Dipolar and ionic relaxations of polymers containing polar conformationally versatile side chains

Article abstract of DOI:10.1021/ma1004875

This work reports a comparative study of the response of poly(2,3-dimethoxybenzyl methacrylate), poly(2,5-dimethoxybenzyl methacrylate), and poly(3,4-dimethoxybenzyl methacrylate) to electrical perturbation fields over wide frequency and temperature windows with the aim of investigating the influence of the location of the dimethoxy substituentsinthe phenyl moietiesonthe relaxation behavior of the polymers. The dielectric loss isotherms above T_g exhibita blurred relaxation resulting from the overlapping of secondary relaxations with the glass-rubber or α relaxation. At high temperatures and low frequencies, the α relaxation is hidden by the ionic conductive contribution to the dielectric loss. Asusual, the real component of the complex dielectric permittivity in the frequency domain increases with decreasing frequency until a plateau is reached corresponding to the glass-rubber (α) relaxation. However, at high temperatures, the real permittivity starts to increase again with decreasing frequency until a second plateau is reached, a process that presumably reflects a distributed Maxwell-Wagner-Sillars relaxation or α' absorption. The α and α' processes appear respectively as asymmetric and symmetric relaxations in the loss electrical modulus isotherms in the frequency domain. To facilitate the deconvolution of the overlapping absorptions, the time retardation spectra of the polymers were computed from the complex dielectric permittivity in the frequency domain using linear programming regularization parameter techniques. The spectra exhibit three secondary absorptions named, in increasing order of time Γ', Γ, and β followed by the α relaxation. At long times and well separated from the α absorption the α' relaxation appears. The replacement of the hydrogen of the phenyl group in position 2 by the oxymethyl moiety enhances the dielectric activity of the poly-(dimethoxybenzyl methacrylate)s. The temperature dependence of the relaxation times associated with the different relaxations is studied, and the molecular origin of the secondary relaxations is qualitatively discussed.

Full text of DOI:10.1021/ma1004875

Macromolecules 2010, 43, 5723–5733 5723
DOI: 10.1021/ma1004875
Dipolar and Ionic Relaxations of Polymers Containing Polar
Conformationally Versatile Side Chains
M. J. Sanchis, M. Carsı, P. Ortiz-Serna, G. Domınguez-Espinosa, and R. Dıaz-Calleja*
´
ꢀ
ꢀ
Instituto de Tecnologıa Electrica, ITE, ETSII, Universidad Politecnica de Valencia, Valencia, Spain
E. Riande*
´
´
Instituto de Ciencia y Tecnologıa de Polımeros (CSIC) Juan de la Cierva 3, 28003, Madrid, Spain
ꢀ
L. Alegrıa, L. Gargallo, and D. Radic
´
´
ꢀ
Departamento de Quımica Fısica, Pontificia Universidad Catolica de Chile, Santiago, Chile
Received March 5, 2010; Revised Manuscript Received June 2, 2010
ABSTRACT: This work reports a comparative study of the response of poly(2,3-dimethoxybenzyl
methacrylate), poly(2,5-dimethoxybenzyl methacrylate), and poly(3,4-dimethoxybenzyl methacrylate) to
electrical perturbation fields over wide frequency and temperature windows with the aim of investigating the
influence of the location of the dimethoxy substituents in the phenyl moieties on the relaxation behavior of the
polymers. The dielectric loss isotherms above Tg exhibit a blurred relaxation resulting from the overlapping of
secondary relaxations with the glass-rubber or R relaxation. At high temperatures and low frequencies, the R
relaxation is hidden by the ionic conductive contribution to the dielectric loss. As usual, the real component of
the complex dielectric permittivity in the frequency domain increases with decreasing frequency until a
plateau is reached corresponding to the glass-rubber (R) relaxation. However, at high temperatures, the real
permittivity starts to increase again with decreasing frequency until a second plateau is reached, a process that
presumably reflects a distributed Maxwell-Wagner-Sillars relaxation or R0 absorption. The R and R0
processes appear respectively as asymmetric and symmetric relaxations in the loss electrical modulus
isotherms in the frequency domain. To facilitate the deconvolution of the overlapping absorptions, the time
retardation spectra of the polymers were computed from the complex dielectric permittivity in the frequency
domain using linear programming regularization parameter techniques. The spectra exhibit three secondary
absorptions named, in increasing order of time γ0, γ, and β followed by the R relaxation. At long times and
well separated from the R absorption the R0 relaxation appears. The replacement of the hydrogen of the
phenyl group in position 2 by the oxymethyl moiety enhances the dielectric activity of the poly-
(dimethoxybenzyl methacrylate)s. The temperature dependence of the relaxation times associated with the
different relaxations is studied, and the molecular origin of the secondary relaxations is qualitatively
discussed.
1. Introduction
equations that describe the effects of the thermodynamic vari-
ables P, V, T on the average relaxation times in poly(ethyl
methacrylate). These authors found that although both intra-
and intermolecular interactions, controlled respectively by tem-
perature and volume, contribute to the R relaxation, it is the
temperature variable that exerts the stronger influence; in
fact, without thermal energy relaxations could not occur at all.
Moreover, the study of the activated volume reveals that the Rβ
relaxation presents the characteristics of a segmental process and
not the characteristics of the local β absorption whose apparent
activation volume is much smaller.
Dielectric activity in poly(n-alkyl methacrylate)s arises from
motions of the dipole moment associated with the side ester
moiety of the repeating units.9,15,16 The R relaxation is produced
by motions of dipole components μb rigidly attached to the chain
backbone which move when cooperative motions of the back-
bone occurs. Before the crossover region, the dipoles components
μs in the flexible side groups move independently or in concert
withlocal motions of the backbone, giving rise tothe β relaxation.
Above coalescence the side groups move in concert with the
overall motions of the backbone, giving the Rβ process. In spite of
Owing to the rich dynamics of poly(n-alkyl methacrylate)s, the
relaxation processes of a series of these polymers have been
studied using different experimental techniques involving di-
electric and NMR spectroscopies, dynamic mechanical analysis,
dilatometry, and modulated calorimetry.1-15 Many of these
studies have been focused on both the evolution of the relaxation
processes of the homologous series of polymethacrylates with
side chains length and the crossover region where the R and β
relaxations merge to form a single Rβ absorption.10-13,16-18 On
the basis of the fact that the β absorption is a thermally activated
process whereas the glass-rubber or R relaxation also depends
on the free volume, as earlier as in the 1960s Williams19 studied
the influence of pressure on the relaxation behavior of polymers,
finding that merging of the R and β relaxations to form the Rβ
process takes place as temperature is raised, at ambient pressure,
and demerging is accomplished by application of a hydrostatic
pressure. Recently, Mpoukouvalas et al.15 derived the canonical
*To whom correspondence should be addressed.
r 2010 American Chemical Society
Published on Web 06/14/2010
pubs.acs.org/Macromolecules

5724 Macromolecules, Vol. 43, No. 13, 2010
Sanchis et al.
the nonpolarity of the alkyl residues, the dynamics of the chains
of poly(n-alkyl methacrylate)s in the liquid rubbery state is
strongly dependent on the number of methylene groups of the
alkyl residue. A great deal of work has been mainly focused on the
crossover region of the dynamic glass transition where the
R relaxation and the β mode approach each other. At high
temperature, a process appears above the crossover different
from the cooperative R relaxation operative below the crossover.
In principle, an increase in chains length increases the free volume
shifting this scenario to lower frequency and temperature. An
important discovery in these studies is the nanophase separation
of incompatible main- andside-chain parts of the higher members
of the poly(n-alkyl methacrylate)s series.10,20 The existence of two
dynamic glass transitions for the higher members of the series,
the conventional R process, and an additional low-temperature
glass transition RPE, is put in evidence in shear measurements
carried out in combination with dielectric, calorimetric, and
WAXS data.10 The RPE absorption is related to cooperative
motions of the polyethylene-like side-chain parts whereas the R
relaxation arises from segmental motions of the chains backbone
flanking the nanodomains. The presence of static monodomains
in the range 0.5-1.5 nm is confirmed by X-ray scattering data.10
Despite the great amount of work reported in the literature
on the dynamics of poly(n-alkyl methacrylate)s, relatively little
work deals with the dynamics of poly(methacrylate)s with
alcohol residues containing polar moieties in their structure.
Recent experiments21-26 carried out on the relaxations of poly-
(benzyl methacylate)s show that changes in the location of polar
atoms replacing hydrogen atoms in the phenyl group greatly
affects the relaxation behavior of the polymers. For example, the
dynamics of poly(benzyl methacylate)s in which hydrogen atoms
of the phenyl groups are replaced by halogen atoms is strongly
dependent not only on the degree of substitution and nature of
the halogen atoms but also on the location of the substitutions.
Preliminary studies carried out in our laboratories focused on the
response of poly(2,3-dimethoxybenzyl methacrylate) (PDBM23)
to electrical perturbation fields showed that the isochrone at 1 Hz
of the real component ε0 of the complex dielectric permitivitty ε*
apparently exhibits two maxima centered respectively at 45 and
100 ꢀC. The two maxima might be associated with the existence of
polar and nonpolar nanodomains formed respectively by polar
side groups of the chains and the nonpolar backbone. Another
possibility is that the lower temperature maximum corresponds
to the glass-rubber relaxation whereas the second one could be
attributed to charge transport. It must be emphasized that as a
consequence of the conductivity response, the high-temperature
maximum observed in the isochrone ε0 is not detected in the
dielectric loss isotherms. This at first sight anomalous dielectric
behavior prompted us to study in detailthe relaxation behavior of
PDBM23, paying special attention to the processes of charge
transport detected at low frequencies and high temperatures.
Another objective of this work was to carry out a comparative
study of the dielectric behavior of poly(2,3-dimethoxybenzyl
methacrylate) with that of poly(2,5-dimethoxybenzyl methacrylate)
(PDBM25) and poly(3,4-dimethoxybenzyl methacrylate)
(PDBM34) with the aim of assessing how the locations of
the oxymethylene moieties affect dipolar relaxations and
ionic transport.
Figure 1. From left to right schemes of the planar structures of the side
chains of PDBM23, PDBM25, and PDBM34. As an example, rotations
that may produce dielectric activity are indicated in the scheme of
PDBM23 and the backbone (top). Notice that the C(O)-O bond is
planar; i.e., it is restricted to the trans state. Arrows indicate dipole
moments associated with polar moieties of the side chains.
Figure 2. DSC thermograms corresponding to the PDBM23, PDBM25,
and PDBMA34.
monomers were isolated and purified at reduced pressure
(80ꢀ-95ꢀ, 1 mmHg). The purity of the monomers was checked
by 1H NMR spectroscopy (see Supporting Information).
Synthesis and Characterization of the Polymers. Polymeriza-
tion reactions of the respective monomers were carried out at
50 ꢀC in toluene solutions, under a nitrogen atmosphere, using
R,R0-azobis(isobutyronitrile) (AIBN) as initiator. Polymers
were precipitated with methanol, dissolved in chloroform, pre-
cipitated again with methanol, and dried in a vacuum oven at
1
60 ꢀC. The purity of the polymers was checked by H NMR
spectroscopy (see Supporting Information). The weight-average
molecular weights of the polymers determined by GPC were
1.4 ꢀ 105, 2.1 ꢀ 105, and 1.7 ꢀ 105 for PDBM23, PDBM25, and
PDBM34, respectively, and the molecular weight heterodisper-
sity index was about 1.8. The stereochemical structure of the
samples as determined by NMR was atactic. The repeating units
of the polymers are shown in Figure 1.
DSC Measurements. The glass transition temperature was
measured with a TA DSC-Q10 apparatus at a heating rate
of 10 ꢀC/min, under a nitrogen atmosphere, and the pertinent
thermograms obtained in the second run are shown in Figure 2.
The glass transition temperatures of PDBM23, PDBM25, and
PDBM34, estimated as the temperature at the midpoint of the
endotherms, were 47, 37, and 57 ꢀC, respectively.
X-ray Characterization. Wide-angleX-ray diffraction(WAXS)
patterns were recorded at room temperature using a Bruker D8
Advance diffractometer with Cu KR radiation (λ = 0.1542 nm)
operated at 40 kV and 4 mA. The diffraction scans were collected
within the range of 2θ = 5ꢀ-60ꢀ with a 2θ step of 0.024ꢀ and
0.5 s per step.
2. Experimental Part
Dielectric Measurements. The complex dielectric permittivity
of the samples was measured with a Novocontrol broadband
dielectric spectrometer (Hundsagen, Germany) integratedby aSR
830 lock-in amplifier with an Alpha dielectric interface an Agilent
4991 coaxial line reflectometer to carry out the measurement in the
frequency range 10-1-106 and 106-109 Hz, respectively. In the
lattercasethecomplexpermittivitywasobtainedbymeasuring the
Synthesis and Characterization of the Monomers. The mono-
mers 2,3-dimethoxybenzyl-, 2,5-dimethoxybenzyl, and 3,4-di-
methoxybenzyl methacrylates were obtained respectively by
reaction of methacryloyl chloride with 2,3-dimthoxybenzyl
alcohol, 2,5-dimethoxybenzyl alcohol, and 3,4-dimethoxybenzyl
alcohol at reflux temperature using toluene as solvent following
the procedure of Burtle et al.27 improved by Gargallo et al.28 The

Article
Macromolecules, Vol. 43, No. 13, 2010 5725
Figure 3. Dielectric permittivity as a function of temperature for
PDBM25, PDBM23, and PDBM34 at several frequencies: 1.09 ꢀ
10-1, 5.37 ꢀ 10-1, 1.19, 5.86, 1.3 ꢀ 101, 4.29 ꢀ 101, 9.52 ꢀ 101,
4.69 ꢀ 102, 1.04 ꢀ 103, 5.12 ꢀ 103, 1.13 ꢀ 104, 5 ꢀ 58 ꢀ 104, 1.24 ꢀ 105,
4.09 ꢀ 105, and 9.08 ꢀ 105 Hz.
Figure 4. Dielectric permittivity in the frequency domain for PDBM23,
PDBM25, and PDBM34 in the temperature ranges 323-408, 318-373,
and 323-393 K, respectively, at 5 K steps.
The dielectric loss isotherms in the frequency domain, shown in
Figure 5, do not present well-defined relaxations in the high-
frequency regions. However, they exhibit an ostensible relaxation
associated with the glass-rubber relaxation which at higher
temperatures and lower frequencies is apparently hidden by the
conductive contribution. Better definitions of the loss peaks are
obtained by plotting the dielectric results in terms of the dielectric
loss modulus, M00. The isotherms of M00 in the frequency domain,
shown in Figure 6, exhibit two ostensible peaks corresponding in
decreasing order of frequency to the R and R0 relaxations. The
isotherms at different temperatures for M0, the real component of
the complex dielectric modulus M* of the polymers, are shown
in Figure 2 of the Supporting Information. In all the cases the
modulus increases with frequency, reaching a plateau corres-
ponding to the R relaxation, and then the modulus increases
again until a second plateau corresponding to the R0 relaxation
process.
reflection coefficient at a particular reference plane. The electrodes
used were gold disks of 20 and 10 cm for the measurements carried
out in the range 10-1-106 and 106 - 109 Hz, respectively. The
temperature was controlled by a nitrogen jet (QUATRO from
Novocontrol) with a temperature error of 0.1 K during every
single sweep in frequency.
3. Results
Isochrones showing the variation of the real component ε0 of
the dielectric complex permittivity ε* of the polymers with
temperature, at several frequencies, are shown in Figure 3. All
the isochrones display the same pattern in the sense that they
present two steps: a low-temperature step associated with the
glass rubber or R relaxation followed by a second step at higher
temperature, named the R0 absorption, whose nature will be
discussed later. The isochrones corresponding to the dielectric
loss ε00 present an ostensible R relaxation followed by a rather
sharp increase of the loss as temperature increases as a result of
the strong contribution of the conductivity to ε00 . It is worth
noting that in the low-temperature side of the glass-rubber (R)
relaxation a shoulder appears, corresponding to a secondary
relaxation, presumably the β process associated with side chain
motions. For details see Figure 1 of the Supporting Information.
Isotherms for ε0 in the frequency domain corresponding to
PDBM23, PDBM25, and PDBM34, at several temperatures, are
shown in Figure 4. Let us focus on the isotherms corresponding to
PDBM23. As usual, ε0 increases as frequency decreases, reaching a
plateau corresponding to the relaxed dipoles. However, after the
plateau and as frequency decreases further, ε0 increases again,
reaching a second plateau. The two rather steeply changes in the
values of ε0 correspond in the order of decreasing frequency to the R
and R0 relaxations detected in the isochrones of ε0 in Figure 2. The
isotherms of PDBM25 and PDBM34 present the same pattern as
those of PDBM23, though to reach the second plateau would require
data obtained at lower frequencies than those used in this study.
Retardation Spectra. The isotherms for ε0 in frequency
domain corresponding to PDBM23 clearly show the pre-
sence of two ostensible relaxations at T > Tg so that ε*(ω)
can be written as
X
absorp
ε0i - ε¥i
1 þ ðjωτsiÞ
ꢁ
ε ðωÞ ¼ ε¥ þ
asi
i, second:
0
0
ε
0R - ε¥R
ε0R - ε¥R
σ
þ
þ
- j
ð1Þ
aR0
aR bR
0
1 þ ðjωτR Þ
εf ω
½1 þ ðjωτRÞ ꢂ
where εf (= 8.854 pF/m) is the free space dielectric permit-
tivity and σ is the ionic conductivity arising from interfacial
polymer-electrode phenomena. The subscript i in eq 1 refers
to secondary absorptions (β, γ, ...) not well-defined in the
dielectric loss spectra whereas the subscripts 0 and ¥ mean
respectively relaxed and unrelaxed dielectric permittivities.

5726 Macromolecules, Vol. 43, No. 13, 2010
Sanchis et al.
Figure 7. Retardation spectra for PDBM23 in the temperature range
358-408 K, at 5 K steps.
domain, the complex plots are arcs so that the shape para-
meter b is the unit. For a Debye type relaxation a = b = 1.
Deconvolutions of overlapping relaxations are usually car-
ried out utilizing eq 1. However, relaxations are better
defined in the retardation spectra than in the dielectric loss
spectra in the frequency domain owing to the fact that a
Debye relaxation in the frequency domain covers 2.29
decades whereas in the relaxation spectrum is a delta of
Dirac. As a result, time retardation spectra facilitate decon-
volutions of overlapping relaxations. The complex dielectric
permittivity can be expressed in terms of the retardation
spectra by30,31
Z
¥
1
σ
ꢁ
ε ðωÞ - ε¥ ¼ ðε0 - ε¥Þ
Lðln τÞ
d ln τ þ
Figure 5. Dielectric loss in the frequency domain for PDBM23,
PDBM25, and PDBM34 in the temperature ranges 323-408, 318-373,
and 323-393 K, respectively, at 5 K steps.
1 þ jωτ
jωεf
- ¥
ð2Þ
where L is the normalized time retardation spectrum. For a
frequency ωi the retardation spectrum can be written in
discrete form, and eq 2 can approximately be written as
N
X
σ
ꢁ
ꢁ
ikLk þ
ε ðωiÞ - ε¥
=
R
ð3Þ
jωiεf
k ¼ 1
where
Δ ln τk
ꢁ
R
¼
ð4Þ
ik
1 þ jωiτk
and Lk = (ε0 - ε¥)L(ln τk). The computation of the retarda-
tion spectra of the polymers can be accomplished by mini-
mization of the error function32
(
)
2
N
N0
X
X
σ
ꢁ
R
E ¼
εðωiÞ -
ikLk -
- ε¥
ð5Þ
jωεf
i ¼ 1
k ¼ 1
Owing to the ill-conditioned behavior of the error function,
the Tikhonov33 regularization technique was used to mini-
mize E. The pertinent steps to carry out the minimization
that leads to the calculation of the retardation spectrum were
described in detail elsewhere.32
The retardation spectrum of PDBM23, shown in Figure 7,
exhibits two ostensible peaks corresponding in increasing
order of time to the R and R0 relaxations. In addition, three
secondary absorptions can be detected at short times called
in order of decreasing time β, γ, and γ0. The retardation
spectra are strongly sensitive to the location of the dimethoxy
moieties in the phenyl group of the alcohol residue as the
retardation spectra of PDBM23, PDBM25, and PDBM34,
presented at a single temperature in Figure 8, show. It can be
seen that the intensities of the R and R0 relaxation peaks
increase in the order PDBM23 > PDBM25 > PDBM34.
Figure 6. Dielectric loss modulus M00 in the frequency domain for
PDBM23, PDBM25, and PDBM34 in the temperature ranges 323-408,
318-373, and 323-393 K, respectively, at 5 K steps.
The shape parameters a and b are related respectively to the
departure of the complex ε00 vs ε0 plot from a semicircumfer-
ence, at low frequencies, and to the skewness of the plot
along a straight line, at high frequencies.29 Owing to the
symmetry of the secondary absorptions and that of the R0
relaxation observed in the M00 curves in the frequency

Article
Macromolecules, Vol. 43, No. 13, 2010 5727
Figure 8. Retardation spectra for PDBM25, PDBM23, and PDBM34
at 368 K.
Deconvolutions of the retardation spectra can be carried
out by using the analytical retardation spectra for HN type
equations given by31,34,35
aibi
1
Δεiðτ=τHN;i
Þ
sin biθi
ai
Liðln τÞ ¼
2ai
bi=2
π
½ðτ=τHN:i
Þ
þ 2ðτ=τHN:iÞ cos aiπ þ 1ꢂ
ð6Þ
In this expression, 0 < ai bi e 1 and θi is given by
"
#
sin πai
θi ¼ arctan
þ c
ð7Þ
ai
ðτ=τHN;iÞ þ cos πai
where c is 0 or π if the argument of the arctan function is
respectively positive or negative17 and i denotes the relaxa-
tion (γ0, γ, β, R, R0). The parameter Δεi = ε0i - ε¥i is the
strength of the relaxation i. Owing to the fact that the degree
of overlapping between R and R0 relaxations is rather small at
most temperatures, the R0 relaxation was deconvoluted from
the spectrum first. In an initial step, the fitting procedure was
carried out using partial parts of the retardation spectrum as
briefly described below. The high time side of the R relaxa-
tion was used as reference for the deconvolution of this
process; once separated, the R relaxation, the high time side
of the spectrum was used to deconvolute the β relaxation and
so on. Once obtained the starting parameters, we proceeded
to deconvolute the global spectrum delimiting, in the fitting
procedure, the values of HN parameters for each relaxation
in a range that includes the preliminary adjustment para-
meters, with the condition that 0 < ai, bi e 1, and the sum of
the dielectric strengths of the relaxations is equal to the
Figure 9. Retardation spectra for PDBM23 corresponding to R0, R, β,
γ, and γ0 processes (318-408 K, at 5 K steps). The dashed lines indicate
that out of the limits the values of Li(ln τ) should be regarded as
approximate.
PDBM34 are plotted as a function of the reciprocal of
temperature in Figure 10. The strength of the R relaxation
of PDBM23 decreases with increasing temperatures, whereas
that of the β increases until a temperature is reached at which
both relaxations have the same strength. At this temperature
both relaxations form a single absorption whose strength
rises steeply and then decreases as temperature increases.
The evolution of the strengths of the R and β relaxations with
temperature for PDBM34 is similar to that of PDBM23 in the
sense that both processes form a single absorption at the same
temperature, though the strength of the β relaxation at this
temperature is lower than that of the R. For PDBM25, the
strength of the R relaxation decreases with increasing tem-
perature whereas that of the β increases becoming equal to
that of the R at 373 K. The strength of the R0 relaxation of
PDBM23 decreases with increasing temperature, varying
from 4.27 at 358 K to 3.09 at 408 K. The R0 relaxations of
PDBM25 and PDBM34 are only observable at a reduced
number of temperatures. The data available indicate that
the strength of the R0 relaxation of PDBM25 is somewhat
smaller than that of PDBM23, whereas that of PDBM34 is
significantly smaller than the strength of the R0 relaxation of
PDBM23. The strengths of the γ and γ0 relaxations are signi-
ficantly lower thanthoseof the β process, independently of the
polymer considered. The total dielectric strength of the dipo-
lar processes calculated from the retardation spectra follows
the trends Δε(PDBM23) g Δε(PDBM25) > Δε(PDBM34),
in agreement with the results of Figure 4.
global dielectric strength calculated by means of the expres-
sion ε0 - ε¥ = -¥L(ln τ) d ln τ. Finally, the deconvolutions
R
¥
were refined by slightly changing the parameters until the
difference between the original spectrum and that obtained
from the deconvolutions using the expression L(ln τ) =
P
4
i=1Li(ln τ) is lower than 2% for any retardation time.
The retardation spectra for the relaxations γ0, γ, β, R, and
R0 of PDBM23, at 16 temperatures, are presented in Figure 9.
The deconvoluted spectra of these relaxations for PDBM25
and PDBM34 are shown in Figures 3 and 4 of the Supporting
Information. An inspection of Figure 9 shows that the R and
β relaxations coexist in the range of temperatures Tg < T <
365 K; then the β process is apparently swallowed by the R
relaxation forming a single relaxation. The strength of the
relaxations can directly be obtained from the deconvoluted
spectra by means of the following expression
Z
¥
ε0i - ε¥i
¼
Liðln τÞd ln τ
ð8Þ
- ¥
where i denotes the type of relaxation (γ0, γ, β, R, and R0).
Values of the strength for PDBM23, PDBM25, and

5728 Macromolecules, Vol. 43, No. 13, 2010
Sanchis et al.
Figure 12. Arrhenius plot for the R0 (pentagons), R (squares), β (circles),
γ (up triangles), and γ0 (down triangles) relaxations of PDBM25,
PDBM23, and PDBM34.
Figure 10. Temperature dependence of the strengths of the R0
(pentagons), R (squares), β (circles), γ (up triangles), and γ0 (down
triangles) relaxations. Star symbols represent the total dipolar dielectric
strength.
follow a definite trend for the γ0 absorption. For PDBM23,
the b parameter related with the skewness of the ε00 vs ε0 plot
in the R relaxation rises steeply in the vicinity of 368 K;
below and above this temperature, b slightly increases with
temperature. For PDBM25, the value of b is rather low and
nearly independent of temperature, whereas the variation
of b with temperature for PDBM34 follows similar trends
as for PDBM25, though the change in the vicinity of 368 K
is somewhat smaller. Finally, the plots of Figure 11 show
that the shape parameter b for the R0 relaxation lies in the
vicinity of the unit in the whole temperature range, sug-
gesting that the absorption in the retardation spectra is
symmetric.
Temperature Dependence of Retardation Times. Arrhenius
plots for the secondary absorptions and the R relaxation
are plotted in Figure 12. The activation energies Ea of the
secondary absorptions are obtained from the slope of the
plots, and the pertinent values are given in Table 1. In
general, the values of the activation energy of the relaxations
follow the trends Ea(β) > Ea(γ) > Ea(γ0). Moreover, the
activation energies of the γ and γ0 relaxations vary in the
way Ea(PDBM25) > Ea(PDBM23) > Ea(PDBM34). In the
case of the β relaxation, Ea(PDBM34) > Ea(PDBM25) >
Ea(PDBM23). As usual, the average relaxation time asso-
ciated with the R relaxation is described by the Vogel-
Fulcher-Tammann-Hesse(VFTH) equation36-38 expressed
in terms of the fragility parameter D039,40 by
Figure 11. Temperature dependence of the shape parameters (ak, bk)
for the R0 (9), R (2), β (1), γ (!), and γ0 (<) relaxations for PDBM23,
PDBM25, and PDBM34.
ꢀ
ꢁ
D0
τ ¼ τ0 exp
ð9Þ
The shape parameters for the retardation spectra asso-
ciated with the relaxations are shown as a function of
temperature in Figure 11. The value of a for the R relaxation,
higher than that for the β process, moderately increases
with increasing temperature. However, the parameter a for
PDBM23 steeply decreases in the vicinity of 368 K and then
slightly increases as temperature goes up. This parameter
also increases with temperature for the β and γ relaxations,
though for this latter process a undergoes a moderate
decrease as temperature increases. The values of a do not
ðT=TVÞ - 1
where τ0 is a prefactor of the order of picoseconds and TV is
the Vogel temperature currently associated with the tempera-
ture at which the entropies of the glassy system and the crystal
are similar; i.e., the configurational entropy of the glassy
system is nil. Values of the parameters that fit eq 9 to the
experimental results are collected in Table 1. The results show
that D0 is lower than 10, the limit value which separates fragile
materials (D0 < 10) from strong ones (D0 > 10).39,40 It is

Article
Table 1. Activation Energies of the Secondary Relaxation and
Macromolecules, Vol. 43, No. 13, 2010 5729
Parameters of Vogel-Fulcher-Tammann-Hesse Equation for
PDBM25, PDBM23, and PDBM34
sample
PDBM23
PDBM25
PDBM34
Ea,γ (kJ mol-1
)
54 ( 1
73 ( 2
39 ( 5
0
Ea,γ (kJ mol-1
)
95 ( 2
104. ( 3
138 ( 4
136 ( 4
6.5 ( 1.2
252 ( 11
3.5 ( 0.7
6.1 ( 1.3
80 ( 4
E
E
a,β (kJ mol-1
a,σ (kJ mol-1
)
)
132 ( 2
126 ( 2.0
6.1 ( 1.8
265 ( 7
3.4 ( 0.9
6.2 ( 1.3
168 ( 3
167 ( 3
6.7 ( 1.1
271 ( 1
3.3 ( 0.6
5.5 ( 1.2
D0
TV (K)
102(Φg/B)
104Rf/B (K-1
)
Figure 14. X-ray diffraction pattern for PDBM23 (green), PDBM25
(red), and PDBM34 (black).
4. Discussion
For polymers having dipole moment components in the side
groups that can move without necessarily involving motions of
the chain backbone, dipoles of type C according to Stockmayer’s
nomenclature, the dipole moment μ and the end-to-end distance r
of the chains are uncorrelated, i.e.43
Figure 13. Dependence of the ionic conductivity with the temperature
for PDBM23 (9), PDBM25 (b) and PDBM34 (2).
worth noting that TV is about 50 K below the Tg of the
polymers. By comparing eq 9 with the Doolittle equation41
Æμ ræ ¼ 0
ð12Þ
3
ꢂ
ꢃ
Uncorrelation between dipole moment and end-to-end distance
also occurs in polymers having dipoles rigidly attached to the
backbone but perpendicular to the chain contour (dipoles of type
B). However, for polymers with dipoles parallel to the chain
contour (dipoles of type A), the dipole moment of the chain is
correlated with the end to end distance, i.e.43
B
τR ¼ τ0 exp
ð10Þ
Φ
where Φ is the relative free volume and B is a parameter close
to the unit related with ratio between the critical volume
necessary for arelaxationprocesstotake place and the volume
of the segments intervening in the relaxation, it is found that
the relative free volume at Tg, Φg, and the thermal expansion
coefficient Rf = (1/ν)(dν/dT)p are given by42
Æ μ ræ ¼ constÆr2æ
ð13Þ
3
These latter polymers present the normal mode reflecting chains
disentanglement that appears at lower frequencies than the R
relaxation. Owing to the fact that the dipoles of PDBM23 are of
type C, the R0 relaxation is not associated with long-range
motions of the molecular chains. The R0 relaxation could be
attributed to the fact that the PDBM23 used in the experiments is
a mixture of two polymers, but the NMR spectrum of the
polymer and the DSC thermogram rule out this possibility.
X-ray diffraction patterns of poly(n-alkyl methacrylate)s
(PnMAs) show the aggregation of the side groups of different
monomeric units forming self-assembled alkyl nanodomains8,10
whose sizes depend on the side-chain length. The two glass
transition temperatures detected in these polymers by dynamic
heat capacity measurements are believed to be associated with
the freezing of motions within the alkyl nanodomains (RPE) and
main-chain dynamics. By using neutron scattering with istopic
labeling, Arbe et al.44 were able to study separately the dynamics
of the alkyl nanodomains and the main chain. The results obtained
strongly support the suggested nanosegregation of side groups and
main chain.8 Structural studies carried out by WAXS on the poly-
mers used in this work, presented in Figure 14, show the presence
of a peak, centered in the vicinity of q = 5 nm-1 (peak I), and a
second peak (peak II) centered at q = 11.5, 12.1, and 13.8 nm-1
for PDBM23, PDBM34, and PDBM25, respectively.45 Peak II
Tg - TV
D0TV
Φg=B =
;
Rf =B = 1=ðD0TVÞ
ð11Þ
The fact thatthe ratio of constant volume to constant pressure
activation energies for polymers is not zero15 as free volume
theories require raises questions concerning the applicability
of these theories to R relaxations. However, it is an experi-
mental fact that the values of the parameters Φg/B and Rf/B
for most flexible polymers lie in the vicinities of 0.025 (
0.005 and (4-6) ꢀ 10-4 K-1. For PDBM23, PDBM25, and
PDBM34 the values of Φg/B, collected in Table 1, are slightly
higher than the indicated average value of this quantity, but
the results for Rf/B, also shown in Table 1, are in agreement
with those reported for other flexible polymers42 which lie in
the vicinity of 5 ꢀ 10-4 K-1
.
The Arrhenius plot for the retardation time of the R0 relaxa-
tion of PDBM23, shown in Figure 12, suggests that the absorp-
tion may not be a pure thermal activated process. However, the
fact that the data available cover a relatively narrow span of
temperature impedes to reach a definite conclusion concerning
the temperature dependence of this relaxation.
The values of the ionic conductivity obtained by mini-
mization of eq 5 are plotted as a function of the reciprocal of
temperature in Figure 13. The plots show that the conduc-
tivity of the polymers obeys Arrhenius behavior following
the trends σ(PDBM23) > σ(PDBM25) > σ(PDBM34). The
values of the activation energy associated with the ionic
transport of the polymers, shown in the fourth row of
Table 1, are of the same order as those associated with the
β relaxation process of the polymers.
also appears in PnMAs, centered in the vicinity of 12-13 nm-1
.
The fact that this high-q peak is nearly independent of the side-
chain length in PnMAs led to conclude that it is produced by
correlations involving the side group atoms, thus reflecting the
average distance between the nonbonded atoms of the side
chains. According to this interpretation and taking into account
the Bragg approximation, the average distance of the side chains

5730 Macromolecules, Vol. 43, No. 13, 2010
Sanchis et al.
in PDBM23, PDBM25, and PDBM34 is respectively 0.55, 0.52,
and 0.49 nm. Peak I also appears in PnMAs for values of q lying
in the range 6, 5, and 4 nm-1 for poly(ethyl methacrylate),
poly(butyl methacrylate), and poly(hexyl methacrylate). The
shifting of peak I to lower values of q as the length of the alkyl
chains increases suggests that it reflects main-chain correlations,
and therefore it is associated with average distances between
the backbone. In consonance with this, it can be assumed that
peak I in the diffraction patterns of the dimethoxyphenyl-
substituted poly(benzyl methacrylate)s also arises from main-
chain correlations. Then, it could be postulated the existence
of side-chain nanodomains flanked by the backbone in the
polymer melts, the average distance between the backbone being
ca. 1.26 nm. Accordingly, interfaces in the nanodomains of
PDBM23, PDBM25, and PDBM34 may condition charge trans-
port in the polymers melts at low frequencies, as discussed below.
An inspection of the retardation spectra shows that in addition
to the high-frequency absorptions comprising the secondary and
the glass-rubber relaxations processes arising from either inter-
facial and/or electrode polarization must be considered. Elec-
trode polarization proceeds from accumulation of charges at the
electrodes-polymer interfacewhereas the interfacial polarization
is due to the buildup of charges at the interfaces of components of
heterogeneous systems.46 The contribution to the dielectric lossof
the polarization produced at the electrodes-polymer interface
scales with frequency as ω-s, where s is a parameter close to the
unit. This contribution corresponds to the last term of the right-
hand side of eq 1. The interfacial polarization in the bulk is
known as Maxwell-Wagner-Sillars (MWS) relaxation.47-52
For example, MWS relaxations have been found in silicon-
polyester resins,44 nylon/clay nanocomposites,52,53 PZTfibers/
epoxy resins,54 polycarbonate/styrene-acrylonitrile copolymer
multilayer composite,55 amorphous-crystal interface in nylon-
1010,56 etc. The MWS relaxation is associated with polarization
processes produced by charges separated over a considerable
distance with respect to the atomic or segments size. In view of
these antecedents, the MWS polarization of PDBM23 may be
interpreted as caused by nanoheterogeneities arising from the two
types of environments existent in this apparently homogeneous
system. However, the sizes of the nanodomains are not large
enough or the polar side groups are not sufficiently flexible to
develop cooperative motions independently of the backbone. It is
worth noting that cooperative motions of the side chains of
the higher series of poly(n-alkyl methacrylate)s produce a low-
temperature glass-rubber (RPE) relaxation, in addition to the
glass rubber absorption arising from segmental motions of the
backbone.10 Although the symmetry of the R0 relaxation in
PDBM23 fulfills one of the requirements of MWS relaxations,
the process is not described by a single relaxation time. This means
that the R0 absorption is a distributed MWS relaxation produced
by a wide variety of environments. The isotherms corresponding to
the real component of the complex conductivity of these nanohe-
terogeneous systems are characterized by a plateau in the low-
frequency region and a critical frequency ωc describing the onset of
the dispersion of σ0. Empirically, it has been found that ωc =ωM for
a series of systems where ωM is the angular frequency at the peak
maximum of the dielectric loss. Charge transport in these systems
can be interpreted in terms of a random barrier model proposed by
Dyre57,58 which assumes that transport occurs by hopping of
charge carriers in spatially varying random energy landscape.
The time involved in overcoming the highest barrier that deter-
mines the conductivity is one of the parameters characteristic of the
model, denoted by τe. The Dyre model approximates the complex
dielectric permittivity by the following expression
Figure 15. Fitting of the Dyre model (continuous lines) to the experi-
mental real component of the complex dielectric permittivity from 378
to 408 K, at 10 K steps.
Figure 16. Arrhenius plots for the ωc, ωM, ωHN, and ωe parameters (see
text for details).
where ε0 is the relaxed value of the glass rubber relaxation and σ0, the
dc conductivity, is one of the characteristic parameters of the model.
Taking into account that (1 þ jωτe) = (1 þ ω2τe2)1/2 jtan
e
-1(ωτe), the
real and imaginary components of ε* are given by
!
σ0
εf
2
ωτe lnð1 þ ω2τe
Þ
1
2
ε0ðωÞ ¼ εsd
ε00ðωÞ ¼
þ
2
- 1
2
2
ð1=4Þ lnð1 þ ω τe Þ þ ½ tan ðωτeÞꢂ
ð15Þ
ꢂ
ꢃ
σ0
εf
ωτe tan- 1ðωτeÞ
1
2
2
- 1
2
2
ð1=4Þ lnð1 þ ω τe Þ þ ½tan ðωτeÞꢂ
Notice that the model is not applicable at very low frequencies
where electrode polarization effects show up because these effects
are not considered in the model. As can be seen in Figure 15,
eq 15a fits rather well to the ε0 isotherms of PDBM23 in the low-
frequency range provided that the values of σ0 and ωe plotted
as a function of the reciprocal of temperature in Figures 13 and
16, respectively, are used. Although the values of σ0 are roughly a
decade higher than those of σ plotted in Figure 13, the tempera-
ture dependences of both quantities are similar. As can be seen
in Figure 16, the values of ωc, ωM, and ωe apparently obey
Arrhenius behavior, and the results for ωc and ωM nearly fall in
the same curve, suggesting that they describe an identical under-
lying process, i.e., an electrical relaxation. As expected, the values
of ωe are rather close to those of ωc and ωM. Owing to the rather
narrow span of temperature covered by the experiments where
ωM, ωc, and ωe can be obtained, no definitive conclusion can
be reached regarding to whether these parameters are only ther-
mally activated or they are also governed by the volume; i.e.,
the temperature dependence of the parameters is described by
the VFTH equation. It can be noted in this regard that the study
of the temperature dependence of these parameters for low
molecular weight ionic liquids carried out in a wide span of
temperature show that they are governed by the temperature and
volume.59 The study of the ωc, ωM, and ωe (1/ωe) dependence
with temperature has only been made for the PDBM23 because in
the case of PDBM25 and PDBM34 the experimental frequency
does not reach low enough values to get a clear view of the process
under study.
σ0τe
ꢁ
ε ðωÞ ¼ ε0 þ
ð14Þ
εf lnð1 þ ωτeÞ

Article
Macromolecules, Vol. 43, No. 13, 2010 5731
Table 2. Values of the Glass Transition Temperature (Tg), the
Dynamic Fragility Index (m), and the Activation Energy Associated
with the r Relaxation at Tg, Er(Tg), for PDBM23, PDBM25, and
PDBM34a
sample
PDBM23
PDBM25
PDBM34
Tg, K
m
m*
320
74
99
451
579
310
66
96
390
541
330
74
101
467
618
ER(Tg), kJ mol-1
ER*(Tg), kJ mol-1
a The quantities with an asterisk, m* and ER*(Tg), were calculated by
empirical equations given in ref 61 (m* ≈ 0.28((0.067)Tg (K) þ 9((20);
ER*(Tg) = [0.006Tg2 (K) - 35] kJ/mol).
Figure 17. Normalized relaxations curves in the time domain for the R
relaxations of PDBM23 from 363 to 408 K, at 5 K steps. Inset:
temperature dependence of the stretch exponents βKWW and the
characteristic relaxation times τ0 of the KWW equation of PDBM23.
temperatures. However, the results are nearly 30% below those
predicted by the straight line roughly fitting the values of m vs Tg
for several polymers.61 The apparent activation energy associated
with the R relaxation at Tg can be obtained by equating the
fragility index obtained from VFTH and Arrhenius behavior, i.e.
To asses the influence of the fine structure on the stretch
exponent of the decay function that describes the glass-rubber
relaxation, the normalized R relaxation in the time domain was
calculated from the spectra by means of the equation
R
¥
"
#
"
#
LRðln τÞe- t=τ d ln τ
- ¥
d log τA
d log τVFTH
d logðTg=TÞ
R
ð16Þ
φðtÞ ¼
¥
m ¼
¼
ð20Þ
- ¥ LRðln τÞ d ln τ
d logðTg=TÞ
T ¼ Tg
T ¼ Tg
The normalized decay function that depicts the relaxation beha-
vior of PDBM23 in the whole time range was calculated from the
retardation spectra by means of eq 16. The decay functions
obtained for PDBM23 at different temperatures are shown in
Figure 17. As usual, the decay function is inevitably described by
the stretch exponential KWW equation16
Taking into account that τA = exp(-E/RT), eq 20 leads to the
following expression for the activation energy ER at Tg
RD0TV
ERðTgÞ ¼
ð21Þ
2
ð1 - TV=TgÞ
2
3
From eqs 21 and 18, the activation energy can be expressed by the
alternative form
ꢂ
ꢃ
β
t
4
5
φðtÞ ¼ exp
-
ð17Þ
τ0
ERðTgÞ ¼ 2:303RD0TVTg
ð22Þ
where 0 < β e 1 and τ0 is the characteristic relaxation time of the
absorption. Values of the evolution of the stretch exponent and
the characteristic relaxation time with temperature for PDBM23
are depicted in Figure 17. The decay curves for the rest of
polymers are given in Figure 5 of the Supporting Information.
As expected, the temperature dependence of τ0 obeys the VFTH
equation, whereas the stretch exponent seems to increase as
temperature increases. The three polymers exhibit rather low
stretch exponents at low temperature that increase with increas-
ing temperature, without observing differences in behavior that
that can be attributed to the small variations of the fine structure
of the polymers.
Accordingly, the higher Tg, the higher the activation energy,
assuming D0 and TV as constants. The results for the activation
energy associated with the glass-rubber relaxation of PDBM23,
PDBM25, and PDBM34 at Tg, collected in Table 2, increase with
temperature but lie about 25% below those61 predicted by the
straight line roughly fitting the plots of Ea,R(Tg) vs Tg for a wide
variety of polymers.
Aside from other procedures, a method to collect the behavior
of a variety of systems with temperature in a single diagram is to
consider the β relaxation, which obeys Arrhenius behavior, the
elementary relaxation for the R relaxation of liquids.62 Using this
assumption, the R relaxation can be considered associated with
an activation energy that depends on temperature. Then the ratio
between the activation energy of the R relaxation at a temperature
T and that of the β absorption, independent of temperature, may
represent the size of correlate domains in the R relaxation. The
ratio, represented by RR(T), can be written as62
The rapidity with which the physical properties of a super-
cooled liquid varies as temperature approaches the glass transi-
tion temperature is characterized by the dynamic fragility m given
by60,61
!
d log ξ
m ¼ lim
ð18Þ
t
s
f ¥
dðTg=TÞ
RD0TVT2
p
RRðTÞ ¼
ð23Þ
2
EβðT - TVÞ
where ξ is a physical parameter depending of the dynamics of the
system such as the viscosity η or the relaxation time τ. Obviously,
as the fragility parameter increases, the temperature dependence
of the relaxation time of the glass-rubber relaxation comes closer
to Arrhenius behavior. Taking τg as reference and taking into
account eq 9, the fragility parameter can be written as
It can be defined a temperature TB at which RR(T) = 1 represent-
ing the upper bound below which the size of correlate domains
starts to increase reaching a maximum at T = Tg. The values of
TB for PDBM23, PDBM25, and PDBM34 are 388.3, 362.7, and
395.0 K, respectively. The variation of the size of correlate domains
with temperature, shown in Figure 18, indicates that the correlated
domains of PDBM23, PDBM25, and PDBM34, at the respective
glass transition temperatures, are respectively, 3.4, 2.7, and 3.1
times the size of the elementary clusters at TB.
D0TV
m ¼
ð19Þ
2
2:303Tgð1 - TV=TgÞ
The values of m for PDBM23, PDBM25, andPDBM34, collected
in Table 2, slightly increase with the respective glass transition
A few comments should be made concerning the assignment of
the secondary absorptions to specific molecular motions of the

5732 Macromolecules, Vol. 43, No. 13, 2010
Sanchis et al.
behavior of the polymers. The location of the oxymethylene
moiety in the position 2 of the phenyl group causes a significant
enhancement of the dielectric strength of the relaxations. This
study shows that small differences in the fine structure of
polymers produce significant changes in the relaxation behavior.
Acknowledgment. This work was financially supported by
the DGCYT and CAM through Grant MAT2008-06725-C03.
D.R. and L.G. thank Fondecyt, Grants 1080007 and 1080026, for
partial financial help.
Figure 18. Temperature dependence of ratio of the activation energy of
R process to that of β process, RR(T), for PDBM23 (squares), PDBM25
(circles), and PDBM34 (triangles).
Supporting Information Available: RMN characterization
of the monomers and polymers and several figures with the
experimental results and dielectric characterization of materials
analyzed. This material is available free of charge via Internet at
http://pubs.acs.org.
side groups. The CC(O)-OCHH2 residue of the side chain is
associated with a dipole moment of 1.78 D, forming an angle of
123ꢀ with the C-C(O)O bond.63 On the other hand, the dipole
associated with the Car-O-CH3 moiety bisects the Car-O-C
angle and has a value of 1.22 D.63 With the exception of the bonds
restricted to trans states, rotations about the remaining skeletal
bonds of the side groups, including the Car-O-CH3 bonds, give
rise to dielectric activity. However, coplanarity between the
phenyl group and the CarOCH3 moiety is strongly disfavored
due to strong repulsive interactions between the methyl group
and nearby protons of the phenyl group. Then dipoles jumping
between the two alternative gauche states about the Car-OCHH
bonds presumably produce the dielectric activity displayed in the
fastest relaxation or γ0 process. On the other hand, rotations
about the Car-CH2 bonds change the location in the space of the
dipoles associated with the Car-OCHH3 moiety, probably pro-
ducing the dielectric activity reflected in the γ relaxation. In this
case jumping between the two lower energy planar conformations
about the Car-CH2 bonds presumably produces that relaxation.
Finally, the β relaxation arises from motions involving the whole
side group presumably coupled with local motions of the skeletal
bonds of the main chain. In general, the conformations of lower
energy of the side groups of the chains with the Car-O-CH3
bonds anchored to the position 2 of the phenyl group have the
dipole associated with this moiety in a direction forming favor-
able angles with the dipole corresponding to the ester group.
Hence, the high dielectric strength is produced by the motions of
the side chains of PDBM23 and PDBM25. The angles formed by
the dipoles of the Car-O-CH3 bonds in 3,4 positions with the
dipole of the ester groups are not so favorable and as a result the
dielectric strength of PDBM34 is significantly lower than that of
the other polymers.
References and Notes
(1) Ishida, Y.; Yamafuji, K. Kolloid Z. 1961, 177, 97.
(2) (a) Williams, G. Trans. Faraday Soc. 1964, 60, 1556. (b) McCrum,
N. G.; Read, B. E.; Williams, G. Anelastic Effects in Polymeric Solids;
Wiley: New York, 1967.
(3) Sasabe, H.; Saito, S. J. Polym. Sci., Part A2 1968, 6, 1401.
(4) Ishida, Y. J. Polym. Sci., Part A2 1969, 7, 1835.
(5) Kuebler, S. C.; Schaefer, D. J.; Boeffel, C.; Pawelzik, U.; Spiess,
H. W. Macromolecules 1997, 30, 6597.
(6) Floudas, G.; Stepanek, P. Macromolecules 1998, 31, 6951.
(7) Schroter, K.; Unger, R.; Reissig, S.; Garwe, F.; Kahle, S.; Beiner,
M.; Donth, E. Macromolecules 1998, 31, 8966.
€
(8) (a) Beiner, M.; Kahle, S.; Abens, S.; Hempel, E.; Horing, S.;
Meissner, M.; Donth, E. Macromolecules 2001, 34, 5927. (b) Beiner,
M.; Huth, H. Nature Mater. 2003, 2, 595.
ꢀ
(9) Gomez, D.; Alegrıa, A.; Arbe, A.; Colmenero, J. Macromolecules
´
2001, 34, 503.
(10) Beiner, M. Macromol. Rapid Commun. 2001, 22, 869.
(11) Wind, M.; Graf, R.; Heuer, A.; Spiess, H. W. Phys. Rev. Lett. 2003,
91, 155702–I.
(12) Wind, M.; Graf, R.; Renker, S.; Spiess, H. W. J. Chem. Phys. 2005,
122, 014906.
(13) Ngai, K. L.; Gopalkrishnan, T. R.; Beiner, M. Polymer 2006, 47,
7222.
(14) Arbe, A.; Genix, A.-C.; Colmenero, J.; Richter, D.; Fouquet, P.
Soft Matter 2008, 4, 1792.
(15) Mpoukouvalas, K.; Floudas, G.; Williams, G. Macromolecules
2009, 42, 4690.
(16) Williams, G. Adv. Polym. Sci. 1979, 33, 60.
€
(17) Kremer, F., Schonhals, A. In Broadband Dielectric Spectroscopy;
Springer: Berlin, 2003.
(18) Floudas, G. Prog. Polym. Sci. 2004, 29, 1143.
(19) Williams, G. Trans. Faraday Soc. 1966, 6, 2091.
(20) Beiner, M.; Huth, H. Nature Mater. 2003, 2, 595.
~
(21) Dıaz-Calleja, R.; Sanchis, M. J.; Saiz, E.; Martınez Pina, F.;
´
´
5. Conclusions
Miranda, R.; Gargallo, L.; Radic, D.; Riande, E. J. Polym. Sci.,
Polym. Phys. Ed. 2000, 38, 2179.
The dielectric loss isotherms of the polymers in the frequency
domain present a blurred relaxation resulting from the over-
lapping of the secondary absorptions with the glass-rubber (R)
relaxation. The time retardation spectra computed from the
complex dielectric permeability allow a better deconvolution of
overlapping relaxations than performing directly the deconvolu-
tions in the dielectric loss. A distributed MWS relaxation appears
at long times in the retardation spectra at high temperatures
hidden in the dielectric loss spectra by the interfacial polymer-
electrode conductive contribution to the dielectric loss. The
MWS relaxation presumably arises from the buildup of charges
at the interfaces of nanoheterogeneities formed in the bulk by
segregation of the polar side groups from the nonpolar skeletal
bonds. This relaxation is described by the Dyre model, which
assumes that charge transport occurs by hopping of charge
carriers in spatially varying random energy landscape. The
location of the polar oxymethylene substituents on the phenyl
groups of the side chains greatly influences the relaxation
(22) Domı
L.; Radic, D. J. Chem. Phys. 2005, 123, 114904.
(23) Domınguez-Espinosa, G.; Dıaz-Calleja, R.; Riande, E.; Gargallo,
L.; Radic, D. Macromolecules 2006, 39, 3071.
(24) Domınguez-Espinosa, G.; Dıaz-Calleja, R.; Riande, E. Macro-
molecules 2006, 39, 5043.
(25) Dıaz-Calleja, R.; Domınguez-Espinosa, G.; Riande, E. J. Non-
Cryst. Solids 2007, 353, 719.
(26) Sanchis, M. J.; Domınguez-Espinosa, G.; Dı
nguez-Espinosa, G.; Riande, E.; Dıaz-Calleja, R.; Gargallo,
´ ´
´
´
´
´
´
´
´
´
az-Calleja, R.;
ꢀ
Guzman, J.; Riande, E. J. Chem. Phys. 2008, 129, 54903–15.
(27) Burtle, G. J.; Turek, W. N. J. Org. Chem. 1954, 19, 1567.
~
ꢀ
(28) Gargallo, L.; Munoz, M. I.; Radic, D. Polymer 1986, 27, 1416.
(29) Havriliak, S.; Havriliak, S. J. Dielectric and Mechanical Relaxation
in Materials; Hanser: Munich, 1997; p 57.
(30) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric
Effects in Polymeric Solids; Wiley: London, 1967; Chapter 4.
(31) Riande, E.; Dı
Dekker: New York, 2004; Chapter 8.
(32) Domınguez-Espinosa, G.; Ginestar, D.; Sanchis, M. J.; Dı
Calleja, R.; Riande, E. J. Chem. Phys. 2008, 129, 104513.
´
az-Calleja, R. Electrical Properties of Polymers;
´
´
az-

Article
Macromolecules, Vol. 43, No. 13, 2010 5733
(33) (a) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannerty,
B. P. In The Art of Scientific Computing, 2nd ed.; Cambridge
University Press: New York, 1992; Chapter 18. (b) Morozov, V. A.
Methods for Solving Incorrectly Posed Problems; Springer:
New York, 1984.
in samples with isotactic content triad less than 53% (Lemieux, E.;
Prud'homme, R. E. Polym. Bull. 1989, 21, 621). In view of this and
taking into account the atactic nature of PDBM23, PDBM25, and
PDBM34, crystalline order arising from estereoregularity is absent in
these polymers.
(34) Havriliak, S.; Negami, S. J. Polym. Sci., Polym. Symp. 1966, 14, 99.
(35) Zorn, R. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 1043.
(36) Vogel, H. Z. Phys. 1921, 22, 645.
(46) Satti, G.; McLachlan, D. S. J. Mater. Sci. 2007, 42, 6477.
(47) Laredo, E.; Herandez, M. C. J. Polym Sci., Part B: Polym. Phys.
1997, 35, 2879.
(37) Fulcher, G. S. J. Am. Ceram. Soc. 1925, 8, 339.
(48) Maxwell, J. C. Electricity and Magnetism; Clarendon: Oxford, 1893.
(49) Wagner, K. W. Arch. Elektrotech. 1914, 2, 371.
(50) Sillars, R. W. Inst. Electr. Eng. 1937, 80, 378.
(51) Mijovic, J.; Fitz, B. D. Novocontrol Applic Note Dielectrics 1998, 26.
(52) Perrier, G.; Bergeret, A. J. Polym Sci., Part B: Polym. Phys. 1997,
35, 1349.
(38) Tammann, G.; Hesse, W. Z. Anorg. Allg. Chem. 1926, 156, 245.
(39) Angell, C. A. In Complex Behavior of Glassy Systems; Proceedings
of the XIV Sitges Conference, Sitges, Barcelona, Spain, 10-14 June
ꢀ
1996; Rubi, M., Perez-Vicente, C., Eds.; Springer: Berlin, 1997.
(40) Angell, C. A. Science 1995, 262, 1924.
(41) (a) Doolittle, A. K. J. Appl. Phys. 1951, 22, 1471. (b) Doolittle, A. K.
J. Appl. Phys. 1952, 23, 236.
(53) Lee, Y-H.; Bur, A. J.; Roth, S. C.; Start, P. R. Macromolecules
2005, 38, 3828.
(42) Ferry, J. D. Viscoelastic Properties of Polymers, 2nd ed.; John Wiley
& Sons: New York, 1961.
(43) Stockmayer, W. H. Pure Appl. Chem. 1967, 15, 539.
(44) Arbe, A.; Genix, A.-C.; Colmenero, J.; Richter, D.; Fouquet, P.
Soft Matter 2008, 4, 1792.
(45) In principle, tacticity may affect the crystallinity of poly(meth-
acrylate) derivatives and therefore their X-ray patterns. Actually,
iso-poly(methyl methacrylate) develops crystalline order from the
melt, and the same occurs with syndio-poly(methyl methacrylate),
but in this latter case only from solution (Davis, T. P. Polyacrylates.
In Polymer Handbook; Olabisi, O., Ed.; Marcel Dekker: New York,
1997; Chapter 10). However, development of crystallinity in iso-poly-
(methyl methacrylate) melts is slow, even for a nearly monodisperse
sample with isotactic triad content of 100%. Crystallinity is not obtained
(54) Hammami, H.; Arous, M.; Lagache, M.; Kallel, A. J. Alloys
Compd. 2007, 430, 1.
(55) Daly, J. H.; Guest, M. J.; Hayward, D.; Pethrick, R. A. J. Mater.
Sci., Lett. 1992, 11, 1271.
(56) Lu, H.; Zhang, X. J. Macromol. Sci. Phys. 2006, 45, 933.
(57) Dyre, J. C. J. Phys. C: Solid State Phys. 1986, 19, 5655.
(58) Dyre, J. C. J. Appl. Phys. 1988, 64, 5.
(59) Krause, C.; Sangoro, J. R.; Kremer, F. J. Phys. Chem. B 2010,
114, 382.
(60) Plazek, D. J.; Ngai, K. L. Macromolecules 1991, 24, 1222.
(61) Qin, Q.; McKenna, G. J. Non-Cryst. Solids 2006, 352, 2977.
(62) Fujimori, H.; Oguni, M. Solid State Commun. 1995, 94, 157.
(63) Riande, E.; Saiz, E. Dipole Moments and Birefringence of Polymers;
Prentice Hall: Englewood Cliffs, NJ, 1992.