Materials Sciences and Applications, 2011, 2, 624-628
doi:10.4236/msa.2011.26084 Published Online June 2011 (
Copyright © 2011 SciRes. MSA
Activation Volume of Secondary Relaxation
Soheil Sharifi
Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran.
Received January 30th, 2011; revised March 28th, 2011; accepted April 2nd, 2011.
Glass forming materials are characterized by a complex relaxation pattern, which evolves over several time decades.
Dielectric spectroscopy has proven particularly useful for studying such scenario as it is able to monitor the dielectric
dynamics of a system over a range up to 16 time decades. In this work we study effect of thermodynamic history on ac-
tivation volume of secondary relaxation inside the glassy forming systems, Poly[(phenyl glycidyl ether)-co-formaldehyde],
(PPGE) and 1,18-bis (p methoxyphenyl) cyclohexane (BMPC), with two different type of secondary relaxation. Our
results show that at bout systems, activation volume of secondary depends to the thermodynamic history.
Keywords: Activation Volume, Secondary Relaxation, Glassy State, Pressure Effects
1. Introduction
Secondary relaxations are the only dynamic processes
active on a measurable time scale in the glassy state. Its
importance is two folds: usually the secondary relaxation
is the main mechanism of glasses for dissipating external
stresses, [1-4]. Moreover, from the dynamic point of
view secondary relaxation is a suitable easily accessible
source of information about the glassy state. Despite this
importance, the investigation about secondary relaxation
has been usually limited to the description of its tem-
perature and pressure dependences, but scarce attention
has been devoted to other characterizations, [5-11]. For
example, the secondary process is usually investigated in
the glassy state, which is a non equilibrium state of mate-
rials, but not too much is known about its dependence on
the history of formation of the glass, [12,13]. The conse-
quence of the non equilibrium nature of glasses on the
thermodynamic and structural properties has been largely
studied, and interpretations in terms of phenomenological
models have been proposed. Recently thermodynamic
history dependence was noted in some secondary proc-
esses, as for example, different relaxation frequencies of
secondary processes are observed consequently to cool-
ing with different rates, or after verifications combining
different sequences of cooling and compression steps.
The reason why secondary processes are influenced by
the thermodynamic history of the glass is not clear at all,
and the microscopic mechanisms at the basis of such
dependence are unknown. The situation is even more
complicated since the molecular mechanisms at the basis
of secondary process are not clear at all. A greater sensi-
tivity to the thermodynamic history is expected for secon-
dary processes of intermolecular origin, Johari-Goldstein
(JG) but experimental data lack. In this work, we present
experimental studies varying pressure and temperature
pressures of secondary processes in several glass formers.
Also, we will present the study of the influence of ther-
modynamic history on the secondary process of different
molecular glass formers, namely Poly[(phenyl glycidyl
ether)-co-formaldehyde], (PPGE), 1,18-bis (p methoxy-
phenyl) cyclohexane (BMPC).
2. Experimental
2.1. Materials
Poly[(phenyl glycidyl ether)-co-formaldehyde] (PPGE),
with average molecular weight, M.W. = 345 g/mol, and
Tg around 258 ± 1 K, [10], were supplied by Aldrich
Chemicals. and 1,18-bis (p methoxyphenyl) cyclo-
hexane (BMPC), with average molecular weight, M.W.
= 296 gr/mol, and Tg at ambient pressure around 246 ± 1 K,
was synthesised in the laboratory of professor H. Sillescu
and obtained from Prof. M. Paluch. Glassy 1,18-bis (p
methoxyphenyl) cyclohexane (BMPC) show two secon-
dary relaxations whose molecular origin is not clear at all,
2.2. Methods
Dielectric measurements were carried out by a dielectric
spectrometer (Alpha-Novocontrol) in the frequency in-
terval 10–2 - 107 Hz. For measurements at ambient pres-
Activation Volume of Secondary Relaxation625
sure the sample was placed in a parallel plate cell (di-
ameter 30 mm, gap 0.1 mm) and the temperature control
was performed with a precision better than 0.1 K by us-
ing a dry-nitrogen stream based system. For measure-
ments at high pressure the sample was placed in a paral-
lel plate cell (diameter 20 mm, gap 0.05 mm) that, prop-
erly insulated from the external environment, was lo-
cated inside a pressure chamber. Pressure variations
(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
pressure room, allowed the control of temperature (353 -
233 K) within 0.1 K.
3. Results
Representative isothermal dielectric loss spectra of the
investigated glass formers in the glassy state are pre-
sented in Figure 1. We acquired dielectric spectra by
varying pressure from 0.1 MPa up to the maximum value
of 600 MPa. For all the systems we can observe a peak,
corresponding to the secondary relaxation: In the case of
PPGE, we observe at high frequencies a rise in the signal
partly due to the presence of a faster relaxation, which
however is never completely visible with our apparatus
for high pressure measurements. In the case of 1,18-bis
(p methoxyphenyl) cyclohexane (BMPC) at low fre-
quencies the tail of the structural peak is still present in
some spectra. The β-relaxation in Poly[(phenyl glycidyl
ether)-co-formaldehyde],(PPGE), moves to lower fre-
quencies faster than the secondary relaxation in 1,18-bis
(p methoxyphenyl) cyclohexane (BMPC), Figure 1. It is
reported that the β-secondary process of Poly[(phenyl
glycidyl ether)-co-formaldehyde] (PPGE) is of the Jo-
hari-Goldstein (JG) type [12], whereas the β-process of
1,18-bis (p methoxyphenyl) cyclohexane (BMPC) is not
Johari-Goldstein (Non-JG), [13].
In this work, we studying the secondary relaxation in
glassy materials prepared along the thermodynamic paths
represented in Figure 2 and Table 1. In particular we
focused on the β-process of 1,18-bis (p methoxyphenyl)
cyclohexane (BMPC) and Poly[(phenyl glycidyl eth-
er)-co-formaldehyde] (PPGE). Along the path (A), we
vitrify the material by isothermal compression (to the
point B) and finally we cooled the material to the tem-
perature represented by the point D. Subsequently to this
procedure the secondary relaxation was studied during
isothermal decompression (D-C). Along path (B), we
vitrified the system by cooling at ambient pressure (to the
point C having the same value of T of the point D) and
then we investigated the secondary relaxation along the
isothermal path with increase pressure.
Figure 3 shows maxima frequency as a function of
pressure for 1,18-bis (p methoxyphenyl) cyclohexane
Figure 1. (a) Isothermal loss spectra of Poly[(phenyl gly-
cidyl ether)-co-formaldehyde], (PPGE) at different pressure,
The points are results of experiment and lines are the fit of
Equation (1); (b) Isothermal loss spectra of 1,18-bis (p me-
thoxyphenyl) cyclohexane (BMPC) at various pressures in
the glassy state. Secondary peak slightly shifts with pressure
towards lower frequencies. Empty squares represents the
loss spectrum measure at 100 MPa corrected for the con-
tribution of the α-peak. The points are results of experiment
and lines are the fit of Equation (1).
Table 1. Parameters of the thermodynamic paths repre-
sented in Figure 2.
Path A Path B
Ti, Pi Tf, Pf T
g(p) T
i, Pi T
f, Pf
BMPC 260 K
0.1 MPa
234 K
600 MPa
260 K
150 MPa
260 K
0.1 MPa
234 K
600 MPa
PPGE 283 K
0.1 MPa
253 K
450 MPa
283 K
200 MPa
342 K
0.1 MPa
253 K
450 MPa
Copyright © 2011 SciRes. MSA
Activation Volume of Secondary Relaxation
Figure 2. Schematic representation of the thermodynamic
paths for study the thermodynamic history we consider two
path that path (A) is the material by isothermal compres-
sion to the point B and cooled to lower temperature, The
path (B), liquid is cooled at ambient pressure to the glassy
state and then pressure increased.
(BMPC). We analyzed spectra in terms of a HN function
for the structural process, Equation (1) and a Cole-Cole
equation (β = 1 at Equation (1)) for the secondary relaxa-
 
In the case of Poly[(phenyl glycidyl ether)-co-for-
maldehyde], (PPGE), we added a HN equation for fitting
the faster secondary relaxation (γ-relaxation). The shape
parameters used in the HN equation for the γ-relaxation
in these systems were obtained from fitting of spectra at
very low temperature and ambient pressure where the
γ-relaxation can be clearly observed. Moreover, a similar
procedure was used for fitting the tail of the structural
peak when present in the spectra. The pressure depend-
ence of secondary relaxation for 1,18-bis (p methoxy-
phenyl) cyclohexane (BMPC) and Poly[(phenyl glycidyl
ether)-co-formaldehyde], (PPGE) with different origin is
represented in Figure 3 for 1,18-bis (p methoxyphenyl)
cyclohexane (BMPC) and Figure 4 for PPGE. At the
1,18-bis (p methoxyphenyl) cyclohexane (BMPC), the
glass formed along path (A) is less sensitive to change in
pressure than that formed along path (B). In analogy, we
saw the same effect in the PPGE Figures 3 and 4. We
calculate activation volume from Equation (2), which is
reported in Table 2.
max0 exp
Figure 3. log (νmax) as a function of pressure for 1,18-bis (p
methoxyphenyl) cyclohexane (BMPC) with increase of pre-
ssure (circle points-Path (B)) and decrease pressure (squa-
re points-Path (A)).
Figure 4. log(νmax) as a function of pressure for Poly[(phenyl
glycidyl ether)-co-formaldehyde], (PPGE) with increase of
pressure (up triangle points) and decrease pressure (down
triangle points).
Table 2. Activation volume of secondary relaxation in
Poly[(phenyl glycidyl ether)-co-formaldehyde], (PPGE) and
1,18-bis(p methoxyphenyl) cyclohexane (BMPC) with de-
crease and increase pressure and thermodynamic paths of
Table 1.
T(K) Vβ (ml/mol)
Increase Pressure
Vβ (ml/mol)
Decrease Pressure
BMPC 234 5.2 ± 0.1 2.6 ± 0.1
PPGE 253 17.9 ± 0.5 15.2 ± 0.2
where νP = 0 is the relaxation frequency at ambient pres-
sure and temperature corresponding to that of the iso-
therm of investigation, Vβ is the activation volume of
the secondary (β-) process.
Copyright © 2011 SciRes. MSA
Activation Volume of Secondary Relaxation627
4. Discussions
Density variations affect the secondary relaxation pro-
cess in the investigated systems. In fact, the relaxation
frequency decreases on increasing pressure at fixed tem-
perature, which correspond to an increase of density
(Figure 1). The extent of the density effect on the sec-
ondary dynamics depends on the investigated system.
Accordingly, secondary relaxation in Poly[(phenyl gly-
cidyl ether)-co-formaldehyde], (PPGE) is more sensitive
to density (larger values for V) than 1,18-bis (p meth-
oxyphenyl) cyclohexane (BMPC) (smaller values for V)
(Table 2). Systems vitrified along path A are compressed
in the liquid state and then in the glassy state, whereas
systems vitrified along the path B are compressed only in
the glassy state (Figure 2). We can expect that glasses
prepared along path A have larger density than those
prepared along path B. In fact, compressing is usually
more effective in increasing the density than cooling and
the compressibility of the liquid is larger than that of the
glass. This should be reason of the different of the be-
havior of secondary relaxation when we increase pres-
sure or decrease pressure that we can see it on the be-
haviors of activation volume of secondary relaxation
inside the glassy state.
5. Conclusions
In this study, we performed several experiments with the
aim of characterizing the dependence of the secondary
relaxations on the thermodynamic history used to pro-
duce the glass. We observed a relation between the de-
pendence on thermodynamic history of the activation
volume and compressibility. In particular, using different
thermodynamic histories we observed in 1,18-bis (p me-
thoxyphenyl) cyclohexane (BMPC) and Poly[(phenyl
glycidyl ether)-co-formaldehyde], (PPGE), that the β-
process has larger activation volumes (larger pressure
sensitivity) in glasses prepared with lower densities. This
characteristic is independent from the microscopic origin
of the process, as in Poly[(phenyl glycidyl ether)-co-
formaldehyde], (PPGE), it is of the Johari-Goldstein (JG)
type and in 1,18-bis (p methoxyphenyl) cyclohexane
(BMPC) is non- Johari-Goldstein (Non-JG).
6. Acknowledgements
This work was supported by the University of Sistan and
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