Broad-band dielectric spectrocopy of polymer chains containing structurally complex side groups

Article abstract of DOI:10.1021/ma011354t

The temperature dependence of the α and β relaxations of poly(2-phenyl-5-acryloxymethyl-5-ethyl-1,3-dioxacyclohexane) is studied by broad-band dielectric spectroscopy. The strength of the α relaxation decrease with increasing temperature, pointing to an onset temperature (Δε_α = 0) of ca. 97°C. Seen from the high-temperature side, the α relaxation starts with zero intensity at the onset temperature and steeply increases with decreasing temperature until it levels off in the vicinity of T_g. Whereas in the glassy state the strength of the β relaxation is only slightly dependent on temperature, it undergoes a strong increase at temperature above T_g. Arrhenius plots of both relaxations show that the β process remains operative at temperatures above the onset temperature of the α relaxation. The temperature dependence of the stretch exponent does not show a definite trend, most of the values obtained lying in the interval 0.3-0.5.

Full text of DOI:10.1021/ma011354t

Macromolecules 2002, 35, 1785-1790
1785
Broad-Band Dielectric Spectrocopy of Polymer Chains Containing
Structurally Complex Side Groups
†
‡
§
†
,†
Y. Hu a n g, E. Sa iz, T. A. Ezqu er r a , J . Gu zm a´ n , a n d E. Ria n d e*
Instituto de Ciencia y Tecnolog ı´ a de Pol ı´ mros (CSIC), 28006 Madrid, Spain; Departamento de
Qu ı´ mica F ı´ sica, Universidad de Alcal a´ , Madrid, Spain; and Instituto de Estructura de la Materia
(CSIC), 28006 Madrid, Spain
Received J uly 30, 2001; Revised Manuscript Received November 1, 2001
ABSTRACT: The temperature dependence of the R and â relaxations of poly(2-phenyl-5-acryloxymethyl-
5
-ethyl-1,3-dioxacyclohexane) is studied by broad-band dielectric spectroscopy. The strength of the R
relaxation decreases with increasing temperature, pointing to an onset temperature (∆ꢀ
C. Seen from the high-temperature side, the R relaxation starts with zero intensity at the onset
temperature and steeply increases with decreasing temperature until it levels off in the vicinity of T
Whereas in the glassy state the strength of the â relaxation is only slightly dependent on temperature,
it undergoes a strong increase at temperatures above T . Arrhenius plots of both relaxations show that
R
) 0) of ca. 97
°
g
.
g
the â process remains operative at temperatures above the onset temperature of the R relaxation. The
temperature dependence of the stretch exponent does not show a definite trend, most of the values obtained
lying in the interval 0.3-0.5.
In tr od u ction
The R relaxation in the time domain inevitably seems
to display a Kohlrausch-Williams-Watts (KWW)
In the liquid range, and even into the moderately
supercooled regime, the relaxation response of glass
formers to an external perturbation field is a single
absorption in the frequency domain that upon ap-
proaching the glass transition splits into a pair of
1
-3
stretched exponential decay given by
âK
t
τ*
g (t) ) exp -
(3)
R
[
(
)
]
1
-3
maxima, the slow R and the faster â relaxations.
By
in which 0 < âK e 1 and τ* is comparable to τR of eq 1
when T is near Tg. The stretch exponent characterizes
the relaxation strength of the R process in such a way
that the wider is the relaxation, the lower âK is. Thus,
for a Debye type process, âK ) 1. From eqs 1 and 3 it
follows that the average relaxation time associated with
the R relaxation is given by
expressing the functions that describe these relaxations
in the time domain, the mean relaxation times associ-
ated with these processes are given by
∞
〈
τi〉 )
∫
gi(t) dt
(1)
0
where gi (i ) R, â) is the relaxation response in the time
domain in which the initial-time normalization gi(0) )
∞
τ*
1
〈τ〉 )
∫
g(t) dt )
Γ
(4)
0
( ) ( )
â
â
1
is imposed. The temperature dependence of 〈τR〉 shows
K
K
an anomalous increase in the vicinity of the glass
The Fourier transform of eq 3 allows the determina-
tion of the normalized loss in the frequency domain by
means of the following expression
transition temperature described by the Vogel-Fulcher-
Tammann-Hesse (VFTH) equation4
-6
DTV
τ ) τ exp
(2)
ꢀ′′(ω)
0
(
)
T - TV
) -J {iωF[g (t)]}
(5)
R
ꢀ
′′max
where τ0 is a preexponential factor and TV is the Vogel
temperature which is found to be of similar magnitude
as the Kauzmann temperature3 (the temperature at
which the entropy of the supercooled liquid extrapolated
to low temperatures seems to be similar to that of the
crystal). The so-called strength factor7 D is related to
the depth and density of the minima in the potential
energy landscape of glass formers. Its value is lower/
larger than 10 for fragile/strong supercooled liquids.
Whereas the R relaxation becomes frozen at Tg, the â
relaxation remains operative in the glassy state. The
temperature dependence of the â process obeys Arrhe-
nius behavior.
where ω is the angular frequency of the electric alter-
nating field, the symbol F means the Fourier transform
and ꢀ′′max is the value of the dielectric loss at the peak
maximum of the absorption.
Usually, the â peak is more symmetric than the R
peak. The normalized dielectric loss for this process is
often described by the empirical Fuoss-Kirkwood equa-
,8
9
tion
ꢀ
′′(ω)
′′max
ω
ωmax
)
sech m ln
; 0 < m e 1
(6)
(
)
ꢀ
where ωmax represents the frequency at the peak
maximum. The parameter m, like âK in the R relaxation,
accounts for the breadth of the â process in such a way
that the larger is m, the narrower is the absorption.
†
Instituto de Ciencia y Tecnolog ´ı a de Pol ´ı mros (CSIC).
Universidad de Alcal a´ .
‡
§
Instituto de Estructura de la Materia (CSIC).
1
0.1021/ma011354t CCC: $22.00 © 2002 American Chemical Society
Published on Web 02/01/2002

1
786 Huang et al.
Macromolecules, Vol. 35, No. 5, 2002
F igu r e 1. A rough sketch of the repeating unit of poly(5-
(acryloxy)methyl-5-ethyl-1,3-dioxacyclohexane) (PAMED).
Polymers with cycloaliphatic and oxycycloaliphatic
side groups in their structure display a prominent â
absorption attributed to chair to inverse chair confor-
mational transitions occurring in the rings.10 Although
these motions may contribute to the â absorption,
molecular dynamics simulations carried out on low
molecular weight compound models of these polymers
suggest that, aside from the conformational transitions
taking place in the rings, other motions in the side
F igu r e 2. Loss component ꢀ′′(ω) of the complex dielectric
permittivity ꢀ*(ω) of PAMED measured at several tempera-
tures as a function of the angular frequency.
nol, dissolved in benzene, precipitated again with methanol,
and dried at 60 °C in a vacuum.
The complex dielectric permittivity, ꢀ*(ω) ) ꢀ′(ω) - iꢀ′′(ω),
where ꢀ′(ω) and ꢀ′′(ω) are the real and loss components of the
permittivity, respectively, was measured with a SR 830 lock-
in amplifier, the HP 4192, and the HP 4291 coaxial line
reflectometer. The results were obtained at several tempera-
groups may play an important role in the development
of the â absorption.1
1,12
At any rate, the relative high
strength of the fast process in these polymers makes
them suitable to study the evolution with temperature
of the strength of the R and â relaxations until they
merge into the Râ relaxation. For this purpose relax-
ation responses of poly(5-(acryloxy)methyl-5-ethyl-1,3-
dioxacyclohexane) (PAMED) were studied using broad-
band frequency dielectric spectrocospy. The repeating
unit of this polymer is shown in Figure 1. Earlier
-1
10
tures in the frequency range 10 -10 Hz. The relative
accuracy of the measurements is controlled by the sample
thickness and has been estimated to be about (5%.
Exp er im en ta l Resu lts
Illustrative isotherms representing the dielectric loss
in the frequency domain are shown in Figure 2. Below
the glass transition temperature, about 20 °C for the
sample used in this study, the isotherms present a wide
â relaxation whose maximum, as usual, shifts to higher
frequency with increasing temperature. Also, the in-
tensity of the â process increases with increasing
temperature. In the supercooled liquid state and in the
vicinity of Tg, isotherms display in the lower frequency
range the slow R relaxation followed by the weaker â
process in the high-frequency range. As the temperature
augments, the distance separating the â from R peak
decreases as a consequence of the high activation energy
of the latter relaxation process. In the neighborhood of
1
3
studies have shown that the mechanical and dielectric
isochrones of PAMED exhibit a prominent â absorption
centered in the neighborhood of -80 °C at 1 Hz, followed
by the glass-rubber relaxation located nearly 100 °C
above this temperature at the same frequency. In the
frequency domain, the dielectric isotherms show two
peaks, the low- and high-frequency peaks corresponding
respectively to the R and â relaxations. Extrapolation
methods suggest that the formation of a single peak
would take place in the vicinity of 110 °C. However, the
lack of experimental data at high frequencies precluded
the possibility of obtaining reliable information on the
effect of temperature on the overlapping of the R and â
relaxations. This paper focuses on this subject as well
as the temperature dependence of the strengths of both
relaxations. Finally, attention is paid to the variation
of the stretch exponent of the R relaxation, âK, with
temperature.
3
71 K, both relaxations coalesce into a single peak,
named Râ relaxation, whose intensity seems to increase
with increasing temperature.
To obtain information on the variation of the relative
strengths of the R and â relaxation processes with
temperature, it was proceeded to deconvolute the over-
lapping relaxations. Below Tg, i.e., for T ) 193, 213, 233,
253, and 273 K, the experimental results were fitted to
a â relaxation given by eq 6 disregarding the values of
Exp er im en ta l P a r t
5
-(Hydroxymethyl)-5-ethyl-1,3-dioxacyclohexane (HME) was
obtained by reaction of 2-ethyl-2-(hydroxymethyl)propanediol
with paraformaldehyde (1,1), using p-toluenesulfonic acid as
catalyst. By adding dropwise acryloyl chloride to a solution of
HME in chloroform, 5-(((acryloxy)methyl)-5-ethyl-1,3-dioxacy-
clohexane (AMED) was obtained. This reaction was carried
out in the presence of triethylamine to neutralize the hydrogen
chloride evolved during the reaction. Poly(5-(acryloxy)methyl-
ꢀ
′′(ω) obtained in the low-frequency region that show
an upturn. An illustrative example of these fittings is
represented in Figure 3. Values obtained at intermedi-
ate temperatures, i.e., 293 e T e 363 K, were fitted to
a sum of a R plus a â relaxation according to the
expression
5
-ethyl-1,3-dioxacyclohexane) (PAMED) was synthesized by
radical polymerization of 5-(((acryloxy)methyl)-5-ethyl-1,3-
dioxacyclohexane in toluene solution. The polymerization was
carried out at 50 °C, under nitrogen atmosphere, using azobis-
ꢀ′′(ω) ) ꢀ′′ (ω) + ꢀ′′ (ω) )
R
â
ωmax
(isobutyronitrile) as catalyst. After attaining approximately
ꢀ
′′max,R J {iωF{g (t)}} + ꢀ′′
sech m ln( ω
(7)
R
max,â
[
)
]
1
0% of conversion, the polymer was precipitated with metha-

Macromolecules, Vol. 35, No. 5, 2002
Polymer Chains Containing Complex Side Groups 1787
F igu r e 5. Same as Figure 4 for 343 K.
F igu r e 3. Fitting of the experimental values of ꢀ′′(ω) mea-
sured at 253 K, i.e., below T , for PAMDED to a â relaxation
g
Ta ble 1. P a r a m eter s Em p loyed for th e F ittin g of
Exp er im en ta l E′′(ω) Da ta to a â Rela xa tion Accor d in g to
Eq 6 or to th e Su m of a n r p lu s a â Rela xa tion Accor d in g
to Eq 7
according to eq 6 with the parameters of Table 1.
R relaxation
â relaxation
ωmax
(rad/s)
ωmax
(rad/s)
T (K) ꢀ′′max
â
ꢀ′′max
m
1
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
93
13
33
53
0.221
0.253 96.9
0.297
0.407
0.522
6.56
0.341
0.340
0.377
0.453
3
3
1.28 × 10
9.55 × 10
4
73
5.556 × 10 0.485
5
93 1.040
03 0.994
08 0.934 178
13 0.901 714
23 0.959
33 0.888
43 0.757
53 0.424
58 0.337
63 0.185
71
2.56
34.6
0.385 0.671
0.341 0.663
0.363 0.707
0.374 0.730
2.28 × 10
4.77 × 10
6.40 × 10
8.72 × 10
1.58 × 10
2.61 × 10
4.24 × 10
5.24 × 10
6.41 × 10
7.63 × 10
8.33 × 10
1.63 × 10
0.524
0.567
0.571
0.573
0.585
0.628
0.577
0.541
0.543
0.518
0.472
0.490
5
5
5
6
6
6
6
6
6
6
7
3
4.09 × 10 0.382 0.777
4
2.43 × 10 0.326 0.740
5
1.04 × 10 0.478 1.03
5
1.97 × 10 0.497 1.33
5
2.39 × 10 0.630 1.57
5
9.93 × 10 0.381 1.61
F igu r e 4. Deconvolution of the experimental values of ꢀ′′(ω)
measured at 293 K for PAMDED to fit the sum of an R plus a
â relaxations according to eq 7 with the parameters given in
Table 1. Individual contributions of R and â relaxations are
indicated by broken lines while their sum is represented by a
solid line.
1.93
1.99
83
value of 11.5 kcal mol- is obtained for the activation
energy of this relaxation. This value is in good agree-
1
-
1
ment with the value of 11.0 kcal mol obtained for this
parameter from isochrones in the glassy state.13
The temperature dependence of the distance between
the peaks of the R and â relaxations in the supercooled
where F represents the Fourier transform. Illustrative
curves showing the goodness of the fittings are repre-
sented in Figures 4 and 5.
liquid state, expressed as ∆ ) ω
max,â max,R
, is shown in
/ω
All the fittings were performed employing a numerical
routine14 to minimize the sum of squared deviations
between experimental and fitted values taking the
height (ꢀ′′max) and position (ωmax) of the maxima and the
breadth (m and/or âK) of the relaxations as independent
parameters. All the values obtained in the fittings are
summarized in Table 1. In particular, columns seven
and four in Table 1 show respectively the results of m
and âK. It can be seen that m increases with tempera-
ture in the glassy region but remains practically con-
stant in the supercooled and deep liquid state whereas
most of the values of âK lie in the range 0.3-0.5.
Arrhenius plots for the R and â relaxation processes
are shown in Figure 6. The relaxation times associated
with the R absorption are described by the VFTH
equation assuming that TV ) 243-233 K and the
strength factor D is equal to 4.76-6.14. On the other
hand, the plot of the relaxation times associated with
the â process is a straight line from whose slope the
Figure 7. As can be seen in this Figure, ∆ is described
by a Vogel type equation,
m
ln ∆ ) A′ +
(8)
T - TV
This behavior presumably arises from the fact that the
activation energy of the R relaxation is much higher
than that of the â process.
The strength of the R and â relaxations was obtained
from the corresponding deconvoluted isotherms by
means of the expression
2
π
∞
ꢀri - ꢀ )
∫
ꢀ′′(ω) d ln ω
(9)
∞i
-∞
where i ) R, â. Earlier results reported on the dielectric
relaxation behavior of poly(n-alkyl metahcrylate)s, specif-
ically, poly(methyl, ethyl, propyl, and n-butyl methacry-

1
788 Huang et al.
Macromolecules, Vol. 35, No. 5, 2002
F igu r e 6. Arrhenius plots of the angular frequency at the
maximum of the loss component ꢀ′′. Experimental values for
the â relaxation were fitted to the straight line: log(ωmax) )
F igu r e 8. Strength of the R (circles) and â (squares) relaxation
as a function of temperature obtained from eq 9.
1
3.87 - 2510/T shown as a solid line. The dashed line
represents the VFTH equation: log(ωmax) ) 10.49 - 614/(T -
33).
2
F igu r e 9. Five scenarios suggested for the splitting region
in the Arrhenius diagram taken from ref 15: continuous line,
trace with considerable intensity; dashed line, uncertainty in
intensity and trace; points, intensity tending to zero. (See text
for details.)
F igu r e 7. Distance between the peaks of the R and â
relaxations in the supercooled liquid state expressed as ∆ )
ω
∞
max,â/ωmax,R plotted vs the reciprocal of T - T according to
eq 8.
late)s, show that the dielectric â relaxation of these
polymers is symmetrical at low temperatures but be-
comes asymmetric at high temperatures.15 In our case,
the â relaxation was rather symmetric in the whole
temperature range in such a way that its relaxation
strength at each temperature was determined by the
expression
with increasing temperature. Extrapolation to ∆ꢀR ) 0
(
R onset) points to an onset temperature of 97 °C.
Therefore, seen from the high-temperature side, the R
relaxation starts with zero intensity at this temperature
and steeply increases with decreasing temperature until
it levels off in the vicinity of Tg. The strength of the
isotherms expressed as ∆ꢀ ) ∆ꢀR + ∆ꢀâ has a value of
7
.9 ( 0.7 in the whole interval of temperatures in which
2
ꢀ′′max
the R and â relaxations coexist.
On the basis of the analysis of the splitting of the Râ
relaxation of condensed matter, including polymers, it
∆
ꢀ ) ꢀ - ꢀ )
∞â
(10)
â
râ
m
1
5
resulting from substituting eq 6 into eq 9. Values of the
strength of the â relaxation are plotted as a function of
the reciprocal of temperature in Figure 8. In the glassy
state the strength of the â process only exhibits a slight
dependence on temperature. However, above Tg, ∆ꢀâ
experiences a steep increase with temperature.
has been speculated with the possibility of five sce-
narios schematically presented in Figure 9. In the first
one, also called the conventional case, the â process
continues deep in the liquid state whereas in the type
A the separate R onset can be characterized by a minima
cooperativity for R that cannot be continued to a local,
noncooperative process. For the B type there is a locally
coordinative â precursor for the cooperative R process
at high temperatures. The topology of the diagram for
the type C scenario is similar to that of the conventional
one, but here the R relaxation is curved above and below
From eqs 5 and 9 the strength of the a relaxation,
ꢀR ) ꢀrR - ꢀ∞R, is obtained. Values of this quantity,
∆
plotted in Figure 8, show that the strength of this
relaxation has a maximum value at temperatures just
slightly above Tg, and then it undergoes a steep decrease

Macromolecules, Vol. 35, No. 5, 2002
Polymer Chains Containing Complex Side Groups 1789
the splitting and â is not the tangent to R. In the type
D scenario16 there are two different but touching R
relaxations with a sharp crossover between them and
a â trace aiming to this common tangential point with
constant of increasing intensity again. Examples of
conventional, A, B, C, and D scenarios are respectively
solutions of chlorobenzene in cis-decalin, poly(n-butyl
methacrylate), poly(ethyl methacrylate), poly(propylene
glycol), and o-terphenyl. Although different approaches
have been proposed to describe the origin of the ob-
served dielectric response of polymer systems in the
Comparison of âK for the responses of PVAc and
PAMED in the time domain suggests a greater com-
plexity in the response of the latter polymer, presumably
arising from the conformational changes taking place
in the bulky side group that involve complex chair-to-
inverse chair conformational transitions presumably
coupled with motions of the main chain.
Con clu sion s
The temperature dependence of the distance between
the R and â peaks in the frequency domain, expressed
in terms of the ratio of the frequencies at the peaks
maximum (ωmax,â/ωmax,R), obeys Vogel behavior. As the
temperature increases, an onset temperature is reached
at which the strength of the R relaxation vanishes
whereas the â relaxation undergoes a sharp increase.
Since side chains contain the electric dipoles, most of
the polarization at temperatures not far above the glass
transition temperature relaxes through the â relaxation
and only a smaller part through the main chain dynam-
ics reflected in the R relaxation.
1
5,17
merging region,
it seems that most of the experi-
mental cases fall within any of the above-described
scenarios. Comparison of the results of Figure 6 with
the different scenarios suggests that the relaxation
behavior of PAMED resemble the scenario A schemati-
cally depicted in Figure 9.
A few comments should be made concerning the
temperature dependence of the stretch exponent in the
supoercooled and even in the deep liquid states. There
is some dispute concerning the high-temperature be-
havior of âK arising from inconsistent results reported
in the literature.8 Experiments have been cited
suggesting that âK increases as the temperature goes
up, approaching âK ) 1 at high temperatures. Variation
of âK with temperature was also found in some dielectric
18-20
Ack n ow led gm en t. This work was supported by the
DGICYT through Grants PB97-0778 and MAT 1999-
1127-C04-01.
2
1-23
experiments.
Refer en ces a n d Notes
Experimental evidence supporting the temperature
independence of âK mainly arises from light scattering
(
1) Williams, G. Adv. Polym. Sci. 1979, 33, 60.
2
4-30
experiments.
For example, the R absorption in
(2) Williams, G. Dielectric Relaxation Spctroscopy of Amorphous
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1
995.
°
C is fitted by eq 2 with âK ) 0.54. Moreover, a
(
(
3) Stillinger, F. H. Science 1995, 267, 1935.
4) Vogel, V. Z. Phys. 1921, 22, 645.
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havior of propylene carbonate and glycerol, carried out
recently,8 shows a tendency of âK to level off at a
constant value, smaller than unity, at high tempera-
tures. Discrepancies observed in the experimental val-
ues of the stretch exponent obtained at high tempera-
tures arise from various sources of error. The most
important one is that when the loss peak shifts toward
the high-frequency limit of the available frequency
window, there are less and less experimental data in
the high-frequency side of the peaks, and as a result
the error involved in the determination of âK is en-
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Recent studies31 on the relaxation behavior of poly-
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(
unexpected fact: the widths of the absorption simulated
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(
(
(
15) Garwe, F.; Sch o¨ nhals, A.; Lockwenz, H.; Beiner, M.; Schr o¨ ter,
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arises from the difficulty of fitting the simulated time-
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unlikely. This conclusion is supported by the analysis
of the temperature dependence of âK for PVAc in the
bulk and its toluene solutions. The extrapolation of
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of the order of 0.57 ( 0.05.
1
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