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044510-3Secondary processes in an epoxy systemJ. Chem. Phys. 134, 044510 (2011)
FIG. 3. Isothermal pressure dependencies of α- (open symbols) and β-
(closed symbols) relaxation frequencies at several temperatures (as labeled
in the figure) for PPGE. The solid lines represent fits (for details see text).
with the addition of a power law to take into account the
high frequency increase of the signal due to the γ-relaxation,
Fig. 1. At low frequency no contribution from the structural
peak can be detected. The logarithm of the peak frequencies
for the β- and the structural relaxation (νβ
a function of pressure are shown in the Fig. 3. The data of
the structural relaxation are obtained by measurements in the
supercooled liquid state previously published.15The pressure
dependence of log να
pecially for isotherms at higher temperatures, and a Vogel–
Fulcher-Tamman like να
is used for fitting, although other models are proposed in
literature (for example, Refs. 27 and 28). Instead, log νβ
has a linear pressure dependence in the entire interval of
temperature and pressure, and an Arrhenius like behavior
[Eq. (2)] has been used to reproduce the data. In order to
compare the pressure dependence of νβ
to that of να
vation volume of the structural process has been calculated
at Tgaccording to ?Vα= –kBTB/(Pg–P0), where Pgis de-
fined such as να
Table I the parameters from fitting of data are reported. As
max and να
max) as
maxdeviates from the linear behavior, es-
max= ναexp[BP0/(P-P0)] equation
max
maxin the glassy state
maxclose/above to the glass transition, the acti-
max(Pg) = 0.016 Hz (i.e., τα
max(Pg) = 10 s) In
TABLE I. Characteristic parameters for the pressure dependence of the
α- and β-relaxation frequency of PPGE. First column: temperature of
the isotherm of the investigation; second column: pressure corresponding to
the glass transition; third column: activation volume of the structural relax-
ation at the glass transition; fourth column: activation volume of the sec-
ondary relaxation in the glassy state.
T
[K]
Pg
?Vα
?Vβ
[MPa] [cm3/mol][ cm3/mol]
293
283
267.6
263
253
243
245
167
72
0.1
0.1
0.1
178 ± 9
205 ± 10
232 ± 10
14.8 ± 0.7
16.2 ± 0.8
18.2 ± 0.9
18.6 ± 0.9
18.0 ± 0.9
17.1 ± 0.9
temperature decreases, molecular motions become usually
slower and more constrained. This phenomenology for the α-
process manifests as an increase of its activation volume at the
glass transition when the temperature of the isothermal inves-
tigation is decreased (Fig. 4) (see, for example, Refs. 29,30,
and 31). Such an increase for the structural process is tenta-
tively explained in terms of an increase of cooperativity and a
reduction of the free volume in the material.32
Secondary relaxations are sometimes dependent on pres-
sure, as for example the JG process,33,34and sometimes are
practically pressure independent, as for example the side
chain motions in polymers or very local relaxation in small
molecular glass formers having activation volume less than
about 5 cm3/mol.26,36Moreover, we have to mention that,
even in the case of JG process, the activation volume has an
abrupt reduction on entering in the glassy state.13Investiga-
tions of the temperature dependence of ?Vβ are rare. Here
we report data of the activation volume of the JG process
over a temperature range of about 50 K. ?Vβfirst increases
by decreasing the temperature in region I [a rate of about
0.13 cm3/(mol K)], after that, in region II, it slowly decreases
with temperature (0.048 cm3/K) [Fig. 4(a)]. It is important
to remind that all the values of ?Vβreported are evaluated
inside the glassy state. These results indicate that the tem-
perature dependence of ?Vαis qualitatively similar to that
of ?Vβ, in region I [inset in Fig. 4(a)]. However, the latter
FIG. 4. (a) Activation volume of JG relaxation of PPGE (?Vβ) and (inset)
activation volume of the structural relaxation of PPGE (?Vα) as a function
of temperature. The value of ?Vαat 273 K is calculated from data in Ref. 46.
(b) Activation volume of secondary relaxation from literature data: BMPC
(square),PDE(downwardtriangle),PEMA(star),andPET(upwardtriangle).
Vertical dotted line shows the ambient pressure glass transition temperature,
continuous lines are guides for the eyes.
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Page 4

044510-4 Sharifi et al.J. Chem. Phys. 134, 044510 (2011)
evidences a nonmonotonous dependence when investigated
over the whole temperature range.
This phenomenology is not peculiar for PPGE, even
though in this system it is more evident because of the
several available data. Some literature data are reported in
Fig. 4(b) for comparison. Referring to two samples previ-
ously studied by some of us, we can find similar tempera-
ture dependences.35The activation volume data of the sec-
ondary (non-JG) process of 1,1-bis 4-methoxyphenyl cyclo-
hexane (BMPC, Table I in Ref. 35) agree with the presence of
a maximum in proximity of Tg. The presence of ?Vβvalues
for only three temperatures did not allow pointing out such
behavior in our previous publication, but it is evident that the
result is in agreement with the present finding. In phenolph-
thalein dimethylether, PDE, instead we have data of ?Vβ(the
microscopic origin of this relaxation is still under discussion)
only in the corresponding region II where the system is al-
ready in the glassy state at ambient pressure (Table. I in Ref.
35). Close to the glass transition temperature at ambient pres-
sure [Tg(Patm)], ?Vβis almost insensitive to temperature, as
for PPGE, and only at much lower temperatures than Tgit
sligthly increases. In the case of PPGE, we do not have data
at such low temperatures (deep inside the glassy state) and a
comparison cannot be performed. An increase of ?Vβwith
lowering T in region I was observed in polyethyl methacry-
late (PEMA).36This secondary relaxation is due to the car-
bonyl group rotation involving the rocking motion of seg-
mental unit, as demonstrated in Ref. 37 and consequently it
is likely of JG origin. A decrease of ?Vβin region II was ob-
served in polyethylene terephthalate (PET)38for a secondary
relaxation whose origin is not clear at all. In other glass form-
ers, a different phenomenology was observed with ?Vβbeing
almost temperature insensitive31,39or decreasing with T.30It
is to be noted that all the last mentioned investigations refer
to hydrogen bonded materials, where the specific temperature
and pressure behavior of the hydrogen bonding network could
be the source of the different behavior of ?Vβ.
In order to better understand the origin at a microscopic
level of the activation volume we can look at the density or
the free volume distribution at molecular scale. In fact, the
secondary relaxation in polymers or in monomeric organic
glass formers, being a local process, can be very sensitive to
such distributions. One of the best way for investigating the
hole size is measuring the characteristic times of positronium
anihilation (PALS) within the material, at different tempera-
tures and pressures. Unfortunately PALS data on PPGE are
not available. However, recent works combining PALS and
macroscopic pressure-volume-temperature measurements in
polymers evidenced that the specific macroscopic volume, V,
is proportional to the mean hole volume, vh, (as calculated
from PALS) both during compression and cooling in the su-
percooled liquid region even though with different propor-
tionality constant (see, for example, Refs. 40 and 41). More-
over, it can be observed that the mean hole volume dispersion
has the same temperature and pressure trend as vh(see, for
example, Refs. 42–44). As a consequence, larger specific vol-
umes correspond to larger dispersions in the mean hole vol-
ume, reflecting a larger distribution of volume characterizing
the different states where molecules reside. If we calculate the
FIG. 5. Molar volume of PPGE as at ambient pressure as a function of tem-
peratureinthesupercooledliquid(closedsquare)andintheglassystate(open
squares). Crossed circles represent the values of the specific volume calcu-
lated isothermally in the supercooled liquid as a function of pressure at the
following conditions: 293 K up to 220 MPa, 283 K up to 140 MPa and 268
K up to 70 MPa. In the inset the specific volume calculated at the glass tran-
sition at different pressures, V(T,P)g(pressure values as reported in Table I) is
reported as a function of temperature. The data are derived from Ref. 46.
specific volume of PPGE at the glass transition, V(T,P)g,we can
observe that its temperature dependence (inset in Fig. 5) has
a similar trend as ?Vβ. In fact, it increases in region I and
decreases in region II. This kind of behavior for V(T,P)gis very
general and it has already been reported in polymers.45Con-
sequently, ?Vβhas the similar trend as the mean hole volume
dispersion. We can then speculate that ?Vβreflects the vol-
ume difference of the available holes between which the tran-
sitions related to the secondary relaxation occur. The larger is
the distribution in the mean hole volume and the larger is the
volume difference between the two states involved in the ro-
tation: consequently the larger will be ?Vβ. It is noteworthy
that a relation between the relaxation frequency of the JG re-
laxation and the fluctuations of free volume has been recently
suggested to interpret the effect of thermodynamic history on
the JG process of polyvinylethylene.10Of course, such specu-
lationshouldbesupportedbyspecificmeasurementsonPALS
on the same condition of the dynamics one, which however
now are not available.
B. Pressure dependence of activation entropy and
enthalpy
The temperature dependence of β-relaxation in PPGE at
different pressures is represented in Fig. 6 together with the
analysis from fitting to the Eyring equation Eq. (1). This rela-
tion considers the process to be thermally activated, in anal-
ogy to the Arrhenius equation, but explicitly considers the
contributions of activation enthalpy, ?Hβ, and entropy, ?Sβ,
to the activation energy (see Table II). In particular, ?Sβcan
be considered a measure of the local molecular reorganiza-
tion induced by the relaxation. The choice of fitting data to
the Eyring equation has been suggested by the possibility of
directly obtaining an estimation of ?Sβfrom the fitting, with-
out any further elaboration of the data. Anyway, it is possible
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Page 5

044510-5Secondary processes in an epoxy systemJ. Chem. Phys. 134, 044510 (2011)
FIG. 6. Temperature dependence of maximum loss frequency of the β-
relaxation of PPGE at three isobaric conditions: 0.1 MPa (squares), 240 MPa
(triangles), 500 MPa (circles). Open stars represent data of the γ-relaxation
at ambient pressure. Red lines are fits with Eq. (2).
estimating ?Sβalso by fitting the data to the Arrhenius equa-
tion and following the procedure proposed in Ref. 47. Regard-
ing the capability of Eyring equation to reproduce the temper-
ature dependence of our data, we verified that it is the same
of the Arrhenius equation.
In the case of secondary relaxations, which involve lo-
cal motion of the molecules, ?Sβreflects the intramolecular
cooperativity of the process. In other words, it reflects the co-
operativity among different sub-groups of the same molecule.
The larger is the contribution from the entropic energy, T?Sβ,
to the energy barrier, the most important is the intra-molecular
cooperativity of the secondary process.18–24,48
The β-process of PPGE is of the JG type, i.e. it involves
the motion of the whole molecule, or at least a large por-
tion of it. Consequently, we expect that the entropic contri-
bution should be non-negligible. In Ref. 47 ?S for secondary
relaxations was estimated to be about 10R J/(mol K) (R is
the gas constant). We can observe that the values estimated
here for PPGE are of the correct order of magnitude (see
Table II), both for the β- and γ-relaxations. Moreover ?Sβ
is larger by a factor 2 than ?Sγ. To have a more complete
understanding, we can compare the contribution of the en-
tropic barrier (T?S) to the total energy barrier to be over-
come for the relaxation to occur (?H–T?S). If we compare
the values at ambient pressure and at the temperature cor-
responding to the relaxation frequency of 1 kHz, we notice
TABLE II. Activation enthalpy and activation entropy of the β- (lines 1–3)
and γ- (line 4) of PPGE at the different pressure values.
P
?H
?S
(MPa) (KJ/mol)(J/mol/K)
PPGE500 β-
240 β-
0.1 β-
0.1 γ-
63 ± 6
57 ± 6
51 ± 5
27 ± 3
35 ± 3
33 ± 3
34 ± 3
16 ± 2
TABLE III. Contribution of the entropic barrier (T·?S) to the total energy
barrier (?H–T·?S) of some systems possessing two secondary relaxations.
As for PPGE the difference in the relative contribution for the two processes
is not large but always present with few exceptions.
βrelaxation
γ-relaxation
DGEBAa
TPMTGEb
DiPGDBc
PDEd
BIBEe
21%
24%
16%
19%
10%
19%
18%
11%
7%
10%
aReferences 25 and 26.
bReference 49.
cReference 50.
dReferences 35 and 51.
eReferences 52 and 53.
that the contribution of T?Sβto the energy barrier is about
9% for the γ- relaxation and 18% for the β-relaxation. In
both cases the contribution is quite small, which is consis-
tent with the local and intermolecular noncooperative nature
of the process, but it is different than zero thus reflecting an
amount of cooperativity among different parts of the same
molecule. Moreover, the contribution of the entropic barrier
to the β-relaxation energy barrier is two times larger than
for the γ-relaxation, such difference being not negligible. The
larger contribution of the entropic energy of the β-relaxation
with respect to the γ-relaxation is consistent with our previ-
ous conclusions that identify the β-relaxation as the JG pro-
cess, intended as the secondary local process involving sev-
eral parts of the molecule moving cooperatively.13,15,26It is
suggested that the activation entropy can be used as an indi-
cator to understand the microscopic origin of secondary pro-
cesses in a particular system. However, we expect its value
to be affected by the molecular structure of the investigated
material, and consequently comparing different materials can
be difficult and misleading. However, it can be used as an in-
dicator to distinguish the microscopic origin of different sec-
ondary process in the same material. The percentage contribu-
tion of the entropic barrier to the total energy barrier has been
reported in Table III for some systems studied by some of
the authors and possessing two secondary relaxations. From
this analysis, we excluded hydrogen bonded system, because
of the peculiarity deriving from this kind of interaction. As
for PPGE, the difference in the relative contribution for the
two processes is not large but always present with few excep-
tions.Infact,theβ-processofdiglycidyletherofbisphenol-A,
DGEBA, dipropyleneglycol dibenzoate, DiPGDB, and triph-
enylolmethane triglycidyl ether, TPMTGE, is recognized to
be the JG process, and has a larger contribution from activa-
tion entropy than the γ-process. The microscopic origin of
secondary processes in PDE is not completely clear. Many
results suggest that the β-process is the JG process, but the
agreement with the criterium proposed by the coupling model
lack as well as for the γ-process.35Our present analysis sug-
gests the β-process to be of the JG type. The β-relaxation of
benzoin-isobutyl ether, BIBE, has been found to be of the JG
type53but the contribution from the activation entropy is the
same as for the γ-process, which is non-JG. We believe that in
this case, the details of the molecular structure highly impact
on the activation entropy of both secondary processes.
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Page 6

044510-6Sharifi et al.J. Chem. Phys. 134, 044510 (2011)
The pressure dependence of the activation entropy and
enthalpy has been calculated only for the β-process since the
γ-process is too fast and too pressure insensitive to allow its
investigation. We observe that ?Sβremains constant with in-
creasing pressure whereas ?Hβ increases. The behavior of
these parameters evidences the expected trend that the in-
crease of density and the reduction of free volume occurring
at high pressure hinder the motions related to the secondary
relaxation. However, the degree of cooperativity is not much
affected, which is consistent with the idea that it is not inter-
molecular in origin but it is a cooperativity among different
parts of the molecule.
IV. CONCLUSIONS
We investigated the temperature and pressure depen-
dences of the secondary β-relaxation of PPGE, in terms of its
activation volume, enthalpy, and entropy. By the pressure de-
pendence of the secondary β-process along several isotherms,
we found that the activation volume in the glassy state first in-
creases and then slightly decreases on lowering T, reaching a
maximum at the ambient pressure Tg. A similarity to the tem-
perature dependence of the mean hole volume dispersion is
proposed basing on literature data. Such an explanation sup-
ports previous works suggesting that this process is of the JG
type. In fact, in order to drive significant free volume fluctua-
tion, we believe that the motion of a large part of the molecule
is required. Moreover, in the region where the activation vol-
ume of the structural process can be observed, a similar trend
is found, which confirms a similarity in properties of the two
processes already proposed in previous papers.
From the temperature dependence of the secondary pro-
cess along several isobars, we evidenced larger activation en-
tropy of the β-process with respect to the γ-process. More-
over, the activation entropy of the β-process is independent on
pressure. Such results are interpreted in terms of a local pro-
cess which presents a certain degree of cooperativity among
different parts of the same molecule, in other words a JG pro-
cess.
1P. G. Debenedetti, and F. H. Stillinger, Nature 410, 259 (2001).
2C. M. Roland, S. Hensel-Bielowka, M. Paluch, and R. Casalini, Rep. Prog.
Phys. 68, 1405 (2005).
3K. L. Ngai, D. Prevosto, S. Capaccioli, and C. M. Roland, J. Phys.: Con-
dens. Matter 20, 244125 (2008).
4K. L. Ngai and M. Paluch, J. Chem. Phys. 120, 857 (2004).
5M. Vogel, P. Medick, and E. A. Rossler, Annu. Rep. NMR Spectrosc. 56,
231 (2005).
6L. Leuzzi, Philos. Mag. 88, 4015 (2008).
7M. Zuriaga, L. C. Pardo, P. Lunkenheimer, J. Li Tamarit, N. Veglio, M.
Barrio, F.J. Bermejo, and A. Loidl, Phy. Rev. Lett., 103, 075701 (2009).
8D. Prevosto, S. Capaccioli, M. Lucchesi, P. A. Rolla, and K. L. Ngai, J.
Non-Cryst Solids 355, 705–711 (2009).
9J. D. Stevenson and P. G. Wolynes, Nat. Phys. 6, 62 (2009).
10R. Casalini and C. M. Roland, J. Chem. Phys. 131, 114501 (2009).
11R. Casalini and C. M. Roland J. Polym. Sci., Part B: Polym. Phys. 48, 582
(2010).
12R. Böhmer, G. Diezemann, B. Geil, G. Hinze, A. Nowaczyk, and M. Win-
terlich, Phys. Rev. Lett. 97, 135701 (2006).
13K. Kessairi, S. Capaccioli, D. Prevosto, M. Lucchesi, S. Sharifi, and P. A.
Rolla, J. Phys. Chem. B 112, 4470 (2008).
14M. Mierzwa, S. Pawlus, M. Paluch, E. Kaminska, and K. L.Ngai, J. Chem.
Phys. 128, 044512 (2008).
15D. Prevosto, S. Capaccioli, S. Sharifi, K. Kessairi, M. Lucchesi, and P. A.
Rolla J. Non-Cryst. Solids 353, 4278 (2007).
16G. P. Johari and M. Goldstein, J. Chem. Phys. 53, 2372 (1970).
17R. Bergman, F. Alvarez, A. Alegria, and J. Colmenero, J. Chem. Phys. 109,
7546 (1998).
18H. W. Starkweather, Jr., Macromolecules 23, 1277 (1981).
19H. W. Starkweather, Jr., Macromolecules 21, 1798 (1988).
20H. W. Starkweather, Jr., Macromolecules 23, 328 (1990).
21K. Kessairi, S. Capaccioli, D. Prevosto, M. Lucchesi, and P. A. Rolla, J.
Chem. Phys. 127, 174502 (2007).
22S. P. Bravard and R. H. Boyd, Macromolecules 36, 741 (2003).
23A. Sanz, A. Nogales, T. A. Ezquerra, N. Lotti, and L. Finelli, Phys. Rev. E
70, 021502 (2004).
24A. Nogales, A. Sanz, and T. A. Ezquerra, J. Non-Cryst. Solids 352, 4649
(2006).
25S. Corezzi, M. Beiner, H. Huth, K. Schröter, S. Capaccioli, R. Casalini, D.
Fioretto, and E. Donth, J. Chem. Phys. 117, 2435 (2002).
26S. Sharifi, D. Prevosto, S. Capaccioli, M. Lucchesi, and M. Paluch. J.
Non-Cryst. Solids 353, 4313 (2007).
27A. N. Papathanassiou, Phys. Rev. E 79, 032501 (2009).
28A. N. Papathanassiou and I. Sakellis J. Chem. Phys. 132, 154503 (2010).
29S. Hensel-Bielowka, J. Ziolo, M. Paluch, and C. M. Roland, J. Chem. Phys.
117, 2317 (2002).
30S. Hensel-Bielowka, J. Ziolo, M. Paluch, and C. M. Roland, J. Phys Chem.
B 106, 12459 (2002).
31R. Casalini and C. M. Roland, Phys. Rev. B 69, 094202 (2004).
32M. Paluch, K. Grzybowska, and A. Grzybowski, J. Phys.: Condens. Matter
19, 205117 (2007).
33K. Kessairi, S. Capaccioli, D. Prevosto, S. Sharifi, and P. A. Rolla, Journal
of Non-Crystalline Solids 353, 4273 (2007).
34S. Capaccioli, K. Kessairi, D. Prevosto, M. Lucchesi, and P. A. Rolla, J.
Phys.: Condens. Matter 19, 205133 (2007).
35D. Prevosto, S. Sharifi, S. Capaccioli, P. A. Rolla, S. Hensel-Bielowka, and
M. Paluch, J. Chem. Phys. 127, 114507 (2007).
36G. Williams, Trans. Faraday Soc. 62, 2091 (1966).
37S. C. Kuebler, D. J. Schaefer, C. Boeffel, U. Pawelzik, and H. W. Spiess,
Macromolecules, 30, 6597 (1997).
38G. Williams, Trans. Faraday Soc. 62, 1321 (1966).
39A. Reiser, G. Kasper, and S. Hunklinger Phys. Rev. Lett. 92, 125701
(2004).
40J. Bohlen and R. Kirchheim, Macromolecules 34, 4210 (2001).
41G. Dlubek, J. Wawryszczuk, J. Pionteck, T. Goworek, H. Kaspar, and
K. Helmut Lochhaas, Macromolecules, 38, 429 (2005).
42G. Dlubek, J. Non-Cryst. Solids 352, 2869 (2006).
43D. Kilburn, J. Wawryszczuk, G. Dlubek, J. Pionteck, R. Häßler, and
M. Ashraf Alam, Macromol. Chem. Phys. 207, 721 (2006).
44G. Dlubek, J. Pionteck, M. Sniegocka, E. M. Hassan, and R. Krause-
Rehberg, J. Polym. Sci., Part B: Polym. Phys. 45, 2519 (2007).
45M. Schmidt, M. Olsson, and F. H. J. Maurer, J. Chem. Phys. 112, 11095
(2000).
46R. Casalini, S. Capaccioli, M. Lucchesi, P. A. Rolla, M. Paluch, S. Corezzi,
and D. Fioretto, Phys. Rev. E 64, 041504 (2001).
47A. Kudlik, C. Tschirwitz, T. Blochowicz, S. Benkhof, and E. Rössler, J.
Non-Cryst. Solids 235–237, 406 (1998).
48K. Kaminski, E. Kaminska, K. L. Ngai, M. Paluch, P. Wlodarczyk,
A. Kasprzycka, and W. Szeja, J. Phys. Chem. B 113, 10088 (2009).
49D. Pisignano, S. Capaccioli, R. Casalini, M. Lucchesi, P. A. Rolla, A. Justl,
and E. Rössler, J. Phys.: Condens. Matter 13, 4405 (2001).
50D. Prevosto, S. Capaccioli, M. Lucchesi, P. A. Rolla, and K. L. Ngai, J.
Chem. Phys. 120, 4808 (2004).
51S. Kahle, J. Gapinski, G. Hinze, A. Patkowski, and G. Meier, J. Chem.
Phys. 122, 074506 (2005).
52S. Kahle, K. Schröter, E. Hempel, and E. Donth, J. Chem. Phys. 111, 6462
(1999).
53S. Capaccioli, D. Prevosto, M. Lucchesi, P. A. Rolla, R. Casalini, and K. L.
Ngai, J. Non-Cryst. Solids 351, 2643 (2005).
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