The Effect of Polymerization of 2.7-Divinylcarbazole-Benzo-Bis-Thiadiazole on Optical Fiber Properties

Abstract

The interest of polymer optical fibers (POF) lies in their low cost compared to silica fibers and in their ease of implementation, i.e. robustness, flexibility, low weight and easier connectivity. The first generation of polymer fibers are of the index jump type and are composed of polymethyl methacrylate (PMMA) for the core and a fluorinated polymer for the cladding. The significant attenuation of OPFs in the red and near IR is due to the harmonics of the different vibrational modes of the C–H bonds. The improvement of this parameter requires a shift in the transmission of the polymer towards longer wavelengths. As in the case of inorganic glasses, this requires the development of materials with low fundamental frequency of vibration. The development of graded index structures also allows limiting the modal dispersion inherent to the multi-mode character of POFs. And before the use of certain materials in the electronic fields a study of certain properties was carried out by the DFT method in order to propose the polymers based on carbazole. This study was carried out by the DFT–B3LYP method as functional with the 6-31G (d, p) atomic base to optimize all systems, from monomer to pentamer.

1. Introduction

The carbazole [1] drifts turns out to be a particularly well adapted material here, since it can be while keeping its optical and thermomechanical qualities exceptional. However, the advantage of polymers for planar technology is their good transparency over short distances, associated with an easier shaping than inorganic glasses.

2,7-Carbazole derivatives [2, 3, 4] are organic materials with the properties of a semiconductor. These oligomers are known for their high stability due to the presence of nitrogen atoms and exhibit important physicochemical and optoelectronic properties. The addition of the methoxy-benzyl group to the nitrogen atom increases the solubility of these oligomers and facilitates their synthesis. During the last decade, conjugated donor-acceptor (D − A) copolymers have been the subject of numerous studies [2]. Among the main advantages of these hetero-junction materials, they have high flexibility and low weight [3, 4, 5]. The objective of this work is to show the interest of π-conjugated polymers by focusing on the electronic structure, the factors influencing the gap energy and the substitution effect of these polymers. We are interested in increasing the efficiency of the organic photovoltaic cell, by seeking to decrease the gap energy (HOMO-LUMO), in characterizing these compounds in terms of geometric and electronic structures to ensure good absorption of radiation and facilitate the charge transfer between the different compounds of our copolymer. This study was carried out on copolymers based on 2,7-divinylcabazole (PCrV) and benzo-bis-thiadiazole (BBT) (Figure 1). We were interested in the effect, on the structural, optoelectronic and photovoltaic properties of the addition of the méthoxy-benzyl group on the N atom of carbazole. This study was carried out by the DFT–B3LYP method as functional with the 6-31G (d, p) [6, 7, 8, 9, 10, 11, 12] atomic base to optimize all systems, from monomer to pentamer. The structural and electronic properties have been demonstrated following this optimization, while the optical properties are obtained by the TD-DFT method at the level of the WB97XD functional and with the 6-31G base [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24].

Figure 1.

The structures of the copolymers studied of 2, 7-divinyl-carbazole and Benzo-bis-thiadiazole (PCrV-BBT); N Substituted and N not Substituted.

The LUMO level of the N-substituted copolymer is more stable than that of unsubstituted copolymer. This shows that the substitution of H by the méthoxy-benzyl group allows to decrease the energy gap of these compounds [25, 26, 27, 28, 29, 30, 31].

2. Structural properties

The structures of the Donor–Acceptor (DA) [32] copolymers based on 2,7-divinyl-carbazole and benzo-bis-thiadiazole (PCrV-BBT) have been optimized with the base B3LYP/6-31G (d, p). The geometric parameters (bond lengths d_i, angles A_i and dihedral angles D_i) (Figure 2) of the most stable conformations obtained after the total optimization of the systems studied are presented in Table 1.

Figure 2.

The structures of the copolymers studied (of 2,7-divinyl-carbazole and benzo-bis-thiadiazole (PCrV-BBT; NH)), and PCrV-BBT; N-Sub (with the addition of methoxy - benzyl on the N atom of carbazole).

	Parameters	PCrV-BBT; N-H)n					PCrV-BTT; N-sub)n
		n = 1	n = 2	n = 3	n = 4	n = 5	n = 1	n = 2	n = 3	n = 4	n = 5
Inter-cyclic distance (Å)	d1	1.455	1.454	1.454	1.454	1.454	1.455	1.454	1.454	1.453	1.453
	d2	1.360	1.362	1.36	1.362	1.362	1.360	1.360	1.362	1.363	1.363
	d3	1.440	1.436	1.436	1.436	1.436	1.439	1.435	1.435	1.435	1.435
Normal angles (°)	A1	117.65	117.74	117.81	117.75	117.74	117.7	117.68	117.68	117.63	117.71
	A2	127.15	127.65	127.68	127.66	127.63	127.36	127.68	127.67	127.59	127.49
Dihedral angles (°)	D1	180.01	179.99	179.93	179.96	180.04	179.72	179.52	179.23	179.56	179.92
	D2	179.99	180.0	179.98	179.98	180.02	179.89	179.88	179.95	179.86	179.80

Table 1.

The structural parameters of the copolymers; d_i: inter-cyclic distances, A_i: normal angles, D_i: dihedral angles.

The values of the inter-cyclic bonds (d_i), the values of the normal angles (A_i) and the values of the dihedral angles (D_i) of the copolymers based on PCrV-BBT with the substituted carbazole nitrogen atom (PCrV-BBT; N-sub) are generally very similar to those of the copolymers based on PCrV-BBT unsubstituted in N carbazole (PCrV-BBT; NH) (Table 1).

The lengths of the inter-cyclic bonds (d_i, i = 1–3) of all the copolymers remain almost constant going from monomer to pentamer while maintaining the double and single bond alternation, i.e. an increase of the length of the conjugation with the extension of the carbon chain. Thus, the lengths of the bonds d₁ and d₃ have values close to the length of the single bond C–C (1.465 Å) and the value of R2 is close to that of the length of double bond C = C (1.361 Å) [33, 34, 35].

From the values mentioned in Table 1, it is observed that the values of the dihedral angles of the systems studied are generally porches of 180°. This indicates that the two benzo-bis-thiadiazole and 2,7-vinyl-carbazole moieties are found in the same plane in all systems (from n = 1 through n = 5). On the other hand, the pentamer has a planar structure with dihedral angle values very close to 180°. This flatness, confirmed by the values of the normal angles (A_i; i = 1, 2) close to 120°, reflects SP2 hybridization.

These results show a good improvement in flatness and an increase in electron conjugation π. This facilitates the possibility of delocalization of electrons along the molecular skeleton.

3. Electronic properties

The study of electronic properties mainly concerns the determination of energy levels HOMO, LUMO and the band gap (energy gap). This determination makes it possible to validate the candidacy of the molecules studied for use in the electronic field. The calculation of the HOMO, LUMO and Energy Gap levels was carried out after the optimization of the systems by the B3LYP/6-31 g (d, p) method.

From Table 2, we note that the gap values decrease going from monomer to pentamer. We also note that the addition of the methoxy-benzyl group on the nitrogen atom of the carbazole causes the gap to decrease by an average of 0.02 eV. This decrease due to a good stability of the energy levels is clearly illustrated in Figure 3. This decrease in the gap is in agreement with the improvement in the flatness of these systems.

Polymers	PCrV-BBT; N-H			PCrV-BBT; N-Sub
	HOMO (eV)	LUMO (eV)	GAP Energy (eV)	HOMO (eV)	LUMO (eV)	GAP Energy (eV)
n = 1	−5.16	−3.40	1.76	−5.09	−3.34	1.75
n = 2	−4.77	−3.49	1.28	−4.68	−3.42	1.26
n = 3	−4.66	−3.53	1.13	−4.58	−3.46	1.12
n = 4	−4.61	−3.54	1.07	−4.53	−3.47	1.06
n = 5	−4.59	−3.56	1.03	−4.49	−3.48	1.01

Table 2.

The values of the energies of the HOMO and LUMO levels and of the energy gap of the copolymers.

Figure 3.

Illustration of the HOMO, LUMO, and Eg levels of the monomer to the pentamer obtained by B3LYP/6-31G (d, p).

The change from monomer to pentamer shows a general reduction in the gap with a strong stability of the LUMO level compared to the HOMO level, which seems a little destabilized (see Figure 3). We also observe that the LUMO levels of PCrV-BBT-N-substituted are more stable than those of unsubstituted PCrV-BBT-N-H. This clearly shows that the substitution of the H atom by the methoxy-benzyl group allows a reduction in the gap of these copolymers.

Concerning the electronic densities of the HOMO and LUMO border molecular orbitals of the copolymers studied, they are presented in Figure 4.

Figure 4.

Illustration of the border orbitals HOMO, LUMO of the copolymers without group (PCrV-BBT; N-H), and with methoxy-benzyl group (PCrV-BBT; N-Sub).

This figure shows that the electron density at the level of HOMO orbitals is distributed along the conjugation chain. In contrast, at LUMO orbitals, the electron cloud is mainly located on the electron acceptor unit (BBT). This phenomenon is due to the Puch-Pull properties of type polymers (D–A). It should be noted that the addition of the methoxy-benzyl group to the nitrogen of the carbazole promoting the flatness of these systems, allows the total displacement of the electron density towards the acceptor unit (Figure 5) and plays an important role at the level of the solubility and stability of the systems [4, 36]. It is also important to note that the transfer of electrons from the HOMO orbital to the LUMO orbital in the N-substituted copolymer is more efficient compared to other N-unsubstituted copolymers and therefore results in energy low gap.

Figure 5.

Data of wavelength according to absorbance of copolymers with the methoxy-benzyl group on N of carbazole obtained at DFT-WB97XD/6-31G.

4. Optical properties and electronic transitions

UV–visible absorption spectra, wavelengths and excitation energies of the copolymers studied were calculated using the TD-DFT-WB97XD/6-31G method, from the optimized geometries of the copolymers. The corresponding values of excitation energies (Eex), wavelengths (λmax), and light harvesting efficiency (LHE) [expressed by Eq. (1)] [37], are gathered in Table 3.

	Type of excitement	Eex (eV)	λ (nm)	LHF	Attributions
PCrV-BBT; N-Sub	S0➔S1	1.8983	653.13	0.6651	H-2➔L (11%); H ➔ L (88%)
	S0➔S2	3.1570	392.73	0.0355	H-5 ➔ L1 5(3%); H-1 ➔ L (86%); H➔L + 1 (6%)
	S0➔S3	3.3028	375.39	0.4563	H-8➔L (2%); H-4➔L (24%); H-2➔L (59%); H-1➔L (2%); H➔L (7%); H➔L + 1 (3%)
PCrV-BBT; N-Sub)2	S0➔S1	1.3976	887.09	0.9244	H-1➔L + 1(4%); H-➔L (77%); H➔L + 1 (14%)
	S0➔S2	1.8953	654.16	0.6036	H-5➔L + 1 (3%); H-4➔L + 1 (4%); H-1➔L (22%); H-1➔L + 1(49%); H➔L + 1 (19%)
	S0➔S3	2.8687	432.20	0.0059	H-8➔L (6%); H-8➔L + 1 (2%); H-5➔L (9%); H-4➔L (24%); H-4➔L + 1 (6%); H-3➔L (2%); H-1➔L (32%); H-1➔L + 1 (9%)
PCrV-BBT; N-Sub)3	S0➔S1	1.3107	945.93	0.9938	H-2➔L + 2 (3%); H-1➔L (3%); H-1➔L + 1 (21%); H-1➔L + 2 (8%); H➔L (54%); H➔L + 1(6%)
	S0➔S2	1.4693	843.82	0.0243	; H-1➔L (34%); H-1➔L + 2 (5%); H➔L + 1 (38%) H➔L + 2 (14%)
	S0➔S3	1.8973	653.49	0.6033	H-7➔L + 2 (2%); H-2➔L (11%); H-2➔L + 1 (19%); H-2➔L + 2 (38%); H-1➔L + 1 (3%); H-1➔L + 2 (12%); H➔L + 2 (7%)
PCrV-BBT; N-Sub)4	S0➔S1	1.2684	977.48	0.9994	H-2➔L + 2 (14%);; H-2➔L + 3 (6%); H-1➔L + 1 (17%); H-1➔L + 2 (3%); H➔L (44%); H➔L + 1 (4%)
	S0➔S2	1.4041	883.05	0.0212	H-2➔L + 1 (12%); H-2➔L + 2 (2%); H-1➔L (27%); H-1➔L + 2 (10%); H-1➔L + 3 (9%); H➔L + 1 (26%); H➔L + 2 (5%);
	S0➔S3	1.4957	828.95	0.2504	H-2➔L (25%); H-2➔L + 1 (3%); H-1➔L + 1 (19%); H-1➔L + 2 (3%); H➔L + 2 (26%); H➔L + 3 (13%)
PCrV-BBT; N-Sub)5	S0➔S1	1.2492	992.49	0.9999	H-3➔L + 2 (2%); H-3➔L + 3 (6%); H-3➔L + 4 (8%); H-2➔L + 1 (3%); H-1➔L + 2 (9%); H-2➔L + 3 (3%); H-1➔L (5%); H-1➔L + 1 (12%); H-1➔L + 2 (5%); H➔L(32%); H➔L + 1 (8%);
	S0➔S2	1.3543	915.48	0.0076	H-3➔L + 1 (2%); H-3➔L + 2 (6%); H-3➔L + 3 (3%); H-2➔L (3%); H-2➔L + 1 (7%); H-2➔L + 3 (4%); H-2➔L + 4 (8%); H-1➔L (23%); H-1➔L + 2 (6%); H➔L + 3 (4%); H➔L + 1 (20%); H➔L + 2 (5%);
	S0➔S3	1.4491	855.60	0.3458	H-3➔L + 1 (7%); H-3➔L + 2 (4%); H-2➔L (18%); H-2➔L + 2 (4%); H-2➔L + 3 (3%); H-1➔L + 1 (13%); H-1➔L + 3 (5%); H-1➔L + 4 (11%); H➔L + 2 (18%); H➔L + 3 (5%);
PCrV-BBT; N-H	S0➔S1	1.9137	647.86	0.6744	H-2➔L (11%); H➔L (88%);
	S0➔S2	3.3145	374.07	0.4419	H-6➔L (2%); H-3➔L (23%); H-2➔L (55%); H-1➔L (8%); H➔L (7%);
	S0➔S3	3.3758	367.28	0.0744	H-4➔L (5%); H-2➔L (5%); H-1➔L (79%); H-1➔L + 1 (6%);
PCrV-BBT; N-H)2	S0➔S1	1.4144	876.58	0.9259	H-1➔L + 1(4%); H➔L (78%); H➔L + 1 (13%);
	S0➔S2	1.9089	649.50	0.5977	H-5➔L + 1 (3%); H-2➔L + 1 (4%); H-1➔L (22%); H-1➔L + 1 (49%); H➔L + 1 (19%);
	S0➔S3	2.8812	430.31	0.0341	H-6➔L (6%); H-6➔L + 1(2%); H-5➔L (10%); H-2➔L (25%); H-2➔L + 1 (6%); H-1➔L (33%); H-1➔L + 1 (9%);
PCrV-BBT; N-H)3	S0➔S1	1.3283	933.38	0.9943	H-2➔L + 2 (3%); H-1➔L (3%); H-1➔L + 1 (22%); H-1➔L + 2 (8%); H➔L (54%); H➔L + 1 (6%);
	S0➔S2	1.4920	830.97	0.0561	H-1➔L (35%); H-1➔L + 1 (4%); H➔L + 1 (38%); H➔L + 2 (14%);
	S0➔S3	1.9109	648.82	0.5951	H-7➔L + 2 (2%); H-2➔L (11%); H-2➔L + 1 (19%); H-2➔L + 2 (38%); H-1➔L + 1 (3%); H-1➔L + 2 (12%); H➔L + 2 (7%)
PCrV-BBT; N-H)4	S0➔S1	1.2846	965.15	0.9994	H-2➔L + 1 (3%); H-2➔L + 2 (12%); H-2➔L + 3 (7%); H-1➔L (4%); H-1➔L + 1 (15%); H-1➔L + 2 (4%); H➔L (42%); H➔L + 1 (7%);
	S0➔S2	1.4199	873.21	0.0043	H-2➔L + 1 (10%); H-2➔L + 2 (3%); H-1➔L (26%); H-1➔L + 2 (10%); H-1➔L + 3(9%); H➔L + 1 (25%); H➔L + 2 (5%);
	S0➔S3	1.5178	816.86	0.2333	H-2➔L (24%); H-2➔L + 1 (4%); H-1➔L + 1 (18%); H-1➔L + 2(3%); H➔L + 1 (2%); H➔L + 2 (26%); H➔L + 3 (13%);
PCrV-BBT; N-H)5	S0➔S1	1.2600	983.96	0.9999	H-3➔L + 2 (3%); H-3➔L + 3 (8%); H-3➔L + 4 (6%); H-2➔L + 1 (4%); H-2➔L + 2 (9%); H-2➔L + 3 (3%); H-1➔L (5%); H-1➔L + 1 (11%); H-1➔L + 2 (5%); H➔L (32%); H➔L + 1 (8%);
	S0➔S2	1.3689	905.75	0.2034	H-3➔L + 1 (2%); H-3➔L + 2 (6%); H-3➔L + 3(2%); H-2➔L (3%); H-2➔L + 1 (7%); H-2➔L + 3 (5%); H-2➔L + 4 (7%); H-1➔L (22%); H-1➔L + 2 (6%); H-1➔L + 3 (4%); H➔L + 1 (20%); H➔L + 2 (6%);
	S0➔S3	1.4661	845.69	0.4410	H-3➔L + 1 (7%); H-3➔L + 2 (3%); H-2➔L (18%); H-2➔L + 2 (4%); H-2➔L + 3 (2%); H-1➔L + 1 (13%); H-1➔L + 3 (6%); H-1➔L + 4 (10%); H➔L + 1 (2%); H➔L + 2 (17%); H➔L + 3 (6%);

Table 3.

Types of excitation, excitation energies, wavelengths and LHE, obtained by the TD-DFT/WB97xd-6-31G method.

To understand the evolution of the short-circuit current density (Jsc), we studied the LHE energy which depends on Jsc according to Eq. (2) [38]. We notice that large values of LHE lead to high values of Jsc. This therefore improves the efficiency of electronic devices.

$$\mathrm{LHE}=1–10-\mathrm{f}$$E1

$$\mathrm{Jsc}=\int \mathrm{\lambda }\mathrm{LHE}\left(\mathrm{\lambda }\right)\mathrm{ɸ}\left(\text{inject}\right)\mathrm{ƞ}\left(\text{collect}\right)\mathrm{d\lambda }$$E2

where: ɸ(inject), Efficiency of electron injection; ƞ(collect), The efficiency of the collection of charges; f, oscillation force.

From the data in Table 3, we have three types of same-spin (S→S) excitation from the lowest occupied molecular orbitals and the highest void levels. In regards to λ_max, this increases going from the monomer to the pentamer. In addition, the addition of the methoxy-benzyl group contributes to increasing the values of maximum absorption lengths. This indicates that these copolymers are good candidates for absorbing the maximum of incident light radiation and therefore further increasing the photoelectric conversion efficiency of the corresponding solar cell from this type of material (Figure 6).

Figure 6.

Data of wavelength according to absorbance of copolymers with the H on N of carbazole obtained at DFT-WB97XD/6-31G.

These absorption spectra show an increase in the magnitude of epsilon directly related to the absorbance of light. This implies very good absorption of light radiation going from the monomer to the pentamer. The value of λ_max increases until it reaches the far IR zone. In other words, it only takes a gentle incident light radiation to have a very good excitation of the electrons. We also find that the width of the excitation plug increases when the methoxy-benzyl group is substituted on the N atom of the carbazole. This is favorable to good absorption of the light ray.

5. NBO analysis and charge transfer

From the optimized geometries of the copolymers, we fragmented the systems into donor fragments and other acceptors. Then we carried out the energy calculation by the DFT-B3LYP/6-31G (d, p) method.

NBO analysis [28, 29, 30] is an efficient method to study the interaction between intra and intermolecular bonds. It also allows the study of charge transfer in the molecular system.

Figure 7 above represents the different fragments of the two types of copolymers studied, we chose to fragment the structure according to the copolymer compositions, then we performed the NBO analysis, the results obtained are grouped together in Table 4.

Figure 7.

Structures of the fragmented systems studied by NBO of copolymers without and with methoxy-benzyl group.

		PCrV-BBT; N-H		PCrV-BBT; N-Sub
PCrV-BBT) n	Fragments	Charges	Types	Charges	Types
n = 1	Frag1	0.50	Donor	0.50	Donor
	Frag2	−0.50	Acceptor	−0.50	Acceptor
n = 2	Frag1	−0.15	Acceptor	0.13	Donor
	Frag2	0.13	Donor	−0.24	Acceptor
	Frag3	−0.23	Acceptor	0.26	Donor
	Frag4	0.25	Donor	−0.15	Acceptor
n = 3	Frag1	0.82	Donor	−0.15	Acceptor
	Frag2	0.13	Donor	0.26	Donor
	Frag3	−0.24	Acceptor	−0.24	Acceptor
	Frag4	0.24	Donor	0.25	Donor
	Frag5	−1.20	Acceptor	−0.24	Acceptor
	Frag6	0.25	Donor	0.13	Donor
n = 4	Frag1	0.24	Donor	0.19	Donor
	Frag2	0.13	Donor	−0.35	Acceptor
	Frag3	−0.24	Acceptor	0.36	Donor
	Frag4	−0.24	Acceptor	−0.36	Acceptor
	Frag5	0.24	Donor	0.37	Donor
	Frag6	−0.24	Acceptor	−0.35	Acceptor
	Frag7	0.25	Donor	0.38	Donor
	Frag8	−0.15	Acceptor	−0.25	Acceptor
n = 5	Frag1	0.13	Donor	−0.15	Acceptor
	Frag2	−0.14	Acceptor	0.26	Donor
	Frag3	0.25	Donor	−0.24	Acceptor
	Frag4	−0.24	Acceptor	0.25	Donor
	Frag5	0.24	Donor	−0.24	Acceptor
	Frag6	−0.24	Acceptor	0.25	Donor
	Frag7	0.24	Donor	−0.25	Acceptor
	Frag8	−0.24	Acceptor	0.24	Donor
	Frag9	0.24	Donor	−0.25	Acceptor
	Frag10	−0.24	Acceptor	0.13	Donor

Table 4.

The electronic charge and the type of fragments of the copolymers obtained by B3LYP/6-31G (d, p).

NBO analysis of the various fragments of the copolymer highlights the role of the interaction of intermolecular orbitals and charge transfer in the system. It is carried out by taking into account all the possible interactions between filled donors and empty acceptors and by estimating their energetic importance by the theory of second order disturbances.

Each positively charged NBO represents a donor (i) and each negatively charged NBO is linked to an acceptor moiety (j). The stabilization energy E associated with electronic delocalization between donor and acceptor is estimated by Eq. (3) [39, 40].

$$\mathrm{E}=\mathrm{qi}\left(\mathrm{Fi}.\mathrm{j}\right)2/\mathrm{\epsilon j}-\mathrm{\epsilon i}$$E3

where: qi is the occupation of the i orbital; εj, εi are diagonal elements; Fi,j is the o-diagonal NBO Fock matrix element.

From Table 4, it is observed that the change from monomer to pentamer leads to the location of charges in the middle of the system; the charge values of the middle fragments are higher than those of the end fragments. The addition of the methoxy-benzyl group further increases the absolute value of charge compared to that of copolymers without a group (PCrV-BBT; N-H).

6. Conclusions

The conjugated copolymers based on 2,7-divinylcabazole (PCrV) and benzo-bis-thiadiazole (BBT) have been studied by suitable quantum methods. It emerges from this study that the electronic and optoelectronic properties are intimately linked to the molecular structure. In this sense, the electron donor and electron acceptor motif alternation approach is an effective strategy for modulating these properties.

The LUMO level of the N-substituted copolymer is more stable than that of unsubstituted copolymer. This shows that the substitution of H by the méthoxy-benzyl group allows to decrease the energy gap of these compounds.

The data obtained from the energy levels of the different molecules indicate that the LUMO and HOMO levels, as well as the values of the energy of gap Eg, vary according to the length of the carbon chain. The majority of the copolymers studied exhibit a high quality P-type semiconductor character. Electronic transitions in this type of material require low energy light radiation. For all the reasons mentioned above, these molecules are good candidates for a good application in electronic.