Determination of transition rate constants of trans-cis isomerization in a poly(malonic ester) containing disperse red 1

Article abstract of DOI:10.1063/1.1487825

A method for obtaining the quantitative transition rate constants of trans-cis isomerization in the pseudo-stilbene-type of azobenzene molecule was discussed. The absorbances of the solution and film of a poly(malonic ester) containing disperse red 1(PDR1) were measured with the pumping beams intensity and were analyzed by the rate equation for the fractions of trans and cis conformers. The rate constants of PDR1 solution and film were also determined.

Full text of DOI:10.1063/1.1487825

Determination of transition rate constants of trans–cis isomerization in a poly(malonic
ester) containing disperse red 1
H. D. Shin, W. J. Joo, C. H. Oh, P. S. Kim, and Y. K. Han
Citation: The Journal of Chemical Physics 117, 1677 (2002); doi: 10.1063/1.1487825
View online: http://dx.doi.org/10.1063/1.1487825
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 117, NUMBER 4
22 JULY 2002
Determination of transition rate constants of trans–cis isomerization
in a poly„malonic ester… containing disperse red 1
H. D. Shin, W. J. Joo, C. H. Oh, and P. S. Kim
Department of Physics, Hanyang University, Seoul 133-791, Korea
Y. K. Han
Department of Chemistry, Hanyang University, Seoul 133-791, Korea
͑
Received 13 August 2001; accepted 1 May 2002͒
We suggested a simple method for obtaining the quantitative transition rate constants of trans–cis
isomerization in the pseudo-stilbene-type of azobenzene molecule. The absorbances of the solution
and film of a poly͑malonic ester͒ containing disperse red 1͑PDR1͒ were measured with the pumping
beam intensity, and analyzed by the rate equation for the fractions of trans and cis conformers. The
rate constants of PDR1 solution and film were successfully determined. © 2002 American Institute
of Physics. ͓DOI: 10.1063/1.1487825͔
I. INTRODUCTION
termining the rate constants. Therefore, another simple
method is needed for determining the quantitative rate con-
stants of trans–cis isomerization in the pseudo-stilbene-type
of azobenzene molecule.
In this article, we analyzed the rate equation of the
trans–cis isomerization and suggested a simple method for
determining the quantitative transition rate constants of
trans–cis isomerization. With this method, we obtained the
rate constants of trans–cis isomerization in a poly͑malonic
ester͒ containing disperse red 1͑PDR1͒.
The polymers containing azobenzene molecules have re-
ceived considerable attention because of the merits of fabri-
cation, reversibility, high birefringence, and photochromic
1
–3
property for optical data storage.
The origin of optical
data storage is founded on the photoinduced birefringence
caused by the reorientation of the azobenzene molecule. The
reorientation is dependent on the rigidity of matrix, spacer
length, temperature, light intensity, and so forth.4 The
mechanism of the reorientation is mainly founded on the
trans–cis isomerization that changes the shape of mesogens
,5
II. EXPERIMENT
͑
rod-shaped trans conformer and banana-shaped cis
6
conformer͒. Recently, several experimental results that can-
not be explained by the trans–cis isomerization were re-
ported. The birefringence induced by pumping at the absorp-
tion edge of the cis conformer was reported,7 and
Andreienko et al. showed that the threshold pumping inten-
sity for the Freedericksz transition decreased greatly in
A. Polymer material
The polymer used in our experiments was a poly͑ma-
lonic ester͒ ͑PDR1͒ with two symmetrical disperse red 1
,8
͓Fig. 1͑a͔͒, which is characterized spectroscopically by the
␲
→␲* band of the trans conformer that overlaps with the
weak n→␲* band of the cis conformer around the wave-
9
azobenzene polymers. Therefore, a detailed study of the ex-
length of 500 nm ͓Fig. 1͑b͔͒.6
act process of the photoinduced birefringence is necessary. In
order to determine the contribution of isomerization to the
photoinduced birefringence, the transition rate constants of
trans–cis isomerization should be obtained quantitatively.
There are a lot of reports to determine the parameters,
such as absorbance and quantum yields from the rate equa-
tion of trans–cis isomerization. In particular, Fischer re-
ported a method to obtain the absorbance of pure cis
New thermotropic liquid crystalline malonic ester mono-
mer ͑MDR1͒ was synthesized by reacting malonyl dichloride
and disperse red 1 in tetrahydrofuran ͑THF͒ at 0 °C for 24 h.
It was then condensed with 1,6-dibromohexane in THF in the
presence of sodium hydride at 65 °C for 24 h to give a poly-
͑malonic ester͒ ͑PDR1͒ with two symmetrical disperse red 1s
a photoresponsive group. The polymeric thin films were cast
from the polymer solution ͑5 wt %͒ in CHCl onto a glass
1
0
3
conformers, and several researchers suggested methods to
15
plate for 30 s using a spin coater.
obtain the quantum yields.1
1–14
However, there are several
problems in the previous methods for determining the tran-
sition rate constants of trans–cis isomerization. Each param-
eter had to be separately measured and calculated for obtain-
ing the transition rate constants. Moreover, the thermal
isomerization was almost neglected in the case of
azobenzene-type and aminoazobenzene-type molecules, be-
cause thermal cis→trans isomerization operates very
B. Experimental setup
We prepared an experimental setup for the real-time
measurements of the absorbance in PDR1 solution and film,
as shown in Fig. 2. The sample was irradiated by a pumping
beam ͑2͒ from a second harmonic generated Nd:YAG laser
͑Coherent 532-200͒ with the wavelength of 532 nm. The
Nd:YAG laser was a continuous wave laser, and the intensity
of the pumping beam was controlled by a variable attenuator.
The absorbance change was measured with a reading beam
1
0–12,14
slowly.
But, in the case of the pseudo-stilbene-type
molecule with relatively fast thermal cis→trans isomeriza-
tion, the thermal isomerization should be considered for de-
0021-9606/2002/117(4)/1677/5/$19.00
1677
© 2002 American Institute of Physics
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2

1678
J. Chem. Phys., Vol. 117, No. 4, 22 July 2002
Shin et al.
as another light source. The absorbance was measured when
the pumping beam was turned on ͑pumping period͒ and off
͑relaxation period͒.
III. THEORY
When azobenzene molecules are irradiated by a mono-
chromatic beam, the rate equation for the fractions of trans
and cis conformers can be expressed by11
dC͑t͒
ϭlϫIϫT͑t͒ϪmϫIϫC͑t͒ϪnϫC͑t͒
dt
ϭlϫIϫ͓1ϪC͑t͔͒ϪmϫIϫC͑t͒ϪnϫC͑t͒,
T͑t͒ϭ1ϪC͑t͔͒
ϭlϫIϪ͓͑lϩm͒ϫIϩn͔ϫC͑t͒,
͑1͒
͑2͒
͓
where I is the pumping beam intensity. C(t) and T(t) are the
fractions of cis and trans conformers at time t, respectively.
The transition rate constants correspond to the following re-
actions:
l : Tϩh␯→C ͑photoisomerization͒;
m : Cϩh␯→T ͑photoisomerization͒;
n : C→T ͑thermal isomerization͒.
FIG. 1. ͑a͒ Chemical structure of PDR1. ͑b͒ Absorption spectrum of PDR1.
The first two terms on the right-hand side of Eq. ͑1͒ are
related to the trans→cis and cis→trans photoisomerizations,
and the third term is related to the thermal cis→trans isomer-
ization. The transition rate constants, l and m, are dependent
͑1͒ split by a beam splitter. The intensity of the reading beam
͑
␮
1͒ was attenuated by a variable attenuator as small as 10
W/cm . Both pumping and reading beams were circularly
on the absorption coefficients, quantum yields and a function
2
ϪD(t)
͓(1Ϫe
)/D(t)͔, where D(t) is the measured absorbance
in pumping period or relaxation period.11 Because the varia-
tion of the function is very small ͑less than 2%͒ during illu-
mination, we can consider this function as a constant param-
eter. In the pumping period, the fraction of cis conformers is
given from Eq. ͑2͒ by
polarized to prevent them from inducing any anisotropy.
Since the pumping beam and reading beam were coherent,
energy transfer between the two beams could occur through
the formation of a grating. To avoid this coupling effect, the
phase of the pumping beam was modulated at about 1 kHz
by a piezoelectric transducer. The reading beam was detected
by a photodiode ͑Hamamatsu, S1336-18BQ͒ interfaced with
a computer, in which the data transfer rate was about 80 Hz.
To determine the absorbance of the pure cis conformers us-
lϫI
Ϫ
C͑t͒ϭ
ϫ͑1Ϫe ͕͑lϩm͒ϫIϩn͖ϫt͒.
͑3͒
͑
lϩm͒ϫIϩn
6
As can be seen in Eq. ͑2͒, the fraction of cis conformers
changes by a single exponentially growing function of time
in the pumping period. Since the trans and cis conformers
coexist in the polymer sample, and each conformer has its
own absorption coefficient, the measured absorbance ͓D(t)͔
of the polymer sample is given by
ing Fischer’s method, an argon ion laser at 514 nm was used
D͑t͒ϭT͑t͒ϫDtransϩC͑t͒ϫDcis
͑
DcisϪDtrans͒ϫlϫI
ϭDtrans
ϩ
͑
lϩm͒ϫIϩn
ϫ͑1Ϫe ͕͑lϩm͒ϫIϩn͖ϫt͒
Ϫ
ϭDtransϪMϫ͑1ϪeϪkϫt͒,
͑4͒
where Dtrans and Dcis represent the absorbances of the pure
trans conformer and the pure cis conformer, respectively.
Dtrans is determined when the sample was kept in the dark
for a long time, and Dcis can be calculated by Fischer’s
FIG. 2. Experimental setup for real-time measurement of the absorbance of
the PDR1 polymer sample in pumping and relaxation periods ͑Mϭmirror,
B.S.ϭbeam splitter, Q.W.P.ϭ␭/4 wave plate, V.A.ϭvariable attenuator, and
P.Z.T.ϭpiezoelectric transducer͒.
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J. Chem. Phys., Vol. 117, No. 4, 22 July 2002
Rate constants of trans–cis isomerization
1679
FIG. 4. ͑a͒ Time constant in the pumping period and ͑b͒ magnitude of
absorbance change vs pumping beam intensity in the PDR1 solution.
FIG. 3. Absorbances at 532 nm in the PDR1 solution with time at various
pumping beam intensities: ͑a͒ in the pumping period; ͑b͒ in the relaxation
period.
IV. RESULTS
Figure 3 shows the absorbance ͓D(t)͔ for a diluted so-
lution of PDR1 at various pumping beam intensities during
pumping ͑a͒ and relaxation ͑b͒ periods. The magnitude of
absorbance change M increased with the intensity of the2
pumping beam ͓Fig. 3͑a͔͒, and was saturated at 15 mW/cm
of the pumping beam intensity. The solid lines are the fitted
curves with Eq. ͑4͒ by nonlinear least-squares fitting method.
The values of M and k obtained from the fitting are shown in
Fig. 4. By fitting the curve of Fig. 3͑b͒ with Eq. ͑7͒, the
value of n was determined to be 0.053Ϯ0.003 irrespective of
the pumping beam intensity. The value of Dtrans was found
to be 0.288 at 532 nm. Dcis was calculated to be 0.173 using
Fischer’s method with high pumping beam intensity, so
DtransϪDcis was 0.115.
Figure 4͑a͒ shows the time constants ͑k͒ with the pump-
ing beam intensity, and the value of lϩm was obtained by
fitting the plots of k with Eq. ͑5͒ in which the already deter-
mined value of n was included:
8
method with the pumping beam of high power. For simplic-
ity, the time constant ͑k͒ in the pumping period is defined as
kϭ͑lϩm͒ϫIϩn
͑5͒
and the magnitude of absorbance change ͑M͒ is as
͑
DtransϪDcis͒ϫlϫI
MϵDtransϪD͑ϱ͒ϭ
.
͑6͒
͑
lϩm͒ϫIϩn
Since the Dtrans is bigger than Dcis in our experimental con-
dition, the M value is positive, and the measured absorbance
also changes by the single exponential decaying function of
time.
The magnitude of absorbance change ͑M͒ and the time
constant ͑k͒ in the pumping period are dependent on the
pumping beam intensity and the transition rate constants.
Therefore, from analyzing the values of M and k for the
various pumping beam intensities, we can determine the
transition rate constants. The values of M and k can be ob-
tained by fitting the measured curve of D(t) in the pumping
period to Eq. ͑4͒.
The process to change the fractions of trans and cis con-
formers in relaxation periods is only the thermal isomeriza-
tion. That is, the absorbance change in the relaxation period
is independent of the pumping beam intensity and can be
described only by the thermal rate constant n. Therefore, the
thermal rate constant ͑n͒ can be obtained by fitting the mea-
sured curve of absorbance ͓D(t)͔ in the relaxation period to
a single exponential growing function:
5
kϭ͑lϩm͒ϫIϩ0.053.
͑8͒
In this case, the linear least-square fitting method was
used. As a result, the value of lϩm was determined to be
0.077Ϯ0.003. Figure 4͑b͒ shows the magnitudes of absor-
bance change M with the pumping beam intensity. The curve
of Fig. 4͑b͒ was fitted by Eq. ͑6͒ with the parameters ob-
tained above, such as lϩm, n, and DtransϪDcis
:
lϫI
Mϭ0.115ϫ
ͫ
ͬ
.
͑9͒
0
.077ϫIϩ0.053
In this case, the nonlinear least-square fitting method
was used. As shown in Fig. 4͑b͒, the fitting result matched
well with the experimental one. As a result, the values of l,
m, and n were determined to be 0.032Ϯ0.0001, 0.045
Ϯ0.0001, and 0.053Ϯ0.003, respectively. Therefore, the rate
equation of both conformers in the PDR1 solution can be
represented quantitatively as
D͑t͒ϭD͑ϱ͒ϩMϫ͑1ϪeϪnϫt͒.
͑7͒
By again fitting the k values with the pumping beam
intensity to Eq. ͑5͒, the value of lϩm can be determined.
Finally, with the obtained values of parameters such as
Dtrans , Dcis , n and lϩm, the individual values of l and m
can be obtained by fitting the M values with the pumping
beam intensity to Eq. ͑6͒.
dC
ϭ0.032ϫIϫTϪ0.045ϫIϫCϪ0.053ϫC.
͑10͒
dt
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1680
J. Chem. Phys., Vol. 117, No. 4, 22 July 2002
Shin et al.
FIG. 6. ͑a͒ Time constant in the pumping period and ͑b͒ magnitude of
FIG. 5. Absorbances in the PDR1 film with time at various pumping beam
absorbance change vs pumping beam intensity in the PDR1 film.
intensities: ͑a͒ in the pumping period; ͑b͒ in the relaxation period.
0
.088 using the ratio between the absorbances of trans and
cis conformers (Dtrans /Dcis) in the case of the PDR1 solu-
tion.
The same method as in the case of the solution was used
for obtaining the rate constants of the trans–cis isomeriza-
tion with some adjustments for the case of the PDR1 film.
The intensity dependence of the absorbance was similar to
the case of solution ͑Fig. 5͒, but as shown in Fig. 5͑a͒, the
variation of absorbance was slower than that of the PDR1
solution. The magnitude of absorbance change was not satu-
rated even though the pumping beam intensity was as large
Finally, the rate constants of isomerization were deter-
mined by lϭ0.0084Ϯ0.000 06, mϭ0.0336Ϯ0.000 06, and
nЈϭ0.21Ϯ0.004. Comparing these constants with those of
the PDR1 solution, the time constant (nЈ) of the film was
about four times higher than that of the solution, because the
strained cis conformers induced the fast anomalous relax-
ation. Also, both l and m were smaller than those of the
solution, because of very low quantum yields in the film.17
2
as 80 mW/cm . Moreover, there might be another effect be-
sides the thermal isomerization in the relaxation period, since
the curve of D(t) in the relaxation period did not match with
a single exponential growing function but with a bi-
exponential growing function. Paik et al. reported that the
anomalous fast relaxation component was caused by cis con-
V. CONCLUSION
A simple method was suggested for determining the
transition rate constants of trans–cis isomerization quantita-
tively in the pseudo-stilbene-type of azobenzene molecule.
The absorbances of the PDR1 solution and film were mea-
sured with the pumping beam intensity, and analyzed by the
rate equation for the fractions of trans and cis conformers.
As the results in the PDR1 solution, the rate constants l,
m, and n were determined to be 0.032Ϯ0.0001, 0.045
Ϯ0.0001, and 0.053Ϯ0.003, respectively. In the PDR1 film,
the rate constants l, m, and nЈ were 0.0084Ϯ0.000 06,
formers trapped in a strained conformation, and a slow one
was due to the thermal isomerization.16 Therefore, we used a
bi-exponentially growing function to obtain the time con-
stants of the thermal isomerization.
D͑t͒ϭD͑ϱ͒ϩMfastϫ͓1Ϫexp͑Ϫnfast•t͔͒
ϩMslowϫ͓1Ϫexp͑Ϫnslow•t͔͒,
͑11͒
0
.0336Ϯ0.000 06, and 0.21Ϯ0.004, respectively.
where nfast and nslow are the time constants of fast and slow
components of relaxation, and Mfast and Mslow are the mag-
nitudes of fast and slow components, respectively. In order to
consider both the rate constants, a thermal rate constant (nЈ)
of cis→trans isomerization was newly defined by
ACKNOWLEDGMENT
This work was supported by Korea Science and Engi-
neering Foundation ͑96-0300-10-01-3͒.
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J. Chem. Phys., Vol. 117, No. 4, 22 July 2002
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2