Nonlinear optical behavior of n-tuple decker phthalocyanines at the nanosecond regime: investigation of change in mechanisms

Abstract

The coordination system of rare-earth n-tuple decker phthalocyanines would be better suited with appropriate metal ions with the correct coordination number and the solvent system of the reaction, amongst other reasons, for the formation of n-tuple decker phthalocyanines. As a result, these complexes are very rare. In this manuscript, we present new n-tuple decker phthalocyanines in the form of double- (complex 2), quadruple- (complex 3a) and sextuple-decker phthalocyanines (complex 3b), all of which contain neodymium and cadmium metal ions. The primary focus is the investigation of the nonlinear optical (NLO) mechanisms responsible for the observed reverse saturable absorption. While the extension of the π-electron system has been found to enhance the nonlinear optical behavior of complexes 3a and 3b, a change in the NLO mechanisms has been observed, with complex 2 lacking the triplet state population, as revealed by a laser flash photolysis technique. It has also been established that the excited state absorption cross sections follow a clear order of magnitude for the complexes under investigation: σ₂₃ (for 3b) > σ₂₃ (for 3a) > σ_1m (for 2). This trend evidences the effects of the extension of the π-electron system.

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1. Introduction

Macroheterocyclic tetraazoporphyrin ring complexes can be modified in such a way that the ligands interact with each other via coordination to transition metals and/or lanthanide ions, as is the case with multi-decker phthalocyaninato molecules. Such complexes are also referred to as advanced materials¹ and find applications in many fields as single-molecule magnets,^2–10 sensors,^11–13 conductive materials,^14–17 optical limiters,^18–28 ambipolar organic field-effect transistors,^29,30 supramolecular spin valves³¹ and self-assembled nanostructures.^32,33 Lanthanide double-decker phthalocyanine (LnPc₂) complexes, in particular, have been the center of interest in research for a long time.^26,34 However, new developments have paved the way for the discovery of even more complex materials in the form of triple-decker,³⁵ quadruple-decker,³⁶ quintuple-decker³⁷ and a sextuple-decker phthalocyanines.³⁸ The sextuple-decker, to the best of our knowledge, has been prepared once. Therefore, it can be concluded that not much has been done in terms of developing such materials. The scarcity of such structures has been attributed to the selection of an appropriate metal ion with the necessary coordination number, geometry, charge, and hard/soft-acid/base characteristics to suit the coordination algorithm of tetrapyrroles.³⁷ For simplicity, all sandwich-type phthalocyaninato complexes, presented in this manuscript, are termed n-tuple decker phthalocyaninato molecules. Quandruple-decker phthalocyaninato molecules have not been investigated for optical limiting, while their sextuple-decker counterparts have been shown to possess good optical limiting properties.³⁷ This manuscript narrows its focus on investigating the mechanisms governing the reverse saturable absorption as well as the effects of π-conjugation on the optical limiting properties of the new n-tuple decker phthalocyanines in solution and thin films. These molecules are based on neodymium and cadmium metal ions. The bulk tert-butyl phenoxy substituents enhance the solubility in nonpolar solvents, hence the choice of dichloromethane as the solvent medium. All the molecules presented in this manuscript are new, since the tert-butyl phenoxy substituted n-tuple decker phthalocyanines have not been reported elsewhere. The molecules are embedded in polymers to form thin films for nonlinear optical (NLO) limiting studies. Poly(bisphenol A carbonate) was selected as the polymer for thin films because of its superior solubility in nonpolar solvents, thereby, limiting the challenges of the manufacturing of thin films.

2. Experimental

2.1 Materials

Deuterated chloroform (CDCl₃), 1-pentanol, 1,2,4-trichlorobenzene (TCB), and neodymium(III) acetate hydrate were purchased from Sigma-Aldrich. Dimethyl formamide (DMF), chloroform and dichloromethane (DCM) were purchased from MINEMA. Cadmium acetate dihydrate, 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) and poly(bisphenol A) carbonate were purchased from Fluka. Water was obtained from Milli-Q Water Systems (Millipore Corp., Bedford, MA, USA). The synthesis of bis-{2(3),9(10),16(17),23(24)-tetra(4-tert-buylphenoxy) phthalocyaninato} neodymium(III) (2) was reported in our previous publication.³⁹

2.2 Synthesis of quadruple-decker phthalocyanine (3a) (Scheme 1)

Complex 2 (40 mg; 16.99 μmol) was placed in a clean round bottom flask (50 mL) that contained cadmium acetate hydrate (4.36 mg; 16.34 μmol). TCB (6 mL) was added to the reaction mixture under a blanket of argon, followed by refluxing for 24 h. Next, TCB was evaporated and the crude product was cooled to room temperature. The mixture of ethanol and water (v/v 1 : 1) was used for further purification under centrifugation at 3000 rpm before the oven-dried blue product was loaded onto a chromatography column packed with silica. A CHCl₃ and n-hexane solvent mixture was first used to remove the unreacted complex 2, after which a CHCl₃ and methanol mixture (v/v 14 : 1) was employed to elute complex 3a as the second band, which was dried in open air. Yield: (67%). IR: [KBr, v, cm⁻¹] 748, 771, 886, 940, 1013 (Pc skeleton), 1040, 1074, 1107, 1173, 1228, 1254 (C–O–C), 1326, 1363, 1392, 1471, 1506, 1600, 1737 (benzene, pyrrole, isoindole and aza), 2866, 2922, 2956 (C–H). UV-Vis (DCM): λ_max nm (log ε), 336 (4.79), 640 (4.85). Anal. calc. for C₂₈₈H₂₅₆N₃₂O₁₆Nd₂Cd: C, 71.73; H, 5.35; N, 9.29%. Found: C, 71.66; H, 5.21; N, 9.32%. ¹H NMR (CDCl₃) for 3a δ, ppm 7.40–7.30 (18H, m, H-Ar), 7.14–6.96 (34H, m, H-Ar), 6.78–6.74 (20H, m, H-Ar), 6.47–6.34 (24H, m, H-Ar), 5.98 (16H, m, H-Ar), 1.49 (22H, m, H-tBu), 1.30–1.27 (34H, m, H-tBu), 1.08–1.05 (17H, H-tBu), 1.01–0.98 (33H, m, H-tBu), 0.86–0.77 (38H, m, H-tBu). MS (MALDI-TOF): (m/z): calc. 4822 amu. Found: 4824 amu [M + 2H]⁺.

Scheme 1 Synthetic pathway to obtain complexes 3a and 3b; i = TCB and cadmium acetate dihydrate at reflux temperature, 24 h.

2.3 Synthesis of sextuple-decker phthalocyanine (3b) (Scheme 1)

Complex 3b was obtained as a by-product from the same reaction as that of complex 3a, except that a CHCl₃ and methanol mixture (v/v 9 : 1) was used for the elution of the third blue band containing the required product. Yield: (22%). IR: [KBr, v, cm⁻¹] 722, 747, 824, 886, 939, 1013 (Pc skeleton), 1041, 1074, 1106, 1173, 1229, 1254, 1289 (C–O–C), 1328, 1363, 1393, 1465, 1507, 1601, 1730 (benzene, pyrrole, isoindole and aza), 2852, 2922, 2954 (C–H). UV-Vis (DCM): λ_max nm (log ε), 338 (4.98), 636 (5.08). Anal. calc. for C₄₃₂H₃₈₄N₄₈O₂₄Nd₃Cd₂: C, 71.18; H, 5.94; N, 9.22%. Found: C, 71.09; H, 6.11; N, 9.26%. ¹H NMR (CDCl₃) for 3b: δ, ppm 7.79–7.71 (26H, m, H-Ar), 7.47–7.24 (42H, m, H-Ar), 7.13–6.93 (51H, m, H-Ar), 6.43–5.63 (49H, m, H-Ar), 1.53–1.35 (72H, m, H-tBu), 1.29 (6H, s, H-tBu), 1.26 (8H, s, H-tBu), 1.21 (7H, s, H-tBu), 1.07–0.94 (63H, m, H-tBu), 0.83–0.76 (60H, m, H-tBu). MS (MALDI-TOF): (m/z): calc. 7290 amu. Found: 7291 amu [M + H]⁺.

2.4 Preparation of thin films

Using 3b and 3c, thin films (3b-TF and 3c-TF) were obtained by following the procedure for the synthesis of the corresponding thin film formed from complex 2 (ref. 39) at the same concentrations (3.0 × 10⁻⁴ M). The thickness of the film was measured to be ∼6 μm using the knife edge attachment of the Bruker D8 Discover X-ray diffraction (XRD) diffractometer.

2.5 Equipment

Infrared spectra were recorded on a Perkin Elmer 100 ART FT-IR spectrometer. Ultraviolet-visible (UV-Vis) spectra were recorded on a Shimadzu UV-Vis 2550 spectrophotometer. Emission spectra were recorded on a Varian Cary Eclipse fluorescence spectrophotometer. Luminescence lifetime measurements were performed using time correlated single photon counting setup (TCSPC) (PicoQuant FluoTime 300). The excitation source was a diode laser (LDH-P-C-485, 480 nm, 10 MHz repetition rate, 44 ps pulse width, Picoquant GmbH). The details were provided previously.^40,41

¹H NMR studies were performed using a Bruker AMX 600 NMR spectrometer. Elemental analysis experiments were carried out on a Vario-Elementar Microcube ELIII. Mass spectral data were collected using a Bruker AutoFLEX III Smart beam TOF/TOF Mass spectrometer. The spectra were acquired using α-cyano-4-hydroxycinnamic acid as the MALDI matrix and a 355 nm Nd:YAG laser as the ion source.

Electron spin resonance (EPR) spectra were recorded on a Bruker EPR 300E X-band (10 GHz) spectrometer equipped with a TM probe with ESR tubes. The spin Hamiltonian parameters were obtained by the simulation of the spectra. The static field (2500 G), center field (3500 G), modulation amplitude (100 G), sweep time (20.97 ms), time constant (10.24 ms), conversion time (5.12 ms), resolution (2048 pts), power (2.00 mW) and modulation frequency (100 kHz) were used as the experimental parameters at 298 K with 10 scans. Scanning electron microscope (SEM) images of thin films (2-TF, 3a-TF, and 3b-TF) were obtained using a JOEL JSM 840 scanning electron microscope operated at 20 kV.

X-ray powder diffraction patterns were recorded on a Bruker D8 Discover equipped with a proportional counter, using Cu-K_α radiation (λ = 1.5405 Å, nickel filter). The details were reported previously.^40,41

All Z-scan experiments described in this study were performed using a frequency-doubled Nd:YAG laser (Quanta-Ray, 1.5 J/10 ns fwhm pulse duration) as the excitation source. A standard quartz cuvette with a lid (0.2 cm), purchased from Purshee, was used for the experiments performed in solution. Details were provided previously.^18,42

3. Results and discussion

3.1 Synthesis of n-tuple decker phthalocyaninato complexes and their respective thin films

The conversion of LnPc₂ complexes into stable quadruple-decker phthalocyanines is achieved by employing cadmium salts in the presence of TCB at reflux temperature.³⁶ Similar methods have been employed to design sextuple-decker phthalocyanines³⁸ using unmetallated phthalocyanine (H₂Pc). Following these methods and placing complex 2 and cadmium acetate dehydrate in the TCB bath at reflux temperature, complexes 3a and 3b were formed. This is the first time when quadruple- and sextuple-decker phthalocyanines were synthesized in the same reaction vessel. It is also the first time when a sextuple-decker phthalocyanine was obtained by sandwiching two Cd(II) ions between three LnPc₂ complexes. The contributing factors to this can be thought of as the mole ratio of complex 2 to the cadmium ion and time. However, the yield of 67% for complex 3a is desirable, considering that complex 3b is simultaneously formed. Separation of such highly stable complexes is, therefore, challenging.

Complexes 2, 3a and 3b dissolve in highly volatile nonpolar solvents such tetrahydrofuran, chloroform and dichloromethane, as is the case with poly(bisphenol A) carbonate. For the preparation of thin films, chloroform was chosen as the best solvent with a controllable rate of evaporation.

3.2 Structural characterization of LnPc₂ complexes and their respective thin films

3.2.1 Vibrational spectroscopy. Complex 2 shows the Pc˙⁻ IR marker at 1313 cm⁻¹. A similar observation has been reported where an LnPc₂ complex showed a Pc˙⁻ IR marker, while the quadruple-decker Pc did not have this marker.⁴³ This difference in the vibrational frequencies of complexes 3a and 3b with respect to that of 2 is very important and characterizes a complete structural change and the nature of complexes under investigation. The core of the Pc skeleton is characterized by vibrational bands located between ∼700 and 1050 cm⁻¹. These bands were observed in the range of 722–1041 cm⁻¹ for complexes 2, 3a and 3b. The C–O–C vibrations, characterizing the link between the benzene ring of the Pc core and the tert-butyl benzene of the substituent, were observed between 1074 and 1228 cm⁻¹. The other vibrational characteristics of the three complexes are the C=C, C=N– and C–N moieties of the benzene ring, azo and the isoindole groups. These vibrations were observed between 1326 and 1601 cm⁻¹ for complexes 2, 3a and 3b. The tert-butyl and C–H vibrations of the tert-butyl benzene or the benzene rings of these complexes appeared at ∼2852 to 2954 cm⁻¹. It was observed that complex 2 absorbed moisture (Fig. 1), which was characterized by the OH– stretch at 3481 cm⁻¹.

Fig. 1 FTIR spectra of complexes 2,³⁹ 3a and 3b.

3.2.2 Proton nuclear magnetic resonance spectroscopy. ¹H NMR signals for complexes 2, 3a and 3b were obtained in CDCl₃ at room temperature. Complex 2 showed two broad aromatic proton (H-Ar) bands in the ranges of 7.57–7.00 and 6.01–5.68 ppm, complemented by the tert-butyl proton signals (H-tBu) found at 1.59–0.65 ppm. Complex 3a showed broad signals between 7.40–5.98 ppm, indicative of aromatic protons. Aliphatic protons were characterized by signals between 1.49–0.77 ppm, as would be expected for protons of the tert-butyl groups. For complex 3b, aromatic protons were found in the range of 7.79–5.63 ppm, while tert-butyl protons were found in the range of 1.53–0.76 ppm. In general, ¹H NMR signals of the three complexes represented the correct number of expected protons corresponding to the predicted structures. Fig. S1† shows the ¹H NMR signatures for complexes 2 and 3a as examples.

3.2.3 Mass spectrometry. Complex 2 was the primary material from which complexes 3a and 3b were formed. Therefore, the comparison of the masses of these complexes is very important and helps to elucidate the structural differences. As a primary material, complex 2 is less bulky than complexes 3a and 3b, with 3b being the bulkiest. The mass of complex 2 has been reported before.³⁹ For complexes 3a and 3b, 4822 and 7290 amu were the expected masses, respectively. These experimentally determined masses correspond well with the structures of the complexes 3a and 3b whose theoretical masses are 4824 and 7291 amu, respectively (Fig. S2†).

3.2.4 Absorption spectroscopy. Neutral LnPc₂ complexes are characterized by a complicated system of ground state electronic transitions which are forbidden in the idealized D_4h or D_4d symmetry,^43–46 resulting in various absorption bands. The B-band (at 326 and 365 nm) for complex 2 in DCM (Fig. 2) was split, while the blue valence (BV)^47–50 and the Q-bands (485 and 690 nm, respectively) were also observed. The absorption spectrum of complex 2 has been discussed in detail before.³⁹ For complexes 3a and 3b, the Q-band appeared to be more blue-shifted (Fig. 2) to about 640 and 636 nm, respectively, with the complete disappearance of the BV band. The absorption spectra of complexes 3a and 3b are also similar to those of other quadruple- and sextuple-decker phthalocyanines. In general, the absorption spectrum of complex 2 is similar to the spectra of other LnPc₂ complexes^19,25,51,52 and resembles the energy diagram that manipulates the electronic transitions in accordance with the Valence-Effective Hamiltonian (VEH) calculation,⁵³ where the Q-band is attributed to the electronic transitions from the π(a_2u) to the orbitals.

Fig. 2 The normalized UV-Vis absorption spectra for complexes 2,³⁹ 3a and 3b, with 2 showing a blue valence band when the Q-bands for 3a and 3b are blue shifted with no blue valence band observed.

The B-band results from the transitions between π(b_2u) and .^51,52 The absorption spectra of complexes 3a and 3b are broader than those of blue forms³⁹ but comparable to those of similar analogues.³⁸

3.2.5 Electron spin resonance spectroscopy. The LnPc₂ complexes are characterized by π-radical related electronic transitions that imply imbalance in the number of electrons in two coordinating Pc entities, given the 3+ oxidation state of lanthanide ions. In this case, one Pc ring would have two electrons and the other would have one, having the formulation (Pc(−2)Nd^IIIPc(−1)). Electron spin resonance (ESR) is, therefore, an efficient technique to manipulate data that depicts the behavior of the moving unpaired electrons in a molecule. For complex 2, an ESR band was observed at ∼3487 to 3496 G with two hyperfines at ∼3482 and 3521 G at g = 2.000 in solid state (Fig. S3†). This observation is in agreement with the behavior of LnPc₂ complexes which are regarded as single-hole complexes, in which an unpaired electron is present in one of the macrocyclic ligands,⁵⁴ formulated as Pc(−2)Ln^IIIPc(−1). The ESR bandwidth of complex 2 at 298 K is ∼8.01 G, which is broader than the bands of the other neodymium based phthalocyanines.⁵⁵ The ESR spectroscopy data for complex 2 was reported earlier³⁹ and is provided in Fig. S3.†

When the emergence of the ESR band is governed by the movement of an unpaired electron originating directly from the π-radicals, it would be expected that a phthalocyanine molecule, obtained via modification of a neutral LnPc₂ complex, should not exhibit an ESR signal. However, for complexes 3a and 3b, ESR bands were observed. These ESR signals were characterized by intensities much higher than that of complex 2. Even though complexes 3a and 3b lack π-radicals, the presence of paramagnetic neodymium ions can encourage the movement of electrons. Since there are more paramagnetic neodymium ions in complexes 3a and 3b than in complex 2 (Fig. S3†), the presence of ESR signals of higher intensity is not surprising.

3.2.6 X-ray diffractometry. The X-ray diffractograms of complex 2 and its corresponding thin film (TF-2) have been reported before³⁹ and are shown in Fig. 3 for comparison. Similar patterns were observed for complexes 3a and 3b and their corresponding thin films (3a-TF and 3b-TF).

Fig. 3 X-ray diffractograms of complexes 2,³⁹ 3a and 3b in powder form as well as their respective thin films 2-TF,³⁹ 3a-TF and 3b-TF.

The only difference between X-ray diffractograms of the films is an additional sharp XRD peak observed at 38° only for 2-TF. The overall change in the XRD pattern signifies the influence of poly(bisphenol A) carbonate on the complex. The sizes of complexes 2, 3a and 3b were determined using the Debye–Scherrer equation⁵⁶ to fit the XRD diffractograms and found to be 0.81, 1.56 and 1.87 nm, respectively.

3.3 Nonlinear optical signatures

The nonlinear optical behavior of a material can be monitored by subjecting the material to highly illuminating laser beams. The behavior is then analyzed as the material moves along the z-axis through the focal point of converging irradiation using the Z-scan technique. The intensity modulation affects the material as it approaches the focal point and, therefore, attenuates the transmittance (herein referred to as the normalized transmittance or T_Norm). The Z-scan is only affected by the nonlinear absorption²² as all the transmitted light is detected. There are two techniques to detect the transmitted light, namely, the closed aperture and the open aperture Z-scans. This manuscript strictly focuses on presenting the data obtained from the open aperture Z-scan experiments performed in solution and solid state.

The nonlinear optical parameters for complex 2 and its corresponding thin film (TF-2) have been discussed in detail before.³⁹ For precise comparison of the nonlinear behavior, all the complexes were subjected to the same experimental conditions in the nanosecond regime. The establishment of the reverse saturable absorption (RSA), characterized by the reduction of T_Norm at focus (z = 0), was achieved upon scanning along the z-axis of the Z-scan under resonant conditions. This behavior is illustrated for complexes 2, 3a and 3b in Fig. 4A and B.

Fig. 4 Open aperture Z-scan signatures of (A) 2,³⁹ 3a and 3b in DCM at 3.0 × 10⁻⁴ M and (B) 3a-TF and 3b-TF. The simulations were performed employing eqn (6)–(12).

As can be seen in Fig. 4, the signature only attenuates about 48% of the input fluence for complex 2 as already discussed previously.³⁹ For simplicity and better understanding of the behavior of this complex, we employed an excited state energy diagram similar to that obtained for LuPc₂ by Orti et al., acquired by performing Valence Effective Hamiltonian (VEH) calculations,^44,53 Fig. 5A.

Fig. 5 (A) Diagram showing singlet excited states of LnPc₂ in comparison to that obtained by Orti et al. using Valence Effective Hamiltonian calculations;^44,53 (B) three-energy-level diagram used to model the excited state cross-section spectrum within the rate equation model of eqn (1)–(3), according to ref. 56 and 57; and (C) general five-energy level diagram employed for the simulation of the NLO mechanisms of complexes 3a, 3b, 3a-TF and 3b-TF using eqn (6)–(12).

This is the strategy, illustrating that the excited molecules at a_2u level undergo the electronic transition when the energy is being pumped into level a_2u. This electronic transition is depicted by the three-energy level diagram (Fig. 5B) describing similar electronic transitions where the ground singlet state, the first singlet excited state and the higher energy singlet state are denoted by S₀, S₁ and S_m, respectively. With S₀, S₁ and S_m corresponding to e_g, a_2u and , respectively, the electronic transitions e_g → a_2u and may describe the transition rates w₀₁ and w_1m, respectively. The excited molecules may relax via the relaxation pathways S_m → S₁ (with decay time τ_m1) and S₁ → S₀ (with the first excited state lifetime τ₁₀). When tuning the energy pump at e_g → a_2u (by transition rate w₀₁ which is around the BV band (i.e., at 532 nm), the molecules at a_2u would get excited to (S_m level) by the transition rate w_1m. The relaxation then takes through and a_2u → e_g (S₁ → S₀) upon losing the photon energy (hv) via τ_m1 and τ₁₀. At both excitation regions, shown in Fig. 5B, the fractions of molecules at each level can be described using the following laser rate equations^57,58 at E = 55 ± 0.1 μJ:

In these eqns, n_i is the population fraction of the state (i = 0, 1 and m) with n₀ + n₁ + n_m = 1; w₀₁ = σ₀₁I(t)/hv and w_1m = σ_1mI(t)/hv, where σ₀₁ and σ_1m, are the ground and the singlet excited state absorption cross-sections, respectively, corresponding to the ground state (w₀₁) and the excited state (w_1m) transitions; τ_m1 and τ₁₀ are the relaxation lifetimes from the highest excited singlet state (S_m) to the first excited singlet state (S₁) and from the singlet excited state (S₁) to the ground state (S₀), respectively. Eqn (1)–(3) can be numerically solved by considering a GAUSSIAN temporal profile for the laser pulse, with the temporal dependence of the absorption coefficient described by eqn (4):

α(t) = N{n₀(t)σ₀₁ + n₁(t)σ_1m} (4)

In eqn (4), N is the sample concentration in molecules per cm³. For all complexes, N was kept constant at 1.869 × 10¹⁷ molecules per cm³. This concentration is lower than the one reported for the YbPc₂ complex.⁵⁷ To calculate the transmittance, the propagation equation, dI(t)/dz(t) = −α(t)I(t), can be integrated over the sample thickness L and the full pulse width (t from −∞ to +∞). The ground state cross section is described by eqn (5):⁵⁸

with the linear absorption coefficient, α₀₁, obtained from resonant conditions at 532 nm of the absorption spectrum of the complex under investigation. This model is applicable to LnPc₂ complexes that exhibit no triplet state population.

However, for the sandwich-type phthalocyanes²⁵ whose triplet population is not affected by ligand–ligand interactions, the singlet excited state may be infinitesimally weaker and the relaxation decay time is far smaller than the laser pulse rate. In this case, a general five-level model (Fig. 5C) can be applied.⁵⁹ This model ignores the vibrational levels of the electronic states such that the laser pulse width is assumed to be longer than any relaxation decay times associated with the levels. To further simplify the model, it is assumed that relaxation from S_m and T₃ is very fast,⁵⁹ hence the neglection of these two levels. Excitation at 532 nm leads to the S₁ population. As highlighted above, even if the electrons undergo S₁ → S_m, S_m lifetime is very fast. Therefore, the S₁ → T₂ transition (τ_isc) occurs via intersystem crossing (ISC). Once T₂ is populated, the electrons undergo T₂ → T₃ transition and then relax back to T₂ via the T₃ → T₂ electronic transition. For complexes 3a and 3b, the relaxation decay time (τ_ph) at T₂ was measured using the laser flash photolysis technique¹⁸ and found to be in the order of microseconds. Using laser flash photolysis, the triplet decay curves for complexes 3a and 3b were recorded (Fig. S4†) and fitted. The obtained triplet lifetimes ranged from 27 to 22 μs for complexes 3a and 3b, respectively. These values are consistent with the proposed τ_ph,⁵⁹ which has to be much longer than τ_isc. Ignoring the stimulated emission from S₁ due to small fluorescence quantum yield, the following modified laser rate equations can be applied to simulate the excitation and relaxation of the system:

where n₂ refers to the population of T₂. In this model, the luminescence lifetimes ranging from τ₁₀ = 4.50 ns to 5.40 ns (Table 1), obtained at 532 nm using the TCSPC technique, were used. The kinetic decay curves for the luminescence lifetimes of complex 2 and its blue form analogues were reported before³⁹ and those of complexes 3a and 3b are shown Fig. S5.† These kinetic decay curves show a good simulation (in red) with the chi-square goodness of fit ranging between 0.998 and 0.999. The propagation equation governs the attenuation of the laser beam with the absorption coefficient including the excited-state absorption from S₁ to T₂:where the triplet state absorption cross section, σ₂₃, is given by w₂₃ = σ₂₃I(t)/hv with w₂₃ being the T₂ → T₃ transition rate.

Table 1 Nonlinear optical parameters obtained by employing the three-level diagram model, where eqn (1)–(3) (for complex 2 and 2-TF) and (6)–(12) (for complexes 3a, 3b, 3a-TF and 3b-TF) were used for simulation at nanosecond regime

Complex	σ01 (cm^2)	σ23 (cm^2)	k	τ10 (ns)
a Values obtained from ref. 39, τph (μs) in brackets.
2	^a4.85 × 10^−18	—	^a8.08	^a5.32
2-TF	^a1.62 × 10^−17	—	^a19.3	—
3a	2.36 × 10^−17	9.92 × 10^−17	4.20	5.40 (22)
3a-TF	1.89 × 10^−17	4.01 × 10^−16	21.2	—
3b	5.53 × 10^−17	2.72 × 10^−16	4.91	4.50 (27)
3b-TF	2.24 × 10^−17	6.92 × 10^−16	30.9	—

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Under the steady-state approximation, governed by the pulse width much longer than the relaxation time,⁶⁰ all the time derivatives are set to zero. The assumption is valid for nanosecond pulses, in the case of phthalocyanines with singlet lifetime in the order of picoseconds.⁶¹ Once eqn (9) has been solved, the intensity-dependent absorption coefficient becomes:

where I_sat = hv/σ₀₁τ₁₀, noting that σ₂₃ and σ_1m are probably of the same order when τ_isc ⋘ τ_ph, and as the triplet yield approaches unity for phthalocyanines, the term can be eliminated with σ_1m in the numerator.⁵⁹ The five-level model can therefore be effectively reduced to a three-level model with the intensity-dependent absorption coefficient given by:where the excited-state absorption cross section is due to σ₂₃; in this case, k = σ₂₃/σ₀₁. It can be noted that there is a direct relationship between I(t) and the pulse energy density (given as F = E_Pulse/πw(z)²), with E_Pulse being the energy per unit pulse and πw(z)² defining the surface area through which the pulse propagates at position z. In eqn (9), I(t)/I_sat can, therefore, be replaced by the pulse energy density per unit energy density saturation F/F_sat. The latter is defined at the output saturation of the energy density pulse.

High k and β_eff, low F_sat and low α₀ values are characteristic of a superior optical limiter.⁵⁰ The value of α(I(t), I_sat, k) has to be substituted back into eqn (9) before application of the nonlinear absorption coefficient to open-aperture Z-scan experimental data. At this stage, the possible integration over a homogeneous sample of thickness L leads to a transcendental equation for transmission T as T = I_out/I_in, derived as:⁶²

The nonlinear optical parameters obtained by fitting the Z-scan experimental signatures of complex 2 and its respective thin film 2-TF³⁹ are listed in Table 1.

The concentration of complexes 3a and 3b at 3.0 × 10⁻⁴ M or 1.869 × 10¹⁷ molecules per cm³ has been selected to match that of complex 2,³⁹ noting that due to saturation, the concentration of particles exceeded this value. This concentration selection creates fair comparison of nonlinear optical parameters for all complexes under investigation. These complexes showed no aggregation when concentration studies aimed at determining the molar extinction coefficients were performed. The open aperture Z-scan signatures of complexes 3a and 3b were more pronounced than those for complex 2 with 3b being the best, Fig. 4A. This enhanced nonlinear behavior can be attributed to a more extensive π-conjugated system in complexes 3a and 3a (Fig. 4A) compared to that of complex 2 and is in agreement with the nonlinear behavior proposed for the extension of π-electron system and heavy lanthanide central metal.^57,63–65 Complexes 3a-TF and 3b-TF (Fig. 4C) exhibited better open aperture Z-scan signals that complexes 3a and 3b, respectively. This observation is similar to that of 2-TF in comparison to complex 2. The σ₂₃ values for complexes 3a, 3b, 3a-TF and 3b-TF are shown in Table 1. The σ₂₃ value is greater for the complex than for its respective thin film, evidencing the observed open aperture Z-scan signatures. It can also be observed that the σ₀₁ values for 3a and 3b are larger than those for 3a-TF and 3b-TF, hence the larger k values of 3a-TF and 3b-TF in comparison to those of 3a and 3b but smaller than those of 2-TF (Table 2). This observation can be attributed to the aggregation which may have directly affected the ground state and the excited state absorption cross sections of thin films in different ways. Similarly, the k values for complexes 3a and 3b are smaller than those for complex 2.

Table 2 Nonlinear optical parameters obtained by using the nonlinear regression technique at 532 nm for all complexes^a

Complex	Im[χ^(3)] (esu)	γ (esu)	Ilim (J cm^−2)	Reduction of TNorm (%)
a — denotes that the Ilim value could not be determined due to less than 50% reduction in TNorm.
2	3.77 × 10^−10	9.74 × 10^−28	—	48
2-TF	1.19 × 10^−8	3.07 × 10^−26	0.31	82
3a	2.00 × 10^−9	5.17 × 10^−27	0.34	66
3a-TF	9.82 × 10^−9	25.3 × 10^−27	0.10	82
3b	4.91 × 10^−9	12.7 × 10^−27	0.10	80
3b-TF	1.25 × 10^−8	32.2 × 10^−27	0.03	90

---

The scanning electron microscopy (SEM) images of 2-TF,³⁹ 3a-TF and 3b-TF were obtained for the samples on thin glass slides. These images were taken after performing the open aperture Z-scan experiments (discussed below) where the hazard of the laser beams pumped into the thin films could possibly result in holes and wrinkles on the surface as result of thermal effect. The SEM images of thin films were taken by focusing on the irradiated area (Fig. S6†). As can be seen in the SEM images (Fig. S6†), the surface exhibited homogeneity without any holes or pockets, proving that thin films were thermally stable.

3.3.1 Other nonlinear optical parameters. Further analysis of the effective intensity dependent nonlinear absorption coefficient (β_eff) was carried out by employing the nonlinear regression technique to manipulate the open aperture Z-scan data. This was performed by employing eqn (13), in which the normalized transmittance (T_Norm (z)) is defined as a function of z-position, described by Sutherland et al.:⁶⁶where I₀ (kept at 0.87 GW cm⁻² throughout the experiment) is the intensity of the beam at focus for n = 2 for two photon absorption, respectively, and z and z₀ are the sample positions with respect to the input intensity and Rayleigh length, defined by (λ = wavelength of the laser beam and w₀ = beam waist (∼2.56 × 10⁻³ cm) at the focus (z = 0)), respectively. We have applied this model to complexes 2 and 2-TF.³⁹ When using eqn (13), there is an assumption that the higher singlet excited-state absorption cross section contributes significantly to the reverse saturable absorption and, therefore, only applies to complex 2 and its thin film, which exhibit lack of triplet–triplet absorption. To accommodate optical limiters, the mechanisms of which are governed by strong triplet–triplet absorption at the nanosecond regime, the effective absorption coefficient can be calculated according to the previously reported theory.⁶⁷ The normalized transmittance in this case is defined by:where F₀(r = 0) is the on-axis fluence at the focus.

Other theories^68,69 can, therefore, be applied to calculate the effective absorption coefficient. T_Norm is then given by:

In this expression, q₀(z) given by:

In eqn (13), (15) and (17), L_eff is commonly described as the effective thickness of the sample given by

In eqn (18), α and L are the linear absorption coefficient and the thickness of the sample, respectively.

Once the β_eff values were obtained applying the nonlinear regression techniques, we could easily compute the proportionality third order optical susceptibility (Im[χ⁽³⁾] in esu), which is an imaginary component, via eqn (19):^70,71

In eqn (19), c and n₀, respectively, are the speed of light in vacuum and the linear refractive index, ε₀ is the permittivity of free space and λ is the wavelength of the laser light.

At the molecular level, there is a direct correlation between Im[χ⁽³⁾] (in esu) and the hyperpolarizability γ (which provides the nonlinear absorption per mole of the sample), expressed by eqn (20):^71,72

N* = C_molN_A (C_mol is the concentration of the active species in the excited state in mol) and f denotes the Lorenz local field factor, given by eqn (21):

The optical limiting threshold is also very important to consider since it indicates the degree by which the transmission of the laser beam intensities to be received by an optical sensor being protected by an optical limiter is reduced. By definition, limiting intensity (I_lim in J cm⁻²) is the incident fluence at which the output fluence is half (50%) of the linear transmission.^73,74 This refers to any strong attenuation, experienced by the photodiode detector when the nonlinear optical material responds to the intense beams. Such attenuations are an indication of an optical limiting effect. The I_lim values for complexes 2,³⁹ 3a and 3b as well as 2-TF,³⁹ 3a-TF and 3b-TF were, therefore, obtained at 50% of the linear transmittance by plotting the T_Norm (related to the output fluence) against the input fluence (Fig. 6).

Fig. 6 The normalized transmittance against the incident intensity plot for complexes 3a and 3b as well as their respective thin films 3a-TF and 3b-TF at the nanosecond regime.

As indicated before, complex 2 (ref. 39) exhibits a different nonlinear optical mechanism to that shown by complexes 3a and 3b. This makes it difficult to compare Im[χ⁽³⁾] and the γ values, calculated for these complexes. However, given the fact that complexes 3a and 3b were designed by sandwiching the Cd(II) ion between the complex 2 molecules, the change in the mechanism is still very interesting. Despite the challenge of comparing the Z-scan experimental data, the assumptions made when deriving eqn (1)–(3) and (6)–(8) help ignore other possible contributions made by S_m and T₃. This way, we can look at the pure processes that govern the nonlinear optical behavior observed for each complex. Although the behavior of complex 2 is based on two-photon absorption (2-PA) while for complex 3a and 3b on one-photon absorption (1-PA), the σ_1m and σ₂₃ values should be comparable. The open-aperture Z-scan experimental data shows the trend: σ₂₃ ≫ σ_1m, with σ₂₃ for complex 3b greater than that of complex 3a, hence the better open aperture Z-scan signatures for complexes 3a and 3b compared to complex 2. The calculated Im[χ⁽³⁾] and γ values follow a similar trend, with those of complexes 3a and 3b (Table 2) being higher than those of complex 2. For 2-TF, the Im[χ⁽³⁾] and γ values (Table 2) were very high and larger than those of complex 2, as discussed previously.³⁹ Similarly the Im[χ⁽³⁾] and γ values for 3a-TF and 3b-TF are greater than those calculated for complexes 3a and 3b. This observation is in agreement with what has been observed before.^42,75 However, the Im[χ⁽³⁾] and γ values for 3a-TF were smaller than those of 2-TF. This overturn in the observed pattern of the Im[χ⁽³⁾] and γ values is attributed to aggregation,⁶⁹ which is a known phenomenon in thin films that can affect the excited state absorption, thereby, deactivating the populated excited state. This observation is subjective since aggregation does not always exist in thin films, resulting in gigantic Im[χ⁽³⁾] and γ values.³⁹ Overall, the better nonlinear optical behavior observed for complexes 3a and 3b compared to that of complex 2 in solution is a good indication of the influence of the extension of π-electron system at the same concentration. This is also evident when comparing complex 3a to complex 3b, with 3a being the best optical limiter. The I_lim values were also analyzed. These values are meant to be minimal for an efficient optical limiter.

Complexes 3a and 3b reduced the T_Norm by more than 50%, hence the signals in Fig. 6 and the I_lim values in Table 2. The I_lim value is lower for complex 3b, indicating that complex 3b is a better optical limiter than complex 3a. A similar behavior was observed for 3a-TF and 3b-TF, with 3b-TF being a better optical limiter in solid state. In general, all thin films exhibited a reduction in T_Norm of greater than 90% and lower I_lim values than those in solution.

4. Conclusions

A rare type of new n-tuple decker phthalocyanines were investigated for optical limiting applications. The broad absorption spectra of complexes 3a and 3b exhibited larger ground state absorption cross sections, which compete with the triplet excited state absorption cross sections, resulting in the lowest k values for complexes 3a and 3b compared to that of complex 2. It was also observed that the lack of interaction between the H₂Pc ligands of complexes 3a and 3b enhanced the triplet population, thus changing the NLO mechanisms that control the reverse saturable absorption. More importantly, the extension of the π-electron system results in enhanced open aperture Z-scan signatures, also evidenced by the large Im[χ⁽³⁾] and γ values for complexes 3a and 3b compared to those of 2.

Author contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Funding sources

Department of Science and Technology (DST) and National Research Foundation (NRF).

Conflicts of interest

There are no conflicts of interest to declare.

Abbreviations

NLO	Nonlinear optical
DMF	Dimethyl formamide
DCM	Dichloromethane
DBU	1,8-Diazabicyclo[5.4.0]undec-7-ene
TCB	1,2,4-Trichlorobenzene
THF	Tetrahydrofuran
MS	Mass spectrum
NMR	Nuclear magnetic resonance
XTD	X-ray diffraction
UV-Vis	Ultraviolet-visible
TCSPC	Time correlated single photon counting
ESR	Electron spin resonance
SEM	Scanning electron microscope
LnPc2	Lanthanide bisphthalocyanine
H2Pc	Unmetallated phthalocyanine
BV	Blue valence
VEH	Valence-Effective Hamiltonian
RSA	Reverse saturable absorption
TNorm	Normalized transmittance
ISC	Intersystem crossing
Ilim	Limiting threshold
2-PA	Two-photon absorption
1-PA	One-photon absorption

Acknowledgements

This study was supported by the Department of Science and Technology (DST) and National Research Foundation (NRF), South Africa, through DST/NRF South African Research Chairs Initiative for Professor of Medicinal Chemistry and Nanotechnology (UID 62620), NRF (UID 110789), and by Rhodes University.

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Footnotes

† Electronic supplementary information (ESI) available: NMR spectra of complexes 2 and 3a, mass spectra 3a and 3b, ESR spectra of 2, 3a and 3b, and SEM images of 2-TF, 3a-TF and 3b-TF. See DOI: 10.1039/c9ra01836k

‡ These authors contributed equally.

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