Photoinduced gratings in functionalized azo-carbazole compounds in picosecond regime

Article abstract of DOI:10.1080/15421400801926396

We report results of diffraction grating inscription on thin films prepared from epoxy resin doped with azo-carbazole based dyes. Diffraction gratings were recorded at the wavelength 532nm and monitored through intensity of first order of diffraction (632nm). Atomic force microscope scans of the gratings show that a surface relief grating also appeared.

Full text of DOI:10.1080/15421400801926396

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Photoinduced Gratings in
Functionalized Azo-Carbazole
Compounds in Picosecond
Regime
Robert Czaplicki a , Sylvie Dabos-Seignon a , Ileana
Rau b , Oksana Krupka* a , Bouchta Sahraoui a ,
c
Jacek Nizioł , Monika Bednarz d , Jan Pielichowski
d , Aurelia Meghea b & Mina Bakasse e
a Laboratory POMA, University of Angers, Angers
Cedex, France
b Faculty of Applied Chemistry and Material Science,
University Politehnica of Bucharest, Bucharest,
Romania
c Faculty of Physics and Applied Computer Science,
AGH – University of Science and Technology, Cracow,
Poland
d Department of Polymer Science and Technology,
Cracow University of Technology, Cracow, Poland
e University of Chouaib Doukkali – Faculty of
Sciences BP, El Jadida, Morocco
Version of record first published: 31 Aug 2012.
To cite this article: Robert Czaplicki , Sylvie Dabos-Seignon , Ileana Rau , Oksana
Krupka* , Bouchta Sahraoui , Jacek Nizioł , Monika Bednarz , Jan Pielichowski ,
Aurelia Meghea & Mina Bakasse (2008): Photoinduced Gratings in Functionalized Azo-
Carbazole Compounds in Picosecond Regime, Molecular Crystals and Liquid Crystals,
485:1, 1030-1042

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Mol. Cryst. Liq. Cryst., Vol. 485, pp. 282=[1030]–294=[1042], 2008
Copyright # Taylor & Francis Group, LLC
ISSN: 1542-1406 print=1563-5287 online
DOI: 10.1080/15421400801926396
Photoinduced Gratings in Functionalized Azo-Carbazole
Compounds in Picosecond Regime
Robert Czaplicki1, Sylvie Dabos-Seignon1, Ileana Rau2,
Oksana Krupka1,ꢀ, Bouchta Sahraoui1, Jacek Nizioł3,
Monika Bednarz4, Jan Pielichowski4, Aurelia Meghea2,
and Mina Bakasse5
1Laboratory POMA, University of Angers, Angers Cedex, France
2Faculty of Applied Chemistry and Material Science, University
Politehnica of Bucharest, Bucharest, Romania
3Faculty of Physics and Applied Computer Science, AGH – University
of Science and Technology, Cracow, Poland
4Department of Polymer Science and Technology, Cracow University
of Technology, Cracow, Poland
5University of Chouaib Doukkali – Faculty of Sciences BP, El Jadida,
Morocco
We report results of diffraction grating inscription on thin films prepared from
epoxy resin doped with azo-carbazole based dyes. Diffraction gratings were
recorded at the wavelength 532 nm and monitored through intensity of first order
of diffraction (632 nm). Atomic force microscope scans of the gratings show that a
surface relief grating also appeared.
Keywords: azo-carbazole compounds; picosecond regime; pulsed-laser grating
inscription; surface relief gratings
ꢀOn leave from Kiev National Taras Shevchenko University, Chemistry Department,
Ukraine.
Some of the authors (Monika-Bednarz-and-Jacek-Niziol) acknowledge the support by
Polish Ministry of Science and Education through the project 3-T08E-083-30. For
Bouchta Sahraoui, Mina Bakasse, Aurelia Meghea financial support from FP 6 Marie
Curie Host Fellowship for the Transfer of Knowledge contract NANOTEC- EST
MTKD-CD-2004-014059 is gratefully acknowledged.
The authors thank Professor Andrzej Miniewicz (Wroclaw University of Technology,
Poland) and for helpful discussion.
Address correspondence to Robert Czaplicki, POMA Laboratory, UMR CNRS 6136,
University of Angers, 2 Boulevard Lavoisier, 49045 Angers, France. E-mail: robert.
czaplicki@etud.univ-angers.fr
282=[1030]

Photoinduced Gratings in Azo-Carbazoles
283=[1031]
INTRODUCTION
Organic compounds combine unique electronic and optical properties.
Polymers containing azo-benzene dyes either as side groups or physi-
cally dispersed, can interact with polarized light. This interaction due
to reorientation of the side groups, results in reversible birefringence
and dichroism. The trans azobenzene derivatives are stable in an elon-
gated molecular form. In contrast, the cis azobenzenes are photoin-
duced isomers, taking a bentform, usually revert back to the trans
form by thermal or light stimulation [1,2]. Photoinduced isomerisation
was studied by many researchers [2–10] and several mechanisms of
surface relief grating formation were proposed [1]. Polymers contain-
ing the azo groups are able to generate surface relief gratings by
irradiation [1,11–13]. This phenomenon enables applications like holo-
graphic data storage, optical switching, optical data storage, etc [14].
Materials typically applied in the field of grating recording are
optically transparent thermoplastic polymers (polymethacrylates,
polycarbonates etc.) containing dyes dispersed on molecular level.
The thermoplastics undergo the glass transition in relatively low tem-
peratures – typically between 90 and 120ꢁC. This feature limits laser
power, which can be exerted on the surface without the risk of
damage. More thermally stable materials are thermosetting resins.
Once they are set, it is not possible to melt them any longer. Due to
this feature, it is more complicated to transform them into thin films
for gratings recording.
In frame of this work, we studied three kinds of thin films prepared
from epoxy resin by different methods. The purpose was to find the
most adapted to grating recording. As dyes we used tailored azo-
functionalized carbazole compounds, already reported for their non-
linear optical properties [15]. This choice was done due to their good
miscibility with the epoxy resin and lack of visible phase separation.
DYES SYNTHESIS
General
All chemicals, were purchased from either Aldrich or Fluka and
used as received with exception of solvents, twice distilled prior to
synthesis.
The carbazole azo dyes can be synthesized either by coupling reac-
tion of carbazolediazonium salts with passive compound or by coupling
reaction between carbazole or its derivatives and diazonium salts of
aromatic amines (very convenient method, which enables synthesis
of multiple carbazole azo dyes [16]).

284=[1032]
R. Czaplicki et al.
FIGURE 1 Amine diazotization, R ¼ ꢂCl, ꢂNO2, ꢂCN.
In this work, we follow the second one. At first, the diazonium salts are
obtained according to the scheme presented in Figure 1. The next stage –
coupling reaction (Fig. 2) is carried out at the interference of a two-phase
system. Usually this system form water and an alcohol of low solubility in
water (like butanol or isobutanol, less than 15 w% at 15ꢁC) [17,18].
Under these conditions, carbazole and its derivatives easily react with
diazonium salts of aromatic amines and the product is a suitable dyes.
The dye formation according to this procedure is particularly rapid, even
using reactants such as carbazole and its N-alkyl derivative, that
normally undergo very hard (if at all) the coupling reaction.
Next, the obtained dye is extracted from the reaction mixture
through filtration. Its purity usually is superior to 90%. Sometimes
before filtering the dye, it is necessary to evaporate the residue of
alcohol by steam distillation. This method provides high yield of the
product, generally more than 80%.
Diazo Salt Solution Preparation
Hot, concentrated hydrochloric acid (18 ml) was added into suspension
of 2-chloro-4-nitroaniline (5.3 g, 0.0264 mol) in water (57 ml). Then the
FIGURE 2 Coupling reaction of diazonium salts of aromatic amines with
carbazole and its derivatives.

Photoinduced Gratings in Azo-Carbazoles
285=[1033]
FIGURE 3 Synthesis of 3-(20,40-chloronitrophenylazo)-N-(b-hydroxyethyl)-
carbazole) (CNHEK).
suspension was cooled in an ice bath until the temperature reached
between 0ꢁ and þ5ꢁC. Then the solution containing sodium nitrite
(2.5 g, 0.0264 mol) in water (13 ml) was slowly added to the suspension.
The mixture was stirred in the ice bath for 30 min.
3-(2’-chloro-4’-nitrophenylazo)-N-(b-hydroxyethyl)-carbazole
(CNHEK)
The filtered diazo solution was run into suspension of N-(b-hydro-
xyethyl)-carbazole (3 g, 0.0142 mol) in n-butanol (22 ml) at 40ꢁC. The
mixture was then stirred overnight at 40ꢁC and meanwhile the dye
precipitated. The dye was filtered, well rinsed on the filter (with
16 ml of n-butanol, and then with water) and finally dried. Resulting
product, a green-yellow powder was obtained with 80% yield (Fig. 3).
IR (KBr), cmꢂ1. 3095, 2933(nAr-H), 1595(nN¼N), 1626, 1595(nC¼C),
1524, 1323(nNO ), 1466, 1439(nCꢂH), 1111(nCꢂCl), 748, 733(cCH
)
2
2
1HNMR(acetone). d ¼ 4.05(d, 2 H), 4.63( t, 2 H), 7.31(dt, 1 H),
7.60(dt, 1 H), 7.71(dd, 1 H), 7.82(d, 1 H), 7.96( m, 3 H), 8.31(dd, 1 H),
8.46(d, 1 H), 8.86(d, 1 H)
3-(2’-chloro-4’-nitrophenyloazo-)-N-(2,3-epoxypropyl)-
carbazole (CNEPK)
First, the 3-(20-chloro-40-nitrophenyloazo-)-N-(2,3-epoxypropyl)-
carbazole was obtained. Acetone (100 ml) was added into suspension
of 3-(20-chloro-40-nitrophenylazo-)carbazole (5.7 g, 0.0158 mol) in epi-
chlorohydrin (7.4 g, 0.0095 mol). The solution was heated up to 35ꢁC
and potassium hydroxide (0.9 g, 0.016 mol), potassium carbonate
(16 g) and TBAB (tetrabutylammonium bromide) (0.5 g, 0.0095 mol)
were added. The mixture, thermostated at 35ꢁC, was stirred vigorously
for 6 h. After evaporation of acetone crude product was crystallized

286=[1034]
R. Czaplicki et al.
FIGURE 4 Synthesis of 3-(20-chloro-40-nitrophenylazo-)-N-(2,3-epoxypropyl)-
carbazole (CNEPK).
from methylene chloride, filtered, well rinsed with water and dried. A
bright red powder was obtained with 70% yield (Fig. 4).
IR (KBr), cmꢂ1. 2933(nAr-H), 1596(nN¼N), 1626, 1559(nC¼C), 1524,
1341(nNO ), 1465, 1450, 1431(nCꢂH), 1114(nCꢂCl), 896(nCꢂOꢂC)750,
2
744(cCH
)
2
1HNMR(acetone). d ¼ 3.45(d, 2 H), 4.56(t, 2 H), 7.36(dt, 1 H),
7.57(dt, 1 H), 7.75(dd, 1 H), 7.87(d, 1 H), 7.98( m, 3 H), 8.33(dd, 1 H),
8.48(d, 1 H), 8.88(d, 1 H)
3-(3,4-dicyanophenylazo)-N-(2,3-epoxypropyl)-carbazole
(DCEPK)
The first step of 3-(3,4-dicyanophenylazo)-N-(2,3-epoxypropyl)-
carbazole synthesis (Fig. 5) was analogous to this of described above
dyes. Further, the freshly obtained diazo-compound was suspended in
acetone and treated with epichlorohydrine in presence of potassium
hydroxide, potassium carbonate and tetrabutylammonium bromide
(TBAB) at 40ꢁC for 8 h. The epoxy functionalized chromophore, collected
by filtration, was washed with acetone and water and finally dried.
IR (KBr), cmꢂ1. 3072(nAr-H), 2230(nCN), 1603(nN¼N), 1627(nC¼C),
1467, 1455, 1431(nCꢂH), 900(nCꢂOꢂC), 751, 736(cCH
)
2
1HNMR(acetone). d ¼ 4.05(d, 2 H), 7.34(dt, 1 H), 7.50(dt, 1 H),
7.71(dd, 1 H), 8.12(d, 1 H), 8.26( m, 3 H), 8.33(dd, 1 H), 8.44(d, 1 H),
8.84(d, 1 H)
Polymer Synthesis (ER þ CNEPK)
In the next stage, 5% wt. of the dye was added to epoxy resin, known
as ‘‘Epidian 6’’ (brand name of the product based on bisphenol A from

Photoinduced Gratings in Azo-Carbazoles
287=[1035]
FIGURE 5 Synthesis of 3-(3,4-dicyanophenylazo)-N-(2,3-epoxypropylo)-
carbazole (DCEPK).
Z.Ch. Organika-Sarzyna, Poland) and heated at 120ꢁC with a small
quantity of 2-methyl-imidazole (setting agent). This curing reaction
was carried one hour. FTIR and NMR spectroscopies results of this
material supported the structure shown in Figure 6. The resulting
material was not a completely set polymer, (forming long-range
network) but had a glass transition of Tg ¼ 95ꢁC and was soluble in
typical organic solvents.
FIGURE 6 Structure of the synthesized polymer (ER þ CNEPK).

288=[1036]
R. Czaplicki et al.
FIGURE 7 Results of thermal conditioning of ER þ CNEPK resin.
A sample of this compound was conditioned in elevated tempera-
tures (up to 240ꢁC, however it was still well below the compound
decomposition). Prolonged heating shifted always the Tg point towards
higher temperatures. Figure 7 shows an example. The sample was
kept in an furnace at 240ꢁC and continually undergo the DSC
calorimetry to monitor the glass transition shift. With prolonging
time of conditioning the Tg rose and completely disappeared after
c.a. 20 hours. These characteristics can be understood as the result
of complete thermosetting. It means that prolonged heating helps to
preserve physical form (recorded grating) of the sample.
Thin Film Preparation
Three types of films were prepared – from resin with already coupled
dye molecules (ER þ CNEPK), from pristine resin and dye containing
epoxy group (DCEPK) and from pristine resin and dye without epoxy
group (CNHEK – in this case the dye rest only physically dispersed).
Thin films were prepared as follows. Resin ERþ CNEPK was
dissolved in 1,1,2 trichloroethane and deposited by spin-coating. The
CNHEK and DCEPK dyes were dissolved in warm epidian resin in
desired proportions, leading to same molar content of the dye as in
case of ER þ CNEPK. The stoichiometric amount of the hardening

Photoinduced Gratings in Azo-Carbazoles
289=[1037]
agent – 4,4-diaminodiphenylene methane was added. The mixtures was
either squeezed between two microscope glass slides or smeared over
one. In this later case, free surface of obtained films was enough glassy.
At the end, all samples were kept in the furnace at 240ꢁC for 24 hours,
to accomplish their setting, according to findings presented in Figure 7.
We supposed that compound DCEPK (initially bearing epoxy group)
after this process was chemically bound to the polymer network while
CNHEK remained physically dispersed. Further we will use abbrevi-
ation ER þ CNHEK and ER þ DCEPK for films containing given dyes.
Spectral Characterization
UV-vis absorption spectra of the thin films are presented in Figure 8.
As expected all films show a peak around 425–440 nm characteristic
for azochromophores.
Absorption at the wavelength 632 nm was insignificant, therefore a
YAG laser at 532 nm was used as the writing beam, and a He-Ne laser
at 632.8 nm was chosen as the reading beam.
EXPERIMENTAL
The schematic experimental setup of the grating experiment is shown in
Figure 9 and it has been described in details by R. Czaplicki et al. [20].
FIGURE 8 UV-vis spectras of prepared thin films.

290=[1038]
R. Czaplicki et al.
FIGURE 9 Schematic setup of the grating experiment, M – mirrors, BS –
beam splitter, S – sample.
Diffracting gratings were recorded by two 30 ps pulses laser beams at
wavelength of 532 nm from Q-switched, mode-locked Nd:YAG laser
with pulse energy 1.2 mJ and repetition 10 Hz. Grating formation
was monitored by He-Ne (30 mW) laser operating at 632.8 nm by
measuring the power (by photodiode Centronic Series OSI 5) of the
first-order diffraction peak in the transmission mode. The signal from
the photodiode was observed on digital oscilloscope (Tektronix TDS
3054). The sample (S) was mounted on a fixed stage.
The surface structure of the grating of polymer film was investi-
gated by Atomic Force Microscopy (with microscope Pico SPM of
Molecular Imagining).
RESULT AND DISCUSSIONS
The s-s polarization configuration was set. We worked within the
Bragg light scattering regime and we observed only one order of
diffraction [21]. The chosen laser wavelength (532 nm) was absorbed
in the sample and induced trans-cis isomerization process of azo-
benzene derivatives [2].
Figure 10 shows the pulsed laser grating recording for ER þ
CNHEK, ER þ CNEPK and ER þ DCEPK compounds. The observed
dynamics of the diffraction signal, which is directly connected to the
inscription of grating, shows nonlinear dependence. We can notice that

Photoinduced Gratings in Azo-Carbazoles
291=[1039]
FIGURE 10 Example of grating build-up process in compounds ER þ
CNHEK, ER þ CNEPK and ER þ DCEPK using 30 ps pulses of 532 nm with
1 Hz repetition rate and monitored by He-Ne laser (large time scale).
inscription of grating is very fast in all cases and irreversible (stable
signal of first order of diffraction during 14 hours after switching off
the inscribing laser light). Samples prepared from ER þ CNHEK and
ER þ DCEPK had their surfaces limited by two squeezing glass plates
and we can suppose that in these cases there were no surface relief
grating formation. However, one of our sample (ER þ CNEPK) was
free to the deform and surface relief grating could be formed. Due to
applied s-s polarisation, we observed intensity grating [1].
During the recording in ER þ CNEPK thin film we observed fast
build-up of grating (immediately after switching on laser light). After
switching off the inscribing laser light we noticed very fast fall (c.a.
20%) of the signal intensity, then the signal stabilized at the attained
value. After switching on 532 nm reading beams once again we
observed continuation of recording of grating (Fig. 10) in the same
manner.
In the case of ER þ CNHEK compound, we observed fast build-up of
grating (but not so fast as in case of ER þ CNEPK sample) followed by
a large decrease (c.a. 60%) before signal stabilized. In addition the
recorded signal was very noisy. It could be attributed to thermally
induced processes concerning the epoxy matrix as well as relaxation
phenomena of the dye molecules, not bound chemically to the matrix.

292=[1040]
R. Czaplicki et al.
FIGURE 11 Kinetics of grating build-up process in compounds (a) ER þ
CNEPK and (b) ER þ DCEPK (short time scale). Signal from the sample con-
taining CNHEPK was too noisy to be representatively shown at this time
scale.
In case of the sample ER þ DCEPK the process of recording grating
was slower than in the case of ER þ CNHEK and ER þ CNEPK
compounds. After switching on inscribing laser light (532 nm) build-
up process of grating started after c.a. 25 s and rapidly progressed.
After switching off the laser, the recorded grating rest stable without
visible intensity decrease of the signal (Fig. 10).
Described above behaviour was observed more or less in a reproduc-
ible manner and did not depend on physical form of samples (squeezed
between two glass slides or one surface free).
Each pulse of laser contributed to grating growth. Examples of this
phenomenon are shown in Figure 11. Each laser pulse was followed by
relaxation. This relaxation was smaller in case of ER þ DCEPK and
more pronounced in case of ER þ CNEPK (Fig. 11(b)). Differences in
height of steps seen in Figure 11 were due to instability of power.
Figure 12 shows typical example of the three dimensional view of
the surface relief grating. The relief grating has a regular sinusoidal
shape up to 15 nm depth. The grating spacing (K), measured from
AFM, was about 0.76 mm and was consistent with the theoretically
ones calculated using Eq. (1):
K ¼ k=ð2 sin hÞ
ð1Þ
where k is the wavelength of the writing beam, 2h is the angle between
the two writing beams [19].

Photoinduced Gratings in Azo-Carbazoles
293=[1041]
FIGURE 12 (a), (c) AFM three-dimensional view of azo carbazole compound
(ER þ CNEPK) with inscribed SRG and (b), (d) surface profile of the grating.
From the Figure 12 (a) it can be seen also that the material exhib-
ited partial burning after long illumination with high energy (central
part of image).
CONCLUSIONS
In this work we used ps pulsed laser and we have successfully
inscribed and studied permanent surface relief gratings into functio-
nalized azo-carbazole compounds in the form of thin film between
two glass plates and film deposited on glass substrate. This behavior
is also confirmed by the relief observed and studied by AFM topogra-
phy. Direct AFM measurements confirmed expectations of the simple
formula (1). This study also proved that good reproducible results can
be obtained when the resin for thin films is pre-polymerized, already
contains chemically bound dye groups. Other tested morphologies lead

294=[1042]
R. Czaplicki et al.
to poorer properties. However obtained results show the damage of the
compound and did not explain the very good mechanism of inscription
of gratings, therefore further investigation is needed.
REFERENCES
[1] Yager, K. G. & Barrett, C. J. (2001). Cur. Op. Sol. Stat. Mat. Sci., 5, 487.
[2] Cojocariu, C. & Rochon, P. (2004). Pure Appl. Chem., 76, 1479.
[3] Todorov, T., Nikolova, L., & Tomova, N. (1984). Appl. Opt., 23, 4309.
[4] Barrett, C. J., Natansohn, A. L., & Rochon, P. L. (1996). J. Phys. Chem., 100, 8836.
[5] Sek, D., Schab-Balcerzak, E., Solyga, M., & Miniewicz, A. (2002). Synth. Met., 127,
89.
[6] Loucif-Saibi, R., Nakatani, K., Delaire, J. A., Dumont, M., Sekkat, Z. (1993). Chem.
Mater., 5, 229.
[7] Kumar, J., Li, L., Jiang, X. L., Kim, D., Lee, T. S., Tripathy, S. (1998). Appl. Phys.
Lett., 72, 2096.
[8] Lefin, P., Fiorini, C., & Nunzi, J-M. (1998). Pure Appl. Opt., 7, 71.
[9] Viswanathan, N. K., Balasubramanin, S., Li, L., Tripathy, S. K., Kumar, J. (1999).
Jpn. J. Appl. Phys., 38, 5928.
[10] Dumont, M. & Osman, A. E. (1999). Chem. Phys., 245, 437.
[11] Kim, D. Y., Tripathy, S. K., Li, L., & Kumar, J. (1995). Appl. Phys. Lett., 66, 1166.
[12] Kim, D. Y., Li, L., Jiang, X. L., Shivshankar, V., Kumar, J., Tripathy, S. (1995).
Macromolecules, 28, 8835.
[13] Viswanathan, N. K., Balasubramanin, S., Li, L., Kumar, J., Tripathy, S. K. (1998).
J. Phys. Chem. B, 102, 6064.
[14] Hagen, R. & Bieringer, T. (2001). Adv. Mater., 13, 1805.
[15] Niziol, J., Kajzar, F., Rau, I., Bednarz, M., Pielichowski, J., Pielichowski, K. (2006).
Mol. Cryst. Liq. Cryst., 447, 167.
ꢀ
[16] Chrza¸szcz, R. (1986). Barwniki karbazolowe, Zeszyt Naukowy PK nr 2, Krakow.
[17] USA Patent 4 313 872, 1982.
[18] European Patent 0 028 464, 1981.
[19] Taunaumang, H., Solyga, M., Tija, M. O., & Miniewicz, A. (2004). Thin Solid Films,
461, 316.
[20] Czaplicki, R., Dabos-Seignon, S., Kajzar, F., Bakasse, M., Nizioł, J., Bednarz, M., &
Sahraoui, B. (2006). Proceedings of IEEE Conference on 8-th International
Conference on Transparent Optical Networks ICTON 2006 (Nottingham, United
Kingdom, 2006), 283.
[21] Moharam, M. G., Gaylord, T. K., Magnusson, R. (1980). Opt. Commun., 32, 19.