Chromophore Relaxation in a Side-Chain Methacrylate Copolymer Functionalized with 4-[N-Ethyl-N-(2-hydroxyethyl)]ammo-2′-chloro-4′- nitroazobenzene

Article abstract of DOI:10.1021/ma035714j

A side-chain methacrylate copolymer functionalized with the nonlinear optical chromophore 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2′-chloro- 4′1-nitroazobenzene, disperse red-13, was prepared and characterized. The chromophore relaxation was investigated measuring the decay of the electrooptic coefficient r₁₃ and the complex dielectric constant at different temperatures. Results obtained below and above T_g were analyzed using the Kohlrausch - Williams - Watts (KWW) equation, through the study of the temperature dependence of the KWW parameters. Above T_g the relaxation time experimental data were fitted to the Williams - Landel - Ferry (WLF) equation and its parameters determined. Chromophore relaxation leading to the decrease of electrooptic properties was found associated with a primary a relaxation. The obtained WLF equation parameters were introduced into the Adam - Gibba - Tool - Narayanaswamy - Moynihan equation, and the overall relaxation time temperature dependence was successfully obtained in terms of the fictive temperature, accounting for the sample thermal treatment and allowing optimized thermal treatment to be found. The copolymer KWW stretching parameter at the glass transition temperature lies close to the limit value for short-range interactions, i.e., 0.6, suggesting that the chromophore group is participating in primary α relaxation.

Full text of DOI:10.1021/ma035714j

2618
Macromolecules 2004, 37, 2618-2624
Chromophore Relaxation in a Side-Chain Methacrylate Copolymer
Functionalized with
4-[N-Ethyl-N-(2-hydroxyethyl)]amino-2′-chloro-4′-nitroazobenzene
P . A. Ribeir o,*,‡ D. T. Ba logh ,† J ose´ L. C. F on seca ,§ a n d J . A. Gia com etti
Instituto de F´ısica de Sa˜o Carlos, Universidade de Sa˜o Paulo, CP 369,
13560-970 Sa˜o Carlos, SP, Brazil; CEFITEC-Centro de F´ısica e Investigac¸a˜o Tecnolo´gica,
Departamento de F´ısica, Faculdade de Cieˆncias e Tecnologia, Universidade Nova de Lisboa,
2829-516 Caparica, Portugal; Departamento de Qu´ımica, Universidade Federal do Rio Grande
do Norte, Campus Universita´rio, Lagoa Nova, CP 1662, 59072-970, Natal, RN, Brazil; and
Faculdade de Cieˆncia e Tecnologia, Universidade Estadual Paulista, 19060-900,
Presidente Prudente, SP, Brazil
Received November 14, 2003; Revised Manuscript Received J anuary 23, 2004
ABSTRACT: A side-chain methacrylate copolymer functionalized with the nonlinear optical chromophore
4-[N-ethyl-N-(2-hydroxyethyl)]amino-2′-chloro-4′-nitroazobenzene, disperse red-13, was prepared and
characterized. The chromophore relaxation was investigated measuring the decay of the electrooptic
coefficient r13 and the complex dielectric constant at different temperatures. Results obtained below and
above Tg were analyzed using the Kohlrausch-Williams-Watts (KWW) equation, through the study of
the temperature dependence of the KWW parameters. Above Tg the relaxation time experimental data
were fitted to the Williams-Landel-Ferry (WLF) equation and its parameters determined. Chromophore
relaxation leading to the decrease of electrooptic properties was found associated with a primary R
relaxation. The obtained WLF equation parameters were introduced into the Adam-Gibbs-Tool-
Narayanaswamy-Moynihan equation, and the overall relaxation time temperature dependence was
successfully obtained in terms of the fictive temperature, accounting for the sample thermal treatment
and allowing optimized thermal treatment to be found. The copolymer KWW stretching parameter at
the glass transition temperature lies close to the limit value for short-range interactions, i.e., 0.6,
suggesting that the chromophore group is participating in primary R relaxation.
I. In tr od u ction
biexponential,6 Kohlrausch-Williams-Watts stretched
exponential (KWW),7,8 single-exponential plus KWW,
van der Vorst,9 and Dissado-Hill power laws.10,11 The
KWW decay function is given by:
The most common polymeric materials with nonlinear
optical (NLO) properties are the side-chain polymers,
which are synthesized by covalently linking organic
NLO chromophore molecules to a given polymeric
backbone.1 The azobenzene chromophore group confers
to polymers their NLO features and also the reversible
cis-trans photoisomerization, leading to optical switch-
ing, optical storage, and surface relief grating forma-
tion.2 For second-order NLO optical processes, such as
second-harmonic generation and the linear electrooptic
effect (Pockel’s effect), polymers must be submitted to
the electric poling in order to generate polar orientation
of the chromophore. Poling is usually performed either
applying a bias voltage3 to the sample or charging it in
a corona triode.4,5 The orientational order of chro-
mophores that results is usually unstable, and a strong
effort has been made to investigate relaxation processes
of such NLO chromophores in order to obtain more
stable polymeric materials. The electric polarization is
a measure of such orientational order, and it is related
to the linear electrooptic and second-harmonic genera-
tion effects.
b
t
Φ(t) ) exp -
(1)
[
( )
]
τ
Usually such an equation provides a good data fitting
and meaningful parameters τ and b, τ representing a
characteristic relaxation time and b the exponential
stretching. The KWW equation was initially considered
an empirical function, found to fit most of the experi-
mental relaxation data, with no particular meaning for
the b parameter. However, physical meaning can be
achieved if one takes into account that the KWW
equation is the solution for the Brownian motion of a
particle interacting with randomly distributed traps or
sinks.12,13 Under this model a defined microscopic
meaning for the b parameter can also be inferred. Thus,
dependences of τ and b on temperature are of great
relevance to understand the microscopic behavior of
polymers and also to predict the final NLO properties
of the glassy state, obtained when cooling the material
from the liquid state. Regarding phenomenological
viscoelasticity, if b ) 1, the relaxation process corre-
sponds to a single relaxation time. For b < 1, the
relaxation process is associated with a relaxation time
distribution, that is, a relaxation spectrum centered at
the characteristic relaxation time τ. The lower the value
of b is, the broader the relaxation spectrum will be.
Tobolsky et al. have shown that an increase in molecular
weight implies a decrease in b,14 and Monteiro et al.
Several relaxation models have been attempted for
NLO polymers. In fact, the decay of the electrooptic
coefficient can be fitted with different functions such as
† Universidade de Sa˜o Paulo.
‡ Universidade Nova de Lisboa.
§ Universidade Federal do Rio Grande do Norte.
Universidade Estadual Paulista.
* To whom correspondence should be addressed: Fax +351 21
294 85 49; e-mail pfr@fct.unl.pt.
10.1021/ma035714j CCC: $27.50 © 2004 American Chemical Society
Published on Web 02/27/2004

Macromolecules, Vol. 37, No. 7, 2004
Chromophore Relaxation in a Methacrylate Copolymer 2619
azobis(butyronitrile) (AIBN) as initiator, at reflux temperature
for 9 h. The resultant copolymer was precipitated, exhaustively
washed with methanol, and dried in a vacuum desiccator for
about 72 h. Different ratios of DR13MA and methyl meth-
acrylate monomers were used to prepare copolymers with
chromophore weight ratios of 9 and 43 wt %, being designated
as MMA-DR13(9 wt %) and MMA-DR13(43 wt %), respectively.
Small quantities of MMA-DR13(4 wt %) were also prepared
to be used as trial samples. Copolymers were characterized
by UV-vis in DMF solution, using a Hitachi U2001 spectro-
photometer, and by FTIR, samples in KBr pellets, using a
BOMEM DA-8 spectrophotometer. Thermal behavior of the
samples was characterized by differential scanning calorimetry
(DSC), using a TA calorimeter model 2910 (ambient to 250
°C, 20 °C/min and under N2), and thermogravimetry mass loss
(TGA), using a Shymadzu Twi50 thermal analyzer (ambient
to 700 °C, 10 °C/min and under N2).
Number-average (Mn) and by weight-average (Mw) molecular
weights, as well the polydispersivity, were obtained by size
exclusion chromatography (SEC) (THF as eluent and polysty-
rene standards). It was found that values of Mn were ca. 23 000
and 18 000 g/mol for the MMA-DR13(9 wt %) and MMA-DR13-
(43 wt %), respectively, while values of Mw were 40 000 and
35 000. Thus, polydispersities are of the order of 1.7 and 1.9,
respectively. Thin-layer chromatography (silica gel using
dichloromethane/n-hexane 70/30) confirmed the absence of
nonreacted monomers.
All copolymers in DMF solution showed a maximum optical
absorption at 505 nm. Copolymer films showed a blue shift of
15 nm compared to the solution spectra, probably due to
aggregation of the chromophores in the film, similarly to
Langmuir-Blodgett films.18 The main IR absorption bands of
MMA were present: 2960, 2850 cm-1 (C-H stretching), 1732
cm-1 (C-O stretching of ester groups), 1242, 1252, and 1134
cm-1 (asymmetric and symmetric C(dO)-O and O-C-C
stretching vibrations of ester group). Regarding DR13MA-
related absorptions, the following bands are present in the
spectra of all copolymers: 1599 and 1500 cm-1 (CdC stretching
in benzene rings), 1518 cm-1 (NO2 asymmetric stretching), and
1336 cm-1 (NO2 symmetric stretching).
F igu r e 1. Chemical structure of the random MMA-DR13
copolymer. X and Y values determine the percentage of each
monomer.
associated the decrease in b with the increase in phase
segregation in polyurethanes.15 In other words, anything
that makes the relaxation process more heterogeneous
such as higher polydispersity or higher molecular
weight implies in more possibilities of entanglements
between the polymer chains and will contribute to a
decrease of b and to the relaxation spectrum broadening.
In the present work, the preparation and character-
ization of the side-chain methyl methacrylate, MMA-
DR13, an acrylic copolymer functionalized with different
percentages of the chromophore disperse red-13, 4-[N-
ethyl-N-(2-hydroxyethyl)]amino-2′-chloro-4-nitroazoben-
zene, DR13, are briefly described. A detailed study of
the relaxation of chromophore orientation was per-
formed by monitoring the electrooptic coefficient decay,
in time domain, below the glass transition temperature,
Tg. Above Tg, dielectric spectroscopy measurements
were used, as the electrooptic decay was too fast to be
measured. Electrooptic coefficient decay and dielectric
spectroscopy results were analyzed using the KWW
function, from which the dependences of τ and b on
temperature were determined. The temperature depen-
dence of the relaxation time was calculated from dielec-
tric data above Tg, and the obtained values were fitted
to the Williams-Landel-Ferry (WLF) equation.16 The
relaxation time values below Tg, obtained from elec-
trooptic measurements, were predicted by introducing
WLF constants into the modified Adams-Gibbs (AG)
equation, which accounts for the glass transition kinet-
ics.17
Films with thickness of about 10 µm were cast from
chloroform copolymer solutions (0.5-2% w/w). All solutions
were filtered with a syringe Millipore Durapore 0.45 µm filter.
Substrates such as optical crown type glass, glass covered with
indium tin oxide (ITO), or aluminum plates were employed.
Samples were dried for 30 min at room conditions and then
submitted to a primary vacuum at 130 °C for 24 h for solvent
removal.
To achieve the second-order NLO properties, i.e., to orient
the side-chain chromophore dipolar groups, a corona triode
setup was used.4,5 Such a technique has been preferred to pole
NLO polymers because it offers better radial uniformity
polarization on sample4 and a good control of final surface
potential, and the metallic grid gives protection against surface
attack from corona species, which are known to deteriorate
polymer surfaces.4,19,20 The corona triode consisted of a sharp
point, a stainless steel grid with a stainless steel mesh of wires
of 0.1 mm diameter, and a metallic sample holder.4 The corona
triode was mounted inside an oven, allowing the temperature
to be controlled. A voltage was applied to the grid, and a high-
voltage supply ((20 kV, operating as a constant current
source) was used to generate the corona discharge. A corona
current of (5 µA was used in the experiments. The electric
contact between the sample holder and the conductive ITO
layer was obtained using silver paint. Such a procedure avoids
the interference of the glass slide on the poling conditions. The
sample was heated to the temperature of 120 °C, a grid voltage
ranging from 400 to 600 V was applied, and the corona
discharge turned on. Poling was performed for 30 min;
subsequently, the sample was cooled to room temperature,
with the corona discharge on, at a rate of about 10 °C/min.
The poling process terminated at room temperature, and power
supplies turned off. The above experimental conditions yielded
maximum electrooptic activity in samples as reported else-
where4 in a detailed study.
The article is organized as follows. Section II gives
the experimental results of the copolymer preparation
and its characterization, corona poling, and measure-
ment techniques. Section III shows the results of the
relaxation measurements, and section IV presents the
discussion and conclusions.
II. Exp er im en ta l Section
The random copolymer, MMA-DR13, shown in Figure 1, was
prepared from solution copolymerization of methyl methacry-
late (MMA, Aldrich) and 4-[N-ethyl-N-(2-methacryloxyethyl)]-
amino-2′-chloro-4′-nitroazobenzene (DR13MA). The DR13MA
monomer was synthesized by the esterification of the com-
mercial dye 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2′-chloro-4′-
nitroazobenzene (DR13, Aldrich) with methacryloyl chloride.18
The copolymerization of DR13MA and MMA monomers was
performed using methyl ethyl ketone as solvent and 2,2′-

2620 Ribeiro et al.
Macromolecules, Vol. 37, No. 7, 2004
F igu r e 2. Normalized heat capacity CNP curves obtained
from differential scanning calorimetry thermograms for MMA-
D13(9 wt %) and MMA-DR13(43 wt %) copolymers and
PMMA.
F igu r e 3. Thermogravimetric loss mass curves for MMA-
DR13(9 wt %) and MMA-DR13(43 wt %) copolymers.
TGA loss mass measurements, shown in Figure 3,
indicated that thermal degradation of the samples
started around 327 °C, much higher than the temper-
atures used in this work. Thus, no degradation of the
copolymer is expected to occur during measurements.
In addition, the copolymer MMA-DR13(43 wt %) showed
a decomposition curve with a different pattern, as
compared to one of MMA-DR13(9 wt %). A possible
explanation is that the highly conjugated chromophores
could produce the cross-linking of the macromolecule
chains with the action of temperature, resulting in
systems that would be more difficult to decompose. As
a consequence, the residual mass at the end of TGA
curves are higher for higher chromophore contents.
3.2. Isoth er m a l Electr oop tic Deca y. Under opti-
mized corona poling conditions4 the maximum values
of r13 achieved, for MMA-DR13 samples with chro-
mophore contents of 9 and 43 wt %, were 3 and 8 pm/V,
respectively. For the sake of clearness, normalized
values of r13 with respect to the initial ones will be
shown.
A scanning Mach-Zhender interferometer was used to
measure the electrooptic coefficient, r13, of the poled MMA-
DR13 copolymer. The experimental setup is similar to the one
described by Singer et al.21 In these measurements, films
deposited onto ITO glass substrates were used. The bare
surface of the film was metallized with an ∼10 nm aluminum
layer by thermal evaporation in a vacuum, which is practically
transparent to the 10 mW, He-Ne, 633 nm laser beam used
in the electrooptic coefficient measurements. The light was
linearly polarized, and the laser beam of diameter 2 mm
impinged the sample at a right angle with respect to its
surface. The electrooptic effect was produced in the samples
by applying a modulation sinusoidal voltage to the aluminum
electrode by means of a soft metallic spring to avoid mechan-
ical stress. Interference fringes were scanned by applying a
ramp voltage to a piezoelectric driven mirror. Measurement
conditions were the following: modulation frequency of 2 kHz,
frequency of fringe displacement within a range from 0.01 to
0.05 s-1, and fringe visibility better than 60%.
The dielectric permittivity measurements were performed
with a Solartron 1260 impedance analyzer in the frequency
range from 1 Hz to 1 MHz, applying a 0.3 V sine voltage. For
these measurements MMA-DR13 films were casted onto 1 mm
aluminum circular plates, the upper electrode being a 200 nm
aluminum layer deposited by vacuum thermal evaporation.
Note that temperature values are given in degrees Celsius,
but in equations and in graphs their correspondig values on
the Kelvin scale were used.
Decay curves of normalized electrooptic coefficient, r13,
at different temperatures are shown in parts a and b of
Figure 4 respectively for the MMA-DR13(9 wt %) and
MMA-DR13(43 wt %) samples. These curves reveal
that the decay increases with temperature and also that
it is more accentuated for the MMA-DR13(43 wt %)
sample.
The decay curves were best fitted to the KWW
equation. Other decay functions such as the exponential,
biexponential, biexponential plus KWW, or van der
Vorst did not allow good fitting as obtained with the
KWW function (results not shown here). As a conse-
quence, the KWW function was used to analyze the
relaxation data. This procedure is usually applied with
success in the literature for NLO polymers.4,23,24 The
fitting curves are shown in Figure 4a,b by the full lines.
3.3. Dielectr ic Rela xa tion . It is worth mentioning
that measurements of r13 could be performed only below
Tg because its decay at higher temperatures is too fast
to be accurately measured using the Mach-Zender
interferometer. An alternative procedure to probe the
chromophore relaxation is from the dielectric response
in the frequency domain. The complex dielectric permit-
tivity ꢀ* ) ꢀ′ + jꢀ′′ is related to the KWW decay function
Φ(t), eq 1, by the Laplace transform as:8
III. Resu lts
3.1. Cop olym er Th er m a l Ch a r a cter iza tion . DSC
thermograms were obtained for some copolymers with
different MMADR13 monomer contents (9 and 43 wt
%), the normalized heat capacity, CNP , being calculated
using the following expression:22
CP(T) - CPL(T)
CPN
)
(2)
CPH(T) - CPL(T)
where CP is the experimental value and CPH and CPL
are the values of CP obtained by extrapolation at high-
and low-temperature limits, i.e., far from Tg. Curves of
Figure 2 show that Tg values, taken at CN = 0.5, are
around 118 °C, decreasing slightly as cPhromophore
content is increased. For comparison, it is also shown
the corresponding curve of poly(methyl methacrylate),
PMMA, sample (Mw ) 350 000). In the data analysis,
to be shown in section IV, a Tg value of 118 °C was
employed for all copolymers.
ꢀ*(ω) - ꢀ(∞)
ꢀ(0) - ꢀ(∞)
dΦ(t)
dt
) - ∞exp(-jωt)
dt
(3)
∫
(
)
0

Macromolecules, Vol. 37, No. 7, 2004
Chromophore Relaxation in a Methacrylate Copolymer 2621
F igu r e 6. Relaxation times vs the inverse of the absolute
temperature. Data represented by solid square and cross
symbols were obtained from electrooptic coefficient measure-
ments respectively for MMA-DR13(9%) and MMA-DR13-
(43%) samples. Solid circle and open square symbols corre-
spond to R relaxation data obtained from dielectric measure-
ments respectively for MMA-DR13(9%) and MMA-DR13-
(43%) samples. Finally, open circle, solid diamond, and open
down triangle symbols correspond to â relaxation data ob-
tained from dielectric measurements respectively for MMA-
DR13(4%), MMA-DR13(9%), and MMA-DR13(43%) samples.
ated with a â relaxation and the higher one, around 140
°C, with an R relaxation. The curve of PMMA (Aldrich,
Mw ) 350 000) is also included for comparison. (Only
the â peak is observable at the frequency of 100 Hz in
the temperature range displayed in the figure.) The â
peak, corresponding to MMA-DR13 samples, should be
attributed to the hindered rotation of the ester
(-COOCH3) group of the MMA.26 In the case of MMA-
DR13(43 wt %) samples, it is believed that the â peak
does not occur because of the higher volume that this
bulky chromophore group occupies, making more hin-
dered the chain rotation. The amplitude of the R peak
is highly dependent on the chromophore content. Thus,
it seems that the chromophore side-group relaxation
follows the R relaxation. This behavior is somehow
expected in side-chain NLO polymers rather than in
guest-host since the chromophore molecules are bound
to the copolymer backbone so that its orientational
relaxation should be linked to the primary R relaxation.
3.4. Tem p er a tu r e Dep en d en ce of P a r a m eter s.
Figure 6 shows a plot of the KWW relaxation time, τ,
versus the reciprocal of temperature. The data were
obtained from the fitting of the r13 decay curves and also
from the tan δ curves employing the Weiss procedure;25
τ values for both R and â peaks were found. It is worth
mentioning two points: first, τ values corresponding to
the â relaxation peaks are much smaller in comparison
to the corresponding ones for the R relaxation and also
of those determined from the electrooptic decay; second,
τ values obtained from r13 decay, below Tg, and from R
peaks, above Tg, seem to lie along the same curve. From
this result one may conclude that the r13 decay and the
tan δ peak arises from the same relaxation processes;
i.e., they are associated with the dipolar chromophore
disordering, the R relaxation process in the copolymer.
Furthermore, the τ(T) vs 1/T dependence for the R
relaxation (Figure 6) clearly shows a deviation from
Arrhenius behavior at high temperatures, indicating the
fragile character12,27 of MMA-DR13 glass former.
Results for the dependence of KWW b parameter on
temperature, not shown here, reveal small changes in
F igu r e 4. (a) Experimental results for electrooptic decay
(points) and KWW fitting curves for MMA-DR13(9 wt %)
sample. Temperatures of measurements are indicated in each
curve. (b) Experimental results for electrooptic decay (points)
and KWW fitting curves for MMA-DR13(43 wt %) sample.
Temperatures of measurements are indicated in each curve.
F igu r e 5. Loss angle tangent data vs temperature taken at
the frequency of 100 Hz, for MMA-DR13(9 wt %), MMA-
DR13(43 wt %), and PMMA samples. The lines are guide lines.
where ꢀ(0) and ꢀ(∞) are the real parts of low- and high-
frequency limits of the dielectric permittivity, respec-
tively. Determination of τ and b KWW function param-
eters using eq 3 is not a straightforward process since
the analytical evaluation of the integral of Laplace
transform is not possible for all values of b. In this work,
the approximations outlined by Weiss et al.25 were used.
The tan δ ) ꢀ′′/ ꢀ′ vs temperature curves, obtained at
100 Hz, are shown in Figure 5. Two relaxation peaks
were observed; the lower one, around 60 °C, is associ-

2622 Ribeiro et al.
Macromolecules, Vol. 37, No. 7, 2004
the investigated temperature range. From nearly con-
stant at low temperatures it presents a small increase
near Tg and stabilizes at higher temperatures. Generally
speaking, one can say that, for both compositions, 98%
of the values fall into the interval 0.50 ( 0.06, and the
value of b at Tg is in the interval 0.55 ( 0.05. The
meaning for these values will be discussed in the next
section. It should be pointed out that the shape of the
electrooptic decay curves of Figure 4 is dependent on
the sample particular aging process. As a consequence,
the τ and b parameters obtained from the fit of these
data to KWW equation will be also dependent on aging,
in such a way that these parameters are seen to increase
as one goes from fast cooling to slow cooling from Tg.
Typically, for a decay at 60 °C, τ can increase up to 1
order of magnitude as one goes from cooling at a rate of
about 20 °C/min to about 0.2 °C/min, while b increases
up to 1.5 times in the same conditions. However, a
general equation accounting for the τ(T) dependence in
terms of the aging process can be found from the
dielectric relaxation data obtained above Tg, as will be
seen in the next section.
4 contains both the high- and the low-temperature
behaviors of the WLF and Arrhenius equations, as
follows:
(a ) Lim it Ca sesAbove Tg. At the limit of high
temperatures one has Tf ≈ T, and eq 4 becomes:
τ(T)
τg
B
B
) exp -
+
(6)
[
]
Tg - T0 T - T0
which is the Vogel-Fulcher-Tammann-Hesse35-37
(VFTH) equation. It shows the same dependence of the
WLF equation, given by:
Cg1 Cg2
τ(T)
log
) -Cg1 +
(7)
(
)
τg
T - T0
where Cg1 and Cg2 are constants. According to the free
volume theory26 Cg ) b′/2.303f (Tg) and Cg ) f (Tg)/Rf-
1
2
(Tg), where b′ is a polymer dependent constant, f (Tg) is
the free volume fraction, and R(Tg) is the volumetric
expansion coefficient both at Tg. It should be noted
that as eq 7 is the logarithm form of eq 6, then B )
2.303Cg1C2g and T0 ) Tg - C2g.38
IV. Discu ssion s a n d Con clu sion s
Before discussing the results, it is worthwhile to
review here the approach usually employed to interpret
the dependence of τ(T) on T. It is known that τ(T) is
well accounted for by the WLF equation28 within a
temperature range from Tg to (Tg + 100 °C) while the
Arrhenius equation16 is suitable below Tg. More general
equations were obtained by Addam-Gibbs17 (AG), when
interpreting the relaxation process as the cooperative
interaction due the packing of polymer segments as
the temperature is decreased from above the glass
transition, and by Tool-Narayanaswamy-Moynihan
(TNM)29-33 as a result of considering enthalpy relax-
ation in terms of a fictive temperature, Tf, as a measure
of departure from thermal equilibrium and accounting
for the glass transition kinetic behavior. These concepts
were reexamined by Hodge and Berens,34 resulting in
the following equation, the Addam-Gibbs-Tool-Naray-
anaswamy-Moynihan (AG-TNM) equation, for the re-
laxation time temperature dependence:
(b) Lim it Ca sesBelow Tg. At the low-temperature
limit, the fictive temperature tends to a constant value,
Tf ) Tf′, and eq 4 becomes:
τ(T)
τg
B
exp -
(8)
T0
T
- 1
[
]
)
(
Tf′
which has the same form as the Arrhenius equation.
Since the WLF behavior usually occurs above Tg,27
one can infer that the Cg1 and C2g WLF parameters can
be used in the AG-TNM equation. Such a parametriza-
tion has been successfully applied to polyimides func-
tionalized with similar size NLO azo chromophres and
allowed a complete relaxation description over more
than 15 orders of magnitude in time.39
The fitting parameters of the experimental data,
using the WLF equation (eq 7) for MMA-DR13(9 wt
%) and MMA-DR13(43 wt %) copolymers, are displayed
in Table 1. Results revealed that for both compositions
the Cg1 parameters are basically the same and the C2g
fall in the same range. Similar values of Cg1 means that
a unique relaxation curve can be obtained if the
relaxation time is plotted normalized to Tg. In fact, eq
8 predicts this behavior if the final fictive temperature
is set equal to Tg. In this case, one obtains:40
τ(T)
τg
B
B
) exp -
+
(4)
Tg - T0
T0
T 1 -
[
]
)
(
Tf(T)
where τg is the relaxation time measured at Tg, B is an
activation temperature, BR, with R the universal gas
constant, being an activation energy per mole, and T0
is the temperature at which the configurational entropy
would be zero. For a process of a glass formation during
a cooling process, at a constant cooling rate q from a
temperature Ti above Tg, the fictive temperature can
be determined by the following equation:34
Tg - T
τ(T)
τg
log
) Cg1
(9)
T
and normalization with respect to (Tg - T)/T arises.
The fitting curves obtained using the Arrhenius and
VFTH functions are shown in Figure 7 by dashed and
full lines, respectively, plotted as a function of (Tg - T)/
T. It should be noticed that eq 5 is expected to account
b
T (T) ) T + TdT′ 1 - exp -
(5)
T
1
dT′′
∫
∫
f
i
{
(
) }
]
T′ τ(T)
Ti
[
q
τ(T) and b are the usual parameters in the KWW
equation, and T′and T′′ are the integration variables.
Determination of Tf(T) requires a cumbersome proce-
dure since b, τ(T), and the cooling/heating dynamics
should be known in all temperature ranges. To circum-
vent such a difficulty, the τ(T) dependence is habitually
analyzed in two limit cases, since the exponential of eq
Ta ble 1. Va lu es of WLF Equ a tion P a r a m eter s Cg1, C2g, a n d
T0 Obta in ed fr om F ittin g th e Exp er im en ta l Nor m a lized
Rela xa tion Tim es a bove Tg
MMA-DR13 (wt %)
C1g
Cg2 (K)
T0 (K)
9
43
12 ( 2
12 ( 2
40 ( 10
50 ( 10
350 ( 20
340 ( 20

Macromolecules, Vol. 37, No. 7, 2004
Chromophore Relaxation in a Methacrylate Copolymer 2623
F igu r e 9. Fictive temperature, Tf, temperature dependence,
for different thermal treatments.
F igu r e 7. Plot of relaxation times (normalized to τg) as a
function of the parameter (Tg - T)/T, for both MMA-DR13-
(9%) and MMA-DR13(43%) samples, and fitting curves to
WLF and Arrhenius equations.
F igu r e 10. Final fictive temperature, Tf′, vs annealing
temperature, Ta, for several annealing times and cooling rates.
The horizontal lines indicate the final fictive temperatures
achieved for the cooling rates of 2, 5, and 10 °C/min.
F igu r e 8. Result from fitting of experimental data to the AG-
TNM equation for both MMA-DR13(9%) and MMA-DR13-
(43%) samples.
possible to the T0 value. In Figure 9 the fictive temper-
ature dependence on the cooling rate for MMA-DR13-
(43 wt %), calculated from eq 5, using b ) 0.5, is shown.
As one can expect, the lower the cooling rate is, the
lower the final fictive temperature is, and a more stable
glass can be obtained. Low cooling rate requires a long
time exposure of the sample to the corona discharge,
leading to the surface sample deterioration. Previous
results obtained for the MMA-DR13 copolymers indi-
cated that the exposure of the sample to the corona
discharge should not exceed much more than 60 min to
minimize sample damage.4 Consequently, cooling rates
smaller than 2 °C/min should be avoided, as the
exposure will exceeds the maximum allowed. Indeed,
at a cooling rate of 2 °C/min, the cooling process will
take about 45 min, which seems to be fine. However,
further thermal stability of the copolymer can be
achieved if one includes an annealing step during the
cooling process at a given rate. The main concern here
is to find the optimum annealing temperature for a
given time interval, compatible with the advisable for
maximum corona exposure of about 60 min. For this
purpose the final fictive temperature has been calcu-
lated at chosen cooling rate for different annealing
temperatures and times. The calculation follows from
eq 5, which has to be modified to include an annealing
step.39 The plot of final fictive temperatures as a
function of the annealing temperature is shown in
for the kinetics of the glass formation for a particular
cooling process, in such a way that when introduced into
eq 8 one expects to fit the experimental data in the
region near Tg. This is shown by the full line in Figure
8, which is the curve obtained with the AG-TNM
equation using Cg1 and C2g parameters listed in Table 1,
a cooling rate of 10 °C/min, and the KWW b parameter
equal to 0.5, which is the average value in the temper-
ature range used in the experiments. Fitting results
indicate that a good prediction of the orientational
stability of NLO chromophores in MMA-DR13 copoly-
mers can be achieved.
The orientational stability can be better understood
using eq 8, as the B parameter is related to the
Arrhenius activation energy, Ea, of the primary R
relaxation, responsible for randomization of the chro-
mophore orientation. The expression for ER in terms of
the final fictive temperature Tf′ follows from eq 8:
2.303Cg1 Cg2
Ea(T) )
(10)
T0
1 -
Tf′
To finish this point, the analysis performed above is
used to predict the thermal treatment process that leads
to the lowest final fictive temperature Tf′ as close as

2624 Ribeiro et al.
Macromolecules, Vol. 37, No. 7, 2004
Figure 10. The curves show a minimum around 110 °C,
indicating that this value is the ideal one to perform
the annealing. The lowest final fictive temperature is
reached for a cooling rate of 2 °C/min and annealing at
110 °C for 15 min. The Tf′ value in this case is 109 °C,
lower than that one achieved when cooling at 2 °C/min
and close to the one achieved when cooling at 1 °C/min
(Figure 9). The total time of exposure to the corona
discharge process will be in this case of 65 min, which
guarantees minor sample surface damage.
As a measure of the fragile characteristic of MMA-
DR13, revealed in the plot of Figure 6, one can estimate
the fragility index, defined in terms of the WLF equation
as:41
and F. D. Nunes for the help with electrooptic experi-
mental setup.
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Ack n ow led gm en t. The authors thank FAPESP,
CAPES, and CNPq, Brazil, and Fundac¸a˜o Cieˆncia e
Tecnologia-PRAXIS XXI, Portugal, for financial sup-
port and to A. C. Hernandez for gently supplying high-
quality electrooptic calibration crystals and to S. C. Zilio
MA035714J