Synthesis and high ranked NLT properties of new sulfonamide-substituted indium phthalocyanines

Article abstract of DOI:10.1016/j.ica.2010.07.062

The synthesis and characterization of three new indium phthalocyanines bearing eight N-alkyl- or N-arylsulfonamide groups is described. The new compounds are {2,3,9,10,16,17,23,24-octakis[4-(4-methoxyphenylaminosulfonyl] phenoxy]phthalocyaninato}indium(III) chloride (7), {2,3,9,10,16,17,23,24- octakis[4-diethylaminosulfonyl)phenoxy]phthalocyaninato}indium(III) chloride (8) and {2,3,9,10,16,17,23,24-octakis[4-didodecylaminosulfonyl)phenoxy] phthalocyaninato}indium(III) chloride (9), and were obtained in 23-49% yields. The precursors of phthalocyanines 7-9 are sulfonamide-substituted phthalonitriles that can be prepared by reacting 4,5-bis(4- chlorosulfonylphenoxy)phthalonitrile (3) with amines. The nonlinear transmission (NLT) of complexes 7-9 was determined at 532 nm using ns pulses. All three phthalocyanines behave as reverse saturable absorbers with increasing efficiency of optical limiting in the order 7 < 8 < 9. A comparative analysis of the NLT results is attempted in terms of the structural differences in 7-9.

Full text of DOI:10.1016/j.ica.2010.07.062

Inorganica Chimica Acta 363 (2010) 3945–3950
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Inorganica Chimica Acta
journal homepage: www.elsevier.com/locate/ica
Synthesis and high ranked NLT properties of new sulfonamide-substituted
indium phthalocyanines
b
Eliana F.A. Carvalho a, Mário J.F. Calvete a, José A.S. Cavaleiro a, Danilo Dini b, , Moreno Meneghetti ,
*
Augusto C. Tomé a,
**
a Department of Chemistry, QOPNA, University of Aveiro, 3810-193 Aveiro, Portugal
b Department of Chemical Sciences, University of Padua, via Marzolo, 1 – 35131 Padua, Italy
a r t i c l e i n f o
a b s t r a c t
Article history:
The synthesis and characterization of three new indium phthalocyanines bearing eight N-alkyl- or N-aryl-
sulfonamide groups is described. The new compounds are {2,3,9,10,16,17,23,24-octakis[4-(4-meth-
oxyphenylaminosulfonyl]phenoxy]phthalocyaninato}indium(III) chloride (7), {2,3,9,10,16,17,23,24-
octakis[4-diethylaminosulfonyl)phenoxy]phthalocyaninato}indium(III) chloride (8) and {2,3,9,10,16,17,
23,24-octakis[4-didodecylaminosulfonyl)phenoxy]phthalocyaninato}indium(III) chloride (9), and were
obtained in 23–49% yields. The precursors of phthalocyanines 7–9 are sulfonamide-substituted phthalo-
nitriles that can be prepared by reacting 4,5-bis(4-chlorosulfonylphenoxy)phthalonitrile (3) with amines.
The nonlinear transmission (NLT) of complexes 7–9 was determined at 532 nm using ns pulses. All three
phthalocyanines behave as reverse saturable absorbers with increasing efficiency of optical limiting in
the order 7 < 8 < 9. A comparative analysis of the NLT results is attempted in terms of the structural
differences in 7–9.
Received 26 January 2010
Received in revised form 14 July 2010
Accepted 20 July 2010
Available online 27 July 2010
Keywords:
Phthalocyanines
Sulfonamides
Nonlinear optics
Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction
occurs, the quality of the vision can still be maintained during
the process of optical limiting (OL).
Peripheral modulation of macrocyclic compounds is a chal-
lengeable and attractive pathway in the search for new materials.
In this respect, peripheral modification of phthalocyanines is
still a rewarding route to new materials suitable for diverse
applications.
Occurrence of RSA via the mechanism of excited-state absorp-
tion in Pcs has inspired several studies with the aim of establishing
systematic correlations between the Pc structure and the corre-
sponding value of excited-state absorption cross section at the
wavelength of analysis [14–18]. In doing so, Pcs and analogues
have found a prominent place as active materials for the important
application of optical limiting in the passive self-activated mode
[19–22].
The reason for the large employment of Pcs in OL is related with
the possibility of varying their electronic configurations in a con-
trolled fashion through peripheral substitution, variation of the
central atom, or modification of the axial ligand [23,24]. These
characteristics of Pcs and analogues derive from the possibility of
forming electronic excited states with a sufficiently long lifetime
to afford the successive efficient absorption of photons under short
pulsed irradiation (usually, in the ps or ns range) [18]. When ex-
cited-state absorption occurs from a triplet excited state the re-
lated OL effect can be further improved in Pcs through the
coordination of heavy central atoms, e.g. Pb [25] or In [26–38],
which accelerate intersystem crossing (ISC) by means of spin–orbit
coupling in the excited complex.
Due to their properties, phthalocyanines have a vast area of
applications [1], namely as dyes [2], catalysts [3,4], chemical sen-
sors [5–8] and as sensitizers in photodynamic therapy of several
diseases [9–13]. Other interesting applications are related with
their nonlinear transmission (NLT) properties [14–18], for instance
the limiting of laser radiation intensity. This is due to their large
nonlinearities, intrinsic fast response time, broadband spectral re-
sponse and processing straightforwardness. Optical limiters,
whose filtering action is instantaneously activated by the incoming
intense light, represent a valid solution for the protection of sen-
sors. In this case, the incoming intense light alters the absorptive
and refractive properties of the materials in such a way that the
resulting transmitted intensity is greatly reduced. Optical limiters
based on reverse saturable absorption (RSA) are transparent to
weak light and get opaque to intense light. Moreover, if only RSA
One disadvantage of unsubstituted phthalocyanines is their ex-
treme insolubility in most organic solvents, due mainly to the
highly planar and aromatic core. Peripheral functionalization of a
* Corresponding author.
** Corresponding author. Tel.: +351 234 370 712; fax: +351 234 370 084.
E-mail addresses: danilo.dini@unipd.it (D. Dini), actome@ua.pt (A.C. Tomé).
0020-1693/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.ica.2010.07.062

3946
E.F.A. Carvalho et al. / Inorganica Chimica Acta 363 (2010) 3945–3950
phthalocyanine with appropriate groups can afford new deriva-
tives with increased solubility in apolar or polar organic solvents
or even in aqueous media. Sulfonated phthalocyanines, both in
the sulfonato and sulfonamide forms, are already described in
the literature [39,40]. Some of these compounds show potential
application in photodynamic therapy [11–13] or in the production
of other materials, due to their interesting photoconductive prop-
erties [6].
NC
NC
O
O
SO2NR1R2
SO2NR1R2
4, R1 = H, R2 = C6H4-4-OCH3
5, R1 = R2 = CH2CH3
6, R1 = R2 = (CH2)11CH3
Electron-withdrawing substituents are known to produce an
enhancement on the NLT properties of phthalocyanines [35,36].
Taking this in consideration, we idealized the synthesis of three
phthalocyanine derivatives bearing eight sulfonamide groups.
The NLT properties of the resulting phthalocyanines were evalu-
ated in order to verify whether these substituents have any pro-
nounced effect and, therefore, if the new compounds could be
considered effective materials for NLT.
InCl3, quinoline, 160 ºC
23-49%
SO2NR1R2
SO2NR1R2
R1R2NO2S
R1R2NO2S
3'
2'
O
O
2
1
O
O
3
2. Experimental
N
4
N
N
N
In Cl
N
2.1. Materials and methods
N
N
Compounds 2–6 (Schemes 1 and 2) were synthesized as previ-
ously described [40]. All other chemicals were of analytical grade
and were used as received from suppliers. Anhydrous solvents
were obtained according to standard distilling procedures. 1H
NMR spectra were recorded at 300 MHz and 13C NMR spectra at
75 MHz using a Bruker DRX 300 spectrometer. Mass spectra were
recorded on a MALDI-TOF/TOF 4800 Applied Biosystems.
N
O
O
O
O
SO2NR1R2
SO2NR1R2
R1R2NO2S
R1R2NO2S
7, R1 = H, R2 = C6H4-4-OCH3
8, R1 = R2 = CH2CH3
2.2. Synthesis of phthalocyanines 7–9: general procedure
9, R1 = R2 = (CH2)11CH3
The appropriate phthalonitrile and InCl3ꢀ4H2O were dissolved in
quinoline (0.5 mL) and the mixture was heated at 160 °C for 10–
Scheme 2. Synthesis of indium chloride sulfonamide substituted phthalocyanines.
NC
NC
Cl
Cl
14 h under nitrogen atmosphere. After cooling, the reaction mix-
ture was poured onto methanol (100 ml). The precipitate was fil-
tered and washed with hot methanol. The solid was subjected to
column chromatography on silica gel using a mixture of CHCl3
and THF (0.5–3%) as the eluent. The main fraction was collected,
evaporated and reprecipitated with methanol.
+
HO
1
2
K2CO3, DMF
90 ºC
NC
NC
O
O
2.2.1. {2,3,9,10,16,17,23,24-octakis[4-(4-methoxyphenylamino-
sulfonyl)phenoxy]phthalocyaninato}indium(III) chloride (7)
For this synthesis were used phthalonitrile
4 (200 mg,
2.93 ꢁ 10ꢂ4 mol) and InCl3ꢀ4H2O (28.66 mg, 9.77 ꢁ 10ꢂ5 mol).
The reaction time was 14 h. Yield: 53 mg (25%). M.p. > 300 °C. 1H
NMR (300 MHz, CDCl3) (d/ppm): 4.14 (s, 24H, CH3), 7.31 (d, 16H,
J = 8.8 Hz, H-300), 7.59 (d, 16H, J = 8.7 Hz, H-20), 7.52 (d, 16H,
J = 8.8 Hz, H-200), 8.16 (d, 16H, J = 8.7 Hz, H-30), 9.46 (s, 8H, PcH).
13C NMR (75 MHz, CDCl3) (d/ppm): 54.8, 113.7, 115.7, 117.1,
123.7, 128.9, 129.6, 134.6, 150.3, 156.6, 158.1, 167.3. MS (MALDI-
HSO3Cl
5-10 ºC
NC
NC
O
O
SO2Cl
SO2Cl
TOF, PEG + NaI): m/z 2879.35 [M]+ꢀ, UV–Vis (DMSO) kmax (log
e):
3
367 (4.58), 625 (4.01), 694 (4.97) nm.
amine
acetonitrile, rt
2.2.2. {2,3,9,10,16,17,23,24-octakis[(4-diethylaminosulfonyl)-
phenoxy]phthalocyaninato}indium(III) chloride (8)
NC
NC
O
O
SO2NR1R2
SO2NR1R2
For this synthesis were used phthalonitrile
5 (180 mg,
3.07 ꢁ 10ꢂ4 mol) and InCl3ꢀ4H2O (28.66 mg, 9.77 ꢁ 10ꢂ5 mol). The
reaction time was 10 h. Yield: 44 mg (23%). M.p. > 300 °C. 1H
NMR (300 MHz, CDCl3) (d/ppm): 1.16 (t, 48H, J = 7.1 Hz, CH3),
3.27 (q, 32H, J = 7.1 Hz, CH2), 7.21 (d, 16H, J = 8.7 Hz, H-20), 7.85
(d, 16H, J = 8.7 Hz, H-30), 9.25 (s, 8H, Pc-H). 13C NMR (75 MHz,
CDCl3) (d/ppm): 14.2, 42.7, 117.0, 117.5, 129.3, 134.9, 135.4,
149.7, 152.8, 160.2. MS (MALDI-TOF, PEG + NaI): m/z 2479.9
4, R1 = H, R2 = C6H4-4-OCH3
5, R1 = R2 = CH2CH3
6, R1 = R2 = (CH2)11CH3
Scheme 1. Synthesis of phthalocyanine precursors [40].

E.F.A. Carvalho et al. / Inorganica Chimica Acta 363 (2010) 3945–3950
3947
[M]+ꢀ, 2502.9 [M+Na]+, UV–Vis (DMSO) kmax (log
(4.70), 697 (5.22) nm.
e): 365 (4.85), 628
phthalocyanine complexes 7–9, respectively (Scheme 2). All char-
acterization data are in agreement with the proposed structures
(see Section 2).
2.2.3. {2,3,9,10,16,17,23,24-octakis[4-didodecylaminosulfonyl)-
phenoxy]phthalocyaninato}indium(III) chloride (9)
3.2. UV–Vis spectra
For this synthesis were used phthalonitrile
6 (335 mg,
2.93 ꢁ 10ꢂ4 mol) and InCl3ꢀ4H2O (28.66 mg, 9.77 ꢁ 10ꢂ5 mol).
The reaction time was 10 h. Yield: 170 mg (49%). 1H NMR
(300 MHz, CDCl3) (d/ppm): 0.87 (br, 48H, CH3), 1.23 (br, 352H,
CH2), 3.11 (q, 32H, CH2), 7.18–7.20 (d, 16H, H-20), 7.82–7.88 (d,
16H, H-30), 9.22 (s, 8H, Pc-H). 13C NMR (75 MHz, CDCl3) (d/ppm):
13.6, 22.1, 23.2, 25.6, 27.1, 29.6, 30.1, 31.4, 48.0, 115.5, 116.7,
128.9, 134.0, 135.8, 147.9, 152.5, 160.2. UV–Vis (toluene) kmax
Absorption spectra of complexes 7–9 were determined in
different solvents (7 and 8 in DMSO, and 9 in toluene) in order to
minimize possible effects of aggregation during the successive
evaluation of their nonlinear transmission properties (vide infra).
All the electronic absorption spectra display the typical spectral
features of Pcs; the characteristic B- and Q-bands [42] appear
respectively at 356 and 690 nm (7), 362 and 689 nm (8), and 368
and 697 nm (9). The group of absorption bands in the range 600–
675 nm are originated from vibronic transitions that are associated
with the main Q-band transition [42].
(log e): 360 (4.96), 628 (4.53), 698 (5.30) nm.
2.3. Spectroscopic measurements
Optical absorption spectra of Pcs 7–9 in DMSO and toluene
were recorded with a Varian (Mod. Cary 5) UV–Vis-NIR spectro-
photometer. Fluorescence and excitation spectra were obtained
with a Perkin–Elmer (Mod. LS-50B) spectrometer.
It is evident from Fig. 1 that the nature of the SO2N-substituent
in Pcs 7–9 does not affect the position of the main absorption
peaks. This indicates that transition energies of 7–9 involve mainly
frontier orbitals that are localized on the phthalocyanine ring.
Therefore, the chosen N-substituents do not alter the extent of
electronic conjugation in 7–9 with respect to an unsubstituted
phthalocyanine. This holds also true in the case of 7, which bears
aryl substituents. These spectra indicate that the new phthalocya-
nines retain their electronic features irrespectively of the nature of
the sulfonamide substituents. This fact can be advantageously used
to obtain new phthalocyanine derivatives with different solubility
profiles just by changing the amine used in step of the sulfonamide
formation (Scheme 1).
2.4. Nonlinear transmission measurements
Nonlinear transmittance of Pcs 7–9 was measured at 532 nm
using 9 ns pulses of a doubled Nd:YAG laser (Quantel YG980E). A
pyroelectric detector (Scientech Mod. SPHD25) was used to mea-
sure the energy transmitted by the sample. Results were obtained
as an average of ten measurements at 1 Hz in the open-aperture
configuration. The intensities of the incident pulses were con-
trolled by a k/2 wave-plate and a polarizing cube beam-splitter.
Cuvettes with 2 mm optical path were used. The area of the illumi-
nated spot on the sample was approximately 0.02 cm2.
3.3. Emission and excitation spectra
The emission and excitation spectra of phthalocyanines 7, 8 and
9 are shown in Figs. 2–4 together with the respective normalized
absorption spectra.
2.5. Pump and probe experiments
The transient absorption of 9 was analyzed by means of the
pump and probe technique [41]. In these experiments the sample
was excited with the same pulses used for the measurements of
nonlinear transmission at the frequency of 10 Hz. The fluence of
excitation was 0.25 J cmꢂ2 per single pulse. Probing of excited-
state absorption of Pc 9 was accomplished by means of the white
light generated by a stabilized 150 W Xe lamp. The time-variation
of nonlinear optical absorption was recorded with a 1 GHz digital
oscilloscope (LeCroy LC564A). One hundred signals were averaged
in order to keep a high signal-to-noise ratio. A Jobin–Yvon Horiba
TRIAX 320 spectrometer, equipped with 600 and 300 groove
mmꢂ1 gratings, and a phototube Hamamatsu R2257 with rise time
2.6 ns, have been used to record the probe signal.
The emission spectra of 7, 8 and 9 display small Stokes shift
with respect to the Q-band position with the main emission band
located at about 700 nm [43]. Structures of vibronic emissions mir-
ror those located at longer wavelengths with respect to the main
emission peak. The lack of any dependence on the presence of oxy-
gen in solution and the observation of small Stokes shift indicate
that the measured emission is due to fluorescence and not phos-
phorescence [44]. The excitation spectra of Pcs 7–9 were deter-
mined recording the emission at 700 nm, i.e. the wavelength of
7
8
0.2
3. Results and discussion
9
3.1. Synthesis
Sulfonamide-substituted phthalonitriles 4–6, immediate pre-
cursors of phthalocyanines 7–9, were synthesized starting from
the commercially available 4,5-dichlorophthalonitrile (1) (Scheme
1) [40]. Reaction of 1 with phenol, in the presence of potassium
carbonate, afforded 4,5-diphenoxyphthalonitrile (2). Treatment of
4,5-diphenoxyphthalonitrile with chlorosulfonic acid produced
the 4,5-bis(4-chlorosulfonyphenoxy)phthalonitrile 3. Reaction of
3 with different amines, namely p-anisidine, diethylamine and did-
odecylamine, gave the desired sulfonamide derivatives 4, 5 and 6,
respectively.
0.1
0.0
400
500
600
λ / nm
700
800
Fig. 1. Absorption spectra of 7 (black trace) and 8 (red trace) in DMSO and 9 (green
trace) in toluene. For the evaluation of the molar extinction coefficients see
analytical data in the Section 2.
Simple cyclotetramerization of precursors 4–6 in quinoline at
160 °C, in the presence of InCl3, gave the desired indium chloride

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E.F.A. Carvalho et al. / Inorganica Chimica Acta 363 (2010) 3945–3950
their maximum emission (Figs. 2–4). As expected, due to the rigid-
ity of the macrocycle, a very small Stokes shift is observed [44].
emission spectrum
absorption spectrum
excitation spectrum
1.0
0.5
0.0
3.4. Nonlinear transmission
Fig. 3 shows the variations of transmittance of DMSO solutions
of 7 and 8, and of a toluene solution of 9 with the incident fluence
at 532 nm.
The decrease of optical transmission with increasing incident
fluence indicates that 7, 8 and 9 are reverse saturable absorbers
[14–19]. Pc 9 displays the better limiting properties reaching a
minimum of 13% of the linear transmission at about 1 J cmꢂ2 of
incident fluence (Fig. 5). The limiting threshold, Flim, i.e. the fluence
at which the transmittance is half the value of linear transmittance
[45], is 0.39 and 0.13 J cmꢂ2 for 8 and 9, respectively (Fig. 5). In the
case of 9, Flim is comparable to that of other indium phthalo- and
naphthalocyanines with axial halogens [26–38]. In the case of
complex 7, the limiting threshold could not be exactly determined
within the experimental range of incident fluences. From the pro-
file of nonlinear transmission it is evaluated Flim (7) >1 J cmꢂ2. The
observed larger limiting thresholds of 7 and 8, with respect to 9,
indicate that the presence of long-chain substituents in 9 is bene-
ficial for the improvement of the nonlinear transmission properties
within this series of sulfonamide substituted phthalocyanines. This
suggests that the nonlinear optical properties of sulfonated com-
pounds 7–9 are mainly dependent on their capability to prevent
intermolecular aggregation [46–50]. The occurrence of RSA by
Pcs 7–9 has three main implications about the nature and the char-
acteristics of their involved excited states: (a) the excited state has
a larger absorption cross-section with respect to the ground state
S0 at the wavelength of excitation; (b) their lifetimes sexc fulfil
300
400
500
600
700
800
/ nm
λ
Fig. 2. Normalized absorption (black trace), emission (red trace) and excitation
spectra for in DMSO. For the determination of the emission spectrum the
excitation wavelength was 622.5 nm. Emission wavelength was 698 nm for the
analysis of excitation spectrum.
7
emission spectrum
absorption spectrum
excitation spectrum
1.0
0.5
0.0
the condition sexc P sp, where sp represents the laser pulse width,
and (c) the formation time of their excited states is much shorter
than the duration of the laser pulse. Since ns pulses are used, the
above considerations confirm that, similar to other indium phtha-
locyanine- and naphthalocyanine-based systems [26–38]. RSA of
Pcs 7–9 is produced by one-photon absorption from the optically
pumped excited triplet state T1 in a process of sequential multi-
photon absorption [51–55].
300
400
500
600
700
800
λ / nm
Among Pcs 7–9 only 9 displays the flattening of the nonlinear
transmission curve when Fin > 0.8 J cmꢂ2 (Fig. 5). This feature al-
lows to calculate a relevant parameter [18] for the evaluation of
the optical power limiting properties of 9. In fact, in correspon-
Fig. 3. Normalized absorption (black trace), emission (red trace) and excitation
spectra for in DMSO. For the determination of the emission spectrum the
excitation wavelength was 622.5 nm. Emission wavelength was 699 nm for the
analysis of excitation spectrum.
8
1.0
1.0
emission spectrum
absorption spectrum
excitation spectrum
0
0.5
7
0.5
0.0
/T
8
9
0.0
0.01
0.1
1
300
400
500
600
700
800
Fin / J cm-2
λ / nm
Fig. 4. Normalized absorption (black trace), emission (red trace) and excitation
spectra for 9 in toluene. For the determination of the emission spectrum the
excitation wavelength was 622.5 nm. Emission wavelength was 715 nm for the
analysis of excitation spectrum.
Fig. 5. Variation of the normalized transmission of Pcs 7–9 at 532 nm (cuvette
thickness: 2 mm). Sample was excited with 9 ns pulses. Linear transmittance was
0.75 for all three solutions. Solutions concentrations were: 2.7 ꢁ 10ꢂ4 M for 7 in
DMSO; 3.6 ꢁ 10ꢂ4 M for 8 in DMSO; 2.0 ꢁ 10ꢂ4 M for 9 in toluene.

E.F.A. Carvalho et al. / Inorganica Chimica Acta 363 (2010) 3945–3950
3949
absorbers of ns pulses with limiting thresholds of >1, 0.39 and
0.13 J cmꢂ2 for 7, 8 and 9, respectively. Such a trend indicates that
nonlinear optical properties of complexes 7–9 are mainly con-
trolled by their tendency of forming molecular aggregates during
the process of nonlinear absorption. In fact, the phthalocyanine 7,
due to the presence of acidic SO2NHAr protons has a higher aggre-
gation propensity than the analogous SO2NR2 substituted phthalo-
cyanines 8 and 9. Comparing phthalocyanines 8 and 9, it is
confirmed that the larger the substituents the better the optical
limiting performance. Only complex 9 display a complete sig-
moid-shaped profile of nonlinear transmission at 532 nm. This fea-
ture allowed the determination of the absorption cross-section of
the excited state of 9 that produced the effect of reverse saturable
absorption at that wavelength. The excited-state absorption
cross-section of 9 was calculated as 9.6 ꢁ 10ꢂ17 cm2, which corre-
sponds to a merit factor of 8. The transient absorption experiment
showed that the excited state responsible for the effect of reverse
saturable absorption of 9 has a triplet manifold with lifetime of
1.25 ꢁ 10ꢂ6 s.
0.002
0.001
0.000
OD.
1.0x10-6 2.0x10-6 3.0x10-6 4.0x10-6 5.0x10-6
0.0
t
/ s
Fig. 6. Temporal variation of the differential absorbance,
DO.D., at 485 nm for 9 in
toluene upon excitation at 532 nm with ns pulses (C1: 2 ꢁ 10ꢂ4 M; Fin: 0.25 J cmꢂ2).
Profile is obtained as an average of 150 consecutive traces with t = 0 s correspond-
ing to the time at which laser pulse starts. Mono-exponential fit (grey line) is also
shown when time constant is 1.25 ls.
Acknowledgments
Thanks are due to Fundação para a Ciência e a Tecnologia (FCT),
(COMPETE – Programa Operacional Factores de Competitividade),
QREN/FEDER for funding the Organic Chemistry Research Unit
and the Projects PPTDC/DG/QUI/82011/2006 and PTDC/QUI/
74150/2006. M.J.F. Calvete also thanks FCT for his post-doc grant
(SFRH/BPD/26775/2006).
dence of such a minimum of transmittance, it can be assumed that
Pc 9 is fully promoted into the excited triplet T1 state (Fig. 4) with
an effective one-photon absorption cross-section r0 given by Eq.
(1):
r0k ¼ ln½1=Tminkꢃ=Nl
ð1Þ
In Eq. (1), N is the concentration of 9 in molecules cmꢂ3, and l
indicates the solution thickness in cm. Tmin represents the mini-
mum transmittance that is achieved by the nonlinear absorber. It
corresponds to the transmittance value at the end of the sigmoid
curve of nonlinear transmission (Fig. 5). From the experimental
data of Fig. 5 one finds r0 = 9.6 ꢁ 10ꢂ17 cm2 at 532 nm, being
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