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Polymer International 40 (1996) 239-249
Multiple Dielectric Relaxation Processes
in an Unequilibrated Bisphenol-A
Polyca r bonate
Graeme J. Pratt* & Michael J. A. Smith
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
(Received 15 December 1995; accepted 12 March 1996)
Abstract: Complex relative permittivity data within the ranges 0-1Hz-3 MHz
and -175°C to + 2 W C are presented for an unequilibrated compressionmoulded bisphenol-A polycarbonate of commercial origin (LEXAN 141). Comparisons are drawn with the nitrogen-equilibrated material in which eight
distinct absorption regions have been identified. One low-frequency region
common to both materials at low temperature is shown to be caused directly by
a processing stabiliser. A second at high temperature is thought to originate in
part from an interfacial polarisation associated with a second phase of polycarbonate. An absorption observed only in the unequilibrated polycarbonate is
attributed to bound water. Two intermediate-temperature losses are differentiated and delineated for the first time. Their origins and reason for diminution
by annealing are examined. The multiplicity of overlapping absorptions, including a low-temperature loss region which is almost continuous at higher frequencies, is consistent with the high impact strength of polycarbonate over an
extended temperature range.
K e y words: dielectric loss, permittivity, polycarbonate, DC-resistance, interfacial
polarisation, low-temperature properties, intermediate-temperature processes,
relaxation processes, impact strength.
ratively high, although some deterioration of properties
occurs where exposure to ultra-violet radiation or other
environmental influences is prolonged. The photodegradation of polycarbonate, as indicated by dielectric
measurement, is the subject of a separate study.'
Comprehensive measurements of dielectric response
at sub-gigahertz frequencies can yield valuable information regarding modes of molecular and segmental
motion in polymers. Characterization of the motion is
often facilitated by the use of complementary techniques
such as dynamic mechanical measurements, thermallystimulated depolarization (TSD), deuterium or carbon13 nuclear magnetic ~ ~ S O ~ a n(NMR),
neutron scattering (SANS) and electron spin resonance
(ESR). In particular, comparisons between absorption
Polycarbonate is much used for its high impact
strength, dimensional stability and low &electric loss
over a wide temperature range. These properties, combined with its transmissibility and low crystallinity,
have led to applications in recent technologies, such as
the optical highway in car area networks (CAN) and the
CD-ROM, in addition to established uses in, for
example, safety-related products and film capacitors.
Resistance to ageing and photo-degradation is cornpa-
* To whom all correspondence should be addressed at:
Department of Mechanical & Manufacturing Engineering,
University of Melbourne, Parkville 3052, Australia.
Polymer International 0959-8103/96/$09.00 0 1996 SCI. Printed in Great Britain
peaks observed by dielectric and dynamic mechanical
methods can elucidate details of the specific molecular,
segmental and side-group motions responsible for transitions and secondary relaxations, as cited for polymethyl metha~rylate~.~
and for polystyrene and related
Dielectric response at the lower frequencies includes
contributions reflecting the phase morphology of the
polymer and its content of mobile charged species.
Material differencesbetween phases cause charge accumulations at the phase boundaries which lead to dielectric spectra characterized by a Debye shape. Such
interfacial polarisations, usually referred to as MaxwellWagner-Sillars (MWS) processes, can produce a high
dielectric increment, particularly when conductivity differences between the phases are pr~nounced.~
shape of a suspended phase may or may not be of particular significance. A further contribution to the imaginary permittivity at the lower frequencies is provided
by any non-dispersive DC conductivity associated with
translational charge motion, normally that of impurities
in the continuous phase. The magnitude and inverse frequency dependence of this loss may cause the imaginary
component of a low-frequency MWS process to be
In an earlier paper6 dielectric data extending over a
wide and continuous range of frequency and temperature were presented for samples of the 141 (basic)
and 143 (W-resistant) grades of LEXAN polycarbonate which had been equilibrated in dry nitrogen
at 30-35°C for at least 24h prior to investigation. We
now report a complementary dielectric investigation of
unequilibrated LEXAN 141. Attention is directed
towards the multiple secondary relaxations occurring in
the glassy state, with particular emphasis on relaxations
observed at intermediate temperatures. Although relaxations in the latter temperature region have been
reported previously by Krum & MUllery7 Watts &
Perry' and othersY9-' considerable disagreement persists regarding the nature, location and origin of these
intermediate processes. One specific area of contention
is the suggestion of Muller and other^^-'*'^ that the
'intermediate process' in polycarbonate is a nonequilibrium effect associated with residual stresses.
G. J . Pratt, M . J . A. Smith
ginary permittivity caused by the quasi-DC conductivity was subtracted from the measured total permittivity.
3.1 Presentation of experimental results
The response of unequilibrated LEXAN 141 to an
applied alternating field, less the small quasi-DC conductivity, is shown in Figs 1-3. Figure 1 is a contour
map of loss tangent (tan 6)as a function of temperature
and frequency. Figure 2 is the corresponding map for
the real relative permittivity E'. The 3-D representation
of the imaginary relative permittivity E" shown in Fig. 3
has axis scales and an aspect chosen to assist the visualisation of absorption regions. Nine distinct regions,
identified as a peak or shoulder of significant extent,
may be distinguished in this representation. The possible existence of a tenth relaxation process is suggested
by the observation that one of the absorption regions
shows a change of slope in its Arrhenius plot, implying
that two processes may be operating over different temperature regimes.
Figure 4 is an Arrhenius plot of the logarithm of the
frequency ( v 3 of maximum loss against reciprocal temperature for the dielectric a-process. Corresponding
plots for the 'intermediate' and b-processes are shown in
Figs 5 and 6 respectively. Figure 5 also includes comparative data for intermediate-temperature absorptions
which have been reported in the literature. The numerical values in Fig. 6 are derived activation energies for
each linear section of the plot.
Three distinct dispersion regions are evident in the
contour map of E' (Fig. 2); a low-temperature region
where the value of E' increases gradually with an
increase in temperature or a decrease in frequency, an
extensive plateau region at intermediate temperatures
throughout which E' is essentially constant (3% total
change), and a high-temperature region where e'
increases rapidly with increasing temperature. The
plateau region extends from about - 119°C to + 164°C
at 0.1 Hz and from about -9°C to + 172°C at 3 MHz.
More detail is apparent in the 3-D representation of E"
(Fig. 3). The individual features are discussed separately
in succeeding sections.
Samples of LEXAN 141 clear bisphenol-A poly3 2 High -temperature processes
carbonate manufactured by General Electric Plastics
were prepared and tested according to the general
experimental procedures described e l s e ~ h e r e . ~ * ' ~3.2.1
~ ~ ~A Maxwell- Wagner-Sillars process. The very
large losses reported in equilibrated LEXAN 141 and
They were exposed to the laboratory atmosphere for at
143 at low frequencies and the highest temperatures
least 1 month before investigation. Immediately prior to
also occur in the unequilibrated material.6 The rise is
a dielectric measurement, the quasi-DC conductivity
particularly apparent in the 3-D representation of E" (v,
was determined after allowing time, typically up to 1h,
7') shown in Fig. 3.
for the decay of current transients. The equivalent imaPOLYMER INTERNATIONAL VOL. 40, NO. 4, 1996
24 1
Multiple dielectric relaxation processes
Fig. 1. Contour map showing the temperaturefrequency variation of tan 6 for unequilibrated LEXAN 141.
The activation energy associated with the slope of the
high tan S contours of Fig. 1 is the same as that of the
quasi-DC conductivity (about 220 kJ mol- I), and the
contour separation at a given temperature, where it can
be discerned, is consistent with an approximate inverse
frequency dependence of the loss. Moreover, the
highest-temperature real-permittivity contour (E' = 3.8)
in Fig. 2 also has a slope indicating a causal link with
200 OC
Fig. 2. Contour map showing the temperaturefrequency variation of real relative permittivity E' for unequilibrated LEXAN 141.
G . J . Pratt, M . J . A. Smith
Fig. 3. 3-D model representation of the temperature-frequency variation of imaginary relative permittivity ~''(v, 7') for a sample of
unequilibrated LEXAN 141 polycarbonate. The annotations DC/MWS, a, i,, i, , pi, #I2,J,, LT and H,O refer to the individual
dispersion regions discussed in the text.
the DC conductivity. This contrasts with the E' contours
between 3-1 and 3-6 at the higher frequencies which are
associated with the more highly activated primary arelaxation. These observations suggest that, in addition
to a direct contribution from the DC conductivity, a
polarisation process involving the DC conductivity
indirectly is providing a significant contribution to the
high-temperature permittivity at the lower frequencies.
The extended form of the equations of Sillars given
by van Beek5 for the case of a continuous phase containing a random suspension of a spheroidal second
phase of lower conductivity and similar real permittivity
can provide an explanation for the present observations. The continuous phase (matrix) is identified with
amorphous polycarbonate and the second phase with a
crystalline or a densified, variant. With the further
assumption of a second phase in the shape of oblate
spheroids (lamellae), the equations can be used to
predict a high-frequency tail of an MWS polarisation of
appropriate magnitude extending into the present lowfrequency region, even for an anticipated second-phase
concentration of a few percent.
24 K . '
Fig. 4. Arrhenius plot (logarithm of frequency v, of maximum
loss plotted against reciprocal temperature) for the a-process
in unequilibrated LEXAN 141.
3.2.2 Alpha process. The primary (a-) relaxation associated with the glass transition appears as an extremely
narrow (about 25°C wide) and very prominent region of
absorption which merges into the combined DC/MWS
absorptions below a few hertz. The a-peak extends from
160°C at 3 Hz to 200°C at 1 MHz. The average activation energy derived from the Arrhenius plot for the aprocess in unequilibrated LEXAN 141 (Fig. 4) is
530 kJ mol-l over the reciprocal temperature interval
(22-24) x 10-4K-'. This value compares with
490kJmol-I for equilibrated LEXAN 141 over the
same interval given in the earlier paper6 where it was
noted that values from 480 to 835 kJ mol-I have been
reported in the literature. The curvature of the Arrhenius plot of Fig. 4 demonstrates -an inadequacy in the
Multiple dielectric relaxation processes
-zE 3 0
1 4T
Fig. 5. Arrhenius plot for the intermediate-temperature processes in bisphenol-A polycarbonate. The symbols 0 and
refer to
equilibrated and unequilibrated LEXAN 141 in the present work. The other symbols refer to previous work reported in the
literature; the associated numbers correspond with those stated in the list of references.
5 -
; *3
Fig. 6. Arrhenius plot for the /Iand
- related processes in equilibrated and unequilibrated LEXAN 141.
G . J . Pratt, M . J . A. Smith
single activation energy, or single relaxation time, representation of the a-process and suggests a range of constraints and environments which affect the large scale
motion of individual molecules and segments in the
solid polymer. A functional decrease in activation
energy with increasing temperature is a well-known
phenomenon for polymeric a-relaxations and is often
described by the semi-empirical Williams-Landel-Ferry
(WLF) equation" or its generalised version." Characterisation by an average activation energy rather than
by WLF or Rusch parameters is used here to facilitate
comparison with other studies.
3.3 Lo w-temperatureprocesses
3.3.1 Beta and related processes. Differences in composition, thermal history and pre-treatment, and limitations
imposed by the experimental method, have led to
apparent conflict in the results of earlier investigations
on polycarbonate. Many diele~tric'~~'~~'~~~~-~~
mechanical' 2 ~ 1 4 * 2 8 ~ 2 9investigations report a single,
broad and unresolved #?-peak. LeGrand & Erhardt"
suggest that they were unable to resolve the 8-peak into
its expected three constituent loss curves because
energies caused
temperature-frequency shifts of the individual curves. In
the present work, as noted below, activation energies for
the three processes are indeed essentially the same. Illers
& B r e ~ e r , ~Nielsen3'
and Watts & Perry' report an
asymmetrical 8-peak for polycarbonate, whilst others
1-33 three34.35
succeed in resolving the peak into
or even four3" components.
The applied inter-electrode field in a dielectric measurement induces, and responds to, motion in the chain
segments containing electric dipoles, such as the carbony1 or carbonate groups in polycarbonate. However,
local motions of non-polar segments may be detected
indirectly provided they are coupled to the dipolar segments of the polymer chain. For instance, motions of
methyl and phenylene groups in polycarbonate require
cooperative carbonate motion^'^*^'^^^ and are, therefore, observable by dielectric methods. Sacher regards
the structural changes induced in polycarbonate by
annealing at temperatures well below the glass temperature as evidence that a high degree of segmental
chain motion must occur in the glassy state." Open
packing of the polymer chains provides considerable
freedom of movement of the carbonate
facilitating the molecular and segmental motions
thought to be associated with the 8-process.
Present measurements indicate a clear asymmetry
and structure in the extremely broad 8-absorption
which occupies about two-thirds of the total
temperature-frequency regime for which permittivity
measurements are reported. At each frequency the
width of the absorption is at least 250°C. Its peak
extends from about - 113°C at 3 Hz to about - 15°C at
3 MHz in unequilibrated LEXAN 141 (Fig. l), and corresponds approximately with the low-temperature
boundary of the plateau in E' (Fig. 2). Closer investigation indicates that at least five individual relaxation
processes contribute to the breadth and shape of this
broad /?-peak3' and that three of these components
persist throughout most of the absorption region. Activation energies derived from Arrhenius plots are
21 f 1kJmol-I for each component. The three peaks
may, therefore, be expected to experience identical shifts
with change of temperature and/or frequency, as suggested by LeGrand & Erhardt."
By comparing the dielectric behaviour of bisphenol-A
polycarbonate and the related ester polyethylene
terephthalate, Krum & Muller7 established the role of
the carbonyl/carbonate group in the 8-absorption of
polycarbonate. Subsequent debate has been concerned
with the details of the molecular motions. Specific
mechanisms considered include hindered local mode
relaxation of carbonate groups restricted by adjacent
phenyl g r o ~ p s ~ and
~ combined
~ ~ ~ motions
~ ~ ~
of carbonate groups and phenyl rings hindered by the
glassy matrix.1.15.1 7.24.25,27-29.31-34.38
MGller & Huff7 and others8.9+15,17,23-26,32-34,36,39
have shown that the mechanical and thermal history of
polycarbonate can affect the magnitude of the /?-peak.
McCrum et a1.18 argue that the manner in which the
8-relaxation in polycarbonate is affected by crystallinity
and other factors indicates that the 8-process does not
arise from independent motion of carbonate groups, but
that interactions with other groups must be involved.
Overall, it would appear that these interactions lead to
forms of restricted local motion on the low-temperature
side of the peak whilst, at higher temperatures, combined motions occur which involve tight coupling of
functional groups such as carbonyl and phenyl.
Considering the 8-absorption as a whole, the E" isotherm response is considerably broader than is expected
on a Debye representation. A closer first approximation
might be to regard E" as independent of frequency
within the absorption, thereby implying constant energy
dissipation per cycle, in sharp contrast to the a-peak.
The broad-banded nature of the 8-absorption almost
certainly arises from a relatively strong interaction of
the driven carbonyl dipole with the surrounding
polymer matrix, and with adjacent phenyl groups in
particular. On the lower-temperature side of the &peak
the phenyl groups are immobile3' and segmental
motion is hindered by adjacent phenyl rings. At higher
temperatures the mobility of the phenyl groups facilitates combined motion of carbonate and phenyl groups.
At moderate and low temperatures the loss component
E" falls towards zero at low frequencies whereas the real
component E' increases marginally, indicating that the
dipoles readily follow the applied field at such frequencies.
Multiple dielectric relaxation processes
3.3.2 A water-related process. Above 30 kHz the path of
the loss peak (Fig. 1) is affected by the admixture of an
additional process found only in the unequilibrated
material. The admixture appears in the 3-D representation (Fig. 3) as a subsidiary peak superimposed on the
main /?-absorption and extending from about - 38°C at
100kHz to - 10°C at 3 MHz. The presence of the additional process is even more clearly indicated by the
change in slope of the Arrhenius plot above 30kHz
(Fig. 6). There is no corresponding change in slope for
the equilibrated material. The activation energy derived
from the Arrhenius plot is 62 kJmol-’ for the combined
processes in unequilibrated LEXAN 141.
All samples are cut from the same polycarbonate
sheet after it has received prolonged exposure to
ambient humidity. The unequilibrated sample is tested
without any pre-conditioning whereas the equilibrated
sample is placed in warm, dry nitrogen gas for at least
24 h before commencement of the dielectric measurement. It seems likely, therefore, that the additional
absorption in unequilibrated LEXAN 141 involves a
water-related relaxation.
The influence of water absorption on the /?-peak in
polycarbonate has been noted previously by Chung &
SauerZ8and by Allen et al.” Both groups observed an
increase in the magnitude of the /?-absorption and a
shift in the peak to higher temperature on the addition
of small amounts of water. The extent of the shift was
independent of water content over the concentration
range investigated. Allen et al.” report further that the
activation energy increases from 36 kJ molto
52 kJmol-’.
They conclude that the water molecules hydrogenbond to the polar groups in the polymer chain so as to
participate in the motion causing the relaxation. Allen
et al.” observed similar effects in other polar polymers
containing para-phenylene linkages. Vanderschueren et
al.34breport that TSD results in this temperature range
are very sensitive to the presence of small amounts of
water. They found a water-dependent peak on the
higher temperature side of the /?-peak and attributed
this feature to relaxation of the hydrogen-bonded water
itself. In a detailed study of the influence of water
absorption on the behaviour of injection-moulded
LEXAN 141 polycarbonate, Bair et aLZ7 also report
that the temperature and magnitude of the /?-peak are
both increased by the addition of water. They suggest
that the increase is due to correlated motion of water
dipoles with the polymer molecules, and note further
that the formation of water clusters in hydrolyticallydegraded polycarbonate causes additional dielectric
adjacent carbonyl and phenyl groups.” As the additional relaxation does not persist below about - 38”C,
the interaction is deemed to be initiated at this temperature. Alternative models might be based on conformational changes around -38°C which lead to water
structures of limited dimension and moderate conductivity in the persistence region.
3.3.3 A lower-temperature process. A distinctive dielectric absorption is apparent in the vicinity of - 120°C to
-150°C below 3Hz (see, for example, Fig. 1). Aoki &
B~ittain,~’Sikka” and other^'^,'^ suggest that local
motions of methyl groups are the cause of loss peaks
observed variously between - 140°C and -200°C.
on the other hand,
Linkens & Vander~chueren,~~
units are responsible
suggest that motions of -COOfor the TSD peak they observed at - 140°C.
For our particular absorption, the variation of 8’‘
with frequency appears narrow, possibly Debye-like,
suggesting that highly-coupled motion is not involved.
The low-frequency nature of the absorption indicates a
mobile segment which is either large or highly constrained, or a form of interfacial effect. It is unlikely that
motion of methyls is responsible, since any process
involving so small a group would be expected to be seen
as a high-frequency absorption, such as is reported by
TOrma1a4’ at 40MHz. T0rmala40 attributes his (6)
relaxation to methyl group orientation and points out
that the effective activation energy (lOkJmol-l) is in
agreement with that estimated for methyl group rotation in polycarbonate.
In an earlier paper6 this low-frequency lowertemperature absorption was attributed tentatively to
the presence of a processing stabiliser. More recently,
permittivity measurements have been repeated for an
equivalent additive-free grade of bisphenol-A polycarbonate (LEXAN 145) which contains no phosphite
processing ~ t a b i l i s e r .In
~ ~ this material no separate
absorption is observed in the vicinity of -120°C to
- 150”C, confirming the hypothesis that the lowertemperature low-frequency absorption is associated
directly with the processing stabiliser.
At these low temperatures the stabiliser has condensed to form an additional phase and, hence, an interfacial polarisation with a peak position determined
primarily by the conductivity of the phosphite condensate.5 The observed fall in the peak height of the
absorption with increasing temperature is consistent
with dispersal of the condensed phase as the temperature is raised.
In the present work, the higher activation energy of
the water-related relaxation relative to the fundamental
/?-process is consistent with the existence of hydrogenbonding or some other form of intermolecular interaction which hinders the cooperative movements of
3.4 Intermediate -temperature processes
A number of workers7-17 have reported absorption
regions at temperatures intermediate between those of
the a- and /?-relaxations, as summarised in Fig. 5.
G.J. Pratt, M . J. A. Smith
or tWo7 frequencies only,
Observation has been by d i e l e c t r i ~ ~ - and
' ~ ~ ~ ~one8-14.16,17,24,25,32,35.39
dynamic m e ~ h a n i c a l ' - ' ~ * ~ ~techniques,
~ ' ~ ~ ' ~ although
and fail to distinguish two separate intermediateNeki & Geili4 report the absorption only for mechanitemperature relaxations in bisphenol-A polycarbonate.
cal tests. The polycarbonate materials are obtained
The earlier paper6 failed to recognise fully the range
from a variety of sources and also differ in their preof the i,-absorption. Its extent is, however, readily
treatment and thermal history. There are considerable
apparent in the constant-frequency E"( T) plots and the
variations in detail between data from the different
3-D model representation of ~ " ( v ,T) (Fig. 3). The i,sources.
absorption appears as a separate loss peak at low and
Dynamic mechanical measurements at approximately
intermediate frequencies which gradually merges with
1Hz on Bayer polycarbonate show an absorption at
the primary absorption region until, at the highest freintermediate temperatures near to 70°C for untreated'
quencies, it becomes a faint shoulder on the lowor compression-moulded samples" and for injectiontemperature side of the a-peak. The i,-absorption most
moulded film." At higher frequencies the absorption
probably corresponds with that reported by Miiller &
occurs in the vicinity of 100-llO"C, although Neki &
c o - ~ o r k e r sSacherI5
and other^.^^'^^'^
GeilI4 report a somewhat lower temperature. Neki &
At kHz frequencies around 100°C Krum & Muller7b
Geil14 tested Mobay MERLON 60 polycarbonate
observed an absorption of moderate intensity only in
whereas LeGrand & Erhardt'' and Litt & Torp13 both
polycarbonate samples which had been injectionused General Electric LEXAN materials in the respecmoulded or cold-drawn. Annealing diminished the magtive forms of compression-moulded and as-received
nitude of the absorption, and they were unable to detect
sheet. The temperature difference at the higher frethe absorption in fully-annealed samples. Watts &
quencies might arise from the difference in materials.
Perry,' Muller & co-workers7 and others'," conclude
Alternatively, two different intermediate-temperature
that the 'intermediate process' in polycarbonate is a
processes may be involved, as is indicated by the evinon-equilibrium effect associated with stresses induced
dence below.
by the moulding process or subsequent mechanical
The dielectric measurements reported in the literature
are concentrated primarily in the vicinity of 1-3 kHz. At
An interfacial origin for the i,-absorption is discounted at this time because a dispersed phase of suffisuch frequencies the quoted temperature for the 'intermediate' process(es) ranges from approximately 55°C to
cient conductivity cannot be identified. Watts & Perry'
120°C. The lowest values are those of Muller & Huff7"
and ~ t h e r ~ ~have
~ suggested
~ ' ~ *that
~ their
~ ~ interme* ~ ~
for quenched Bayer MAKROLON polycarbonate. The
diate process is associated with a pre-T, phenomenon.
At temperatures where there is insufficient thermal
highest reported values are for LEXAN
Variation in the source or manufacture of the polyenergy to excite micro-Brownian motion in complete
the available energy
polymer chains, that is below
carbonate appears to produce greater differences in the
temperature location of the absorption than are caused
may be shared between restricted sequences of repeat
units which could then undergo some form of motion
by variation in thermal or mechanical pre-treatment.
relative to each other. Such behaviour implies that the
In the present work two distinct absorptions of lesser
spatial variation of free volume is such that segmental
magnitude than the high-temperature processes are
motion is possible in some regions and not in others. As
reported in the glassy state at temperatures above
ambient. The first, referred to as the first intermediate
the temperature is raised the energy and free volume
fraction continue to increase until, at T,, continuous
i,, is a region of moderate loss which appears in
sequences of repeat units are excited into motion. Kilian
constant-frequency plots of E"( T) (not presented here) as
a shoulder from about 105°C at 0.1Hz through to
& B ~ u e k ehave
~ ~ presented evidence from X-ray diffraction measurements for the existence in polystyrene
about 140°C at 300Hz, but which cannot be discerned
of organised coils which contain approximately 12 main
above 1kHz. The loss corresponds closely with the
'intermediate' absorption reported previously by Watts
chain carbon atoms and 50 atoms in total and which
& Perry' for lower average molecular weight LEXAN
move relative to each other at temperatures approach101.
ing T,,where all traces of such organisation are lost.44
The second intermediate absorption region (i,) perThe i, relaxation process is now regarded as involving partially-correlated motion of a moderate number
sists throughout the frequency range covered by the
of molecular segments or repeat units. This process
present work, and may be followed from about 60°C at
could be viewed as a precursor to the cooperative but
0-1Hz to approximately 160°C at 3 MHz. Such a wide
uncorrelated micro-Brownian motion which occurs
frequency range for an intermediate-temperature
above q . The primary a-relaxation itself is associated
process has not been reported previously. Indeed, with
with micro-Brownian motion of complete polymer
the exception of the data of SacheP which covers
chains which is sufficiently extensive that correlation
three frequency decades (but which shows a somebetween the motions of the chain repeat units is no
what unusual frequency-temperature dependence),
longer discernible.
most earlier studies report measurements at
Multiple dielectric relaxation processes
The location of, and activation energy for, the i,peak/shoulder in the tan 6 contour map (Fig. 1) are
intermediate between those of the ct- and /?-peaks. It has
been noted above that the /?-process is a consequence of
a range of restricted local motions involving coupled
motions of carbonyl and phenyl groups in the repeat
unit of bisphenol-A polycarbonate. The range of
motions produces an exceedingly broad /?-absorption in
In contrast, the i,-absorption, as well as being of substantially lesser magnitude, is not as diffuse as the /?absorption and is shifted to higher temperature. These
characteristics of the i,-peak are consistent with an
extended local motion which resembles the restricted
local motions associated with the /?-relaxation process
but which involves the cooperative motion of a fairly
specific sub-unit of the polycarbonate molecule consisting of a fixed number of repeat units or an almost constant number of such units.
Sacher' attributes his intermediate (7) absorption in
polycarbonate to a cooperative movement of several
repeat units which resembles wagging and rocking
vibrations of carbonate, methyl and phenylene groups
in the polymer chain. On the other hand, on the basis of
NMR and carbon- 13 chemical shift anisotropy, Jones &
co-workers3' propose that phenyl groups undergo 180"
flips and restricted oscillation. Although this relaxation
process has usually been assumed to occur in the upper
temperature region of the /?-absorption, the same temperature region also encompasses the i,-absorption of
the present work.
and other^^^-^' have also reported
Schaefer et
the occurrence of 180" ring flips of phenyl groups in
bisphenol-A polycarbonate. The defect-diffusion ringflip mechanism proposed by Jones3' involves the interchange of cis-trans and trans-trans transformations (or
equivalent transitions) between adjacent carbonate
groups in the polycarbonate chain. These particular
conformational transitions alter the relative positions of
adjacent carbonate groups in a manner which can activate 180" ring flips of an intervening phenyl group. This
motion produces a volume fluctuation which can diffuse
along the chain as the cis-trans conformation diffuses
along polycarbonate chains composed largely of transtrans units.
In addition to such intrachain influences, the rotational freedom of the phenyl rings is limited by interchain steric interactions due to the proximity of rings in
adjacent chains. Indeed, Schaefer, Perchak and
other^^^,^^ suggest that it is the volume fluctuations
associated with the dilation of the surrounding polycarbonate 'lattice' which relax interchain constraints
and allow the rings to flip. Regardless of whether
volume fluctuations are seen as the controlling
or because constraint relaxation is a consequence of conformational e ~ c h a n g e , ~there is general
agreement that such fluctuations must necessarily create
sufficient free space to allow a ring to flip. The magnitude of the i,-relaxation is substantially less than that of
the /?-relaxation, being consistent with the statistical probability of occurrence and transformation of
the necessary conformations, namely cis-trans
trans-trans or equivalent, to facilitate 180" ring flips of
intervening phenyl groups.
Krum & Muller,7 Watts & Perry'
other^^^.^^,^^^*^^.^^ report that the magnitude of the
intermediate relaxation in polycarbonate is diminished
by annealing at temperatures below T,, and suggest
that their intermediate relaxation arises from a nonequilibrium process associated with residual frozen-in
stresses which are removed by annealing. The
compression-moulded samples used in the present work
would not be expected to retain frozen-in stresses from
the moulding process, and are maintained at elevated
temperature for a considerable period of time during
measurements. No diminution of the intermediatetemperature absorptions was observed. The two
separate intermediate relaxations which are observed
and defined occur in all LEXAN grades which have
been investigated, whether equilibrated or unequilibrated, UV-irradiated or unirradiated. It appears
unlikely, therefore, that either of the intermediatetemperature absorptions observed in the present work
is due to 'moulded-in' stresses.
~ ' ~
Computer simulations by Perchak et ~ 1 . suggest
that phenyl ring motions are greatly affected by the surrounding environment. One consequence of the annealing process in polymers is a reduction in free-volume
fra~tion.'l-~ Annealing and physical ageing lead to
more efficient packing of chains with consequential inhibition of ring flip and phenyl rocking motions.47 Rather
than the relief of frozen-in stresses, this reduction in free
volume is considered to be the underlying cause of the
diminution by annealing of the intermediate relaxa t i o n ~ . ~ - ~A *ring-flip
~ ~ * process
~ ~ ~ *such
~ ~as~ that
~ ~
described by Jones, Schaefer and others38,45-48would
necessitate the existence of substantial packets of free
volume each greater than a critical extent uCRIT to
permit 180" rotation of a phenyl ring whether by
conformational transformations or other process.
Bisphenol-A polycarbonate normally contains free
volume suflicient to permit substantial segmental
motion even in the glassy ~ t a t e . ~ ~However,
~ . ~ ~ , ~ ~ - ~
annealing would reduce the overall free-volume fraction
and, in particular, would reduce the proportion of free
volume in packets of critical extent, thereby inhibiting
the 180"ring-flip process.
Furthermore, the &peak occurs at significantly
higher temperatures (Fig. 5 ) in unequilibrated LEXAN
141 than in the equilibrated material. The &-relaxation
is likely, therefore, to involve a process which is affected
by the presence of absorbed moisture. The higher temperature in the unequilibrated material is consistent
with the occurrence of hydrogen-bonding or similar
influences which hinder motion. Average activation
energies are 172 kJmol-1 and 207 kJmol-1 for equilibrated and unequilibrated LEXAN 141 respectively.
This difference in activation energies is similar to that
associated with the water-related absorption in the /Iregion of unequilibrated LEXAN 141. Intermolecular
and intramolecular hydrogen-bonding would interfere
with the movement of the large sub-unit associated with
the 180" phenyl ring flips which, on balance, are considered to be the origin of the dielectric i,-absorption.
MWS interfacial polarisation arising from the conductivity mismatch between different phases or domains
most probably contributes to the losses at high temperatures and low frequencies in polycarbonate. Acceptable agreement is obtained between experimental data
and a model based on a two-phase morphology containing a small fraction of relatively non-conducting
densified or crystalline lamellar domains in a predominantly amorphous matrix.
Despite considerable conflict in detail between the
various published studies, it is clear that secondary
relaxation processes in bisphenol-A polycarbonate are
affected by thermal and mechanical history.
Evidence has been presented for at least nine
dielectrically-active relaxations in unequilibrated
LEXAN 141 polycarbonate. In many applications polycarbonate is chosen principally for its superior impact
strength over an extended temperature range. The very
broad low-temperature absorption arises from overlapping multiple loss processes involving a range of molecular and segmental motions and is well illustrated in the
3-D representation of ~ " ( v ,T) (Fig. 3). The one relaxation which is absent in the corresponding equilibrated
material is thought to be water-related. Of the relaxations which occur at low temperatures, those associated with the B-processes provide significant
energy-dissipating mechanisms, particularly at the
higher frequencies. The semi-continuum of loss provided by the multiplicity of overlapping absorptions in
polycarbonate at the higher frequencies offers a reason
for the good impact behaviour at low temperature.
The combined evidence from a range of experimental
techniques indicates that suflicient free volume exists in
the glassy state of unannealed bisphenol-A polycarbonate to permit a range of restricted local-mode
motions activated by the strongly polar carbonyl
groups. In the lower temperature range of the Babsorption the immobility of the phenyl groups severely
restricts segmental motion. As temperature is increased
mobility of the phenyl groups permits a range of
carbonyl-driven cooperative localised motions of the
polycarbonate chain backbone.
G. J . Pratt, M . J . A. Smith
In the earlier work6 it was tentatively proposed that
the lower-temperature low-frequency process observed
in commercial polycarbonate materials was due to the
presence of a processing stabiliser. This hypothesis has
been confirmed by measurements for the equivalent
additive-free material.41
Disagreement has persisted regarding details of the
intermediate-temperature relaxations in bisphenol-A
polycarbonate. With the possible exception of the data
of Sacher," previous conflicting reports in the literature
failed to define adequately in the temperature-frequency
regime the extent of either absorption, or even to recognise that the isolated data points arise from separate
dielectric relaxations in bisphenol-A polycarbonate.
In the present work two separate absorptions intermediate between the a- and /I-absorptions are positively
identified and clearly delineated for the first time. The
i,-absorption corresponds with that reported by Watts
8z Perry8 and others1'.17 below 1 kHz, and most probably involves a partially-correlated micro-Brownian
The i,-absorption corresponds with that reported by
Muller and CO-workers,'S a c h e P and ~ t h e r ~ , ~ ~ . ~ ~
and persists throughout the extended frequency range of
the measurements presented here. It is postulated that
the origin of the i,-absorption is a relaxation process in
which the phenyl groups undergo 180" flips as might
arise when adjacent carbonyl groups interchange
between cis-trans and trans-trans conformation^.^^
No evidence has been found to support the
h y p o t h e ~ i s ~that
. ~ the process underlying i, or i,
involves frozen-in stresses of thermal or mechanical
origin. The reduction in free volume by annealing is
proposed as the underlying cause for the reported diminution by annealing of the intermediate absorption@)in
bisphenol-A polycarbonate rather than the relief of
frozen-in residual stresses as hitherto p r ~ p o s e d . ~ - ~
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