Novel multiredox π-conjugated perimidine polymers with
ultra-low band gap

doi:10.21203/rs.3.rs-2594328/v1

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Novel multiredox π-conjugated perimidine polymers with ultra-low band gap

https://doi.org/10.21203/rs.3.rs-2594328/v1

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The electropolymerization of prepared monomers 1 (mixture of perimidino[1',2':1,5]pyrrolo[3,4-m]phthaloperine-9,19-dione and 17H,19H-perimidino[1',2':1,2]pyrrolo[3,4-m]phthaloperine-17,19-dione) and 2 (benzo[lmn]diperimidino[2,1-b:2',1'-i][3,8]phenanthroline-10,21-dione and benzo[lmn]diperimidino[2,1-b:1',2'-j][3,8]phenanthroline-18,21-dione) resulted in the synthesis of electroactive conductive materials with structures similar to fused perinone dyes. Polymer p1 was obtained via the electropolymerization of monomer 1 with low yield and low stability, which was insufficient for further analysis. However, fundamental perinone polymer p2, containing a perimidinobenzophenanthroline skeleton, which was obtained by electropolymerization of 2, where its thickness and structure could be controlled in a one-step electrochemical process. This novel poly(perimidinobenzophenanthroline) polymer was electrically conductive and displayed a complex redox activity, mixed conductivity, and an ultra-low band gap of 0.14 eV. The regular D-A structure and specific intermolecular interactions also played a role in its characteristics. The mechanism of the electrooxidation process, which led to the formation of protonated, semi-ladder, and ladder bis-perimidine segments in polymers, was proposed using electrochemical analysis and quantum-chemical calculations.

Physical sciences/Chemistry/Polymer chemistry/Conjugated polymers

Scientific community and society/Energy and society/Energy efficiency

ultra-low band gap polymer

multiredox polymer

electroactive

conductive polymer

perinone

perimidine

Π-conjugated polymers have various applications because of their electrical conductivity^1,2. Physical agents (photoconductivity^3,4, thermoconductivity^5,6) and chemical changes (oxidation^7,8, reduction i.e. –p and –n doping^9,10) can improve conductivity of these materials, but controlling conductive properties is still challenging. Due to the effects of physical and chemical agents being frequently interdependent, the resulting conductivity is generally of a mixed type (hole, electron, exciton, and/or ionic conductivity). Therefore, designing air-stable, conductive polymers is an issue in polymer chemistry^11,12. n-Doping is a useful technique for increasing the electronic conductivity of organic semiconductors, but only a small amount of the polymers exhibits stable conductivity in the reduced form^13,14. Hence, the question remains, can the electronic conductivity of a π-conjugated polymer be enhanced in a neutral state?

The intra- and intermolecular delocalization of electrons effectively increase the conductivity of a neutral state. The length of the main chain should be considered, and the efficiency of conjugation should be developed in a linear sequence with minimal monomer rotation (increasing coplanarity)^15,16. Creating condensed linear ladder polymers and 2D π-conjugated structures (e.g., graphene) can promote intramolecular π-delocalization¹⁷. However, in certain materials, the presence of excited charge carriers is a contributing factor to the macroscopic organization, such as charge transfer in low- and high-molecular-weight donor-acceptor systems and intermolecular transfer of dipole moments in polar segments of push-pull polymers (charge-transfer complexes)¹⁸. Most often, hazardous substances are utilized in the synthesis of such compounds, for example, organotin materials in Stille coupling reaction, etc.¹⁹ Hence, ladder conductive polymers are still among the most promising organic semiconductors.

The production of ladder connections in polymers is not primarily specific to the condensation of tetraamines with aromatic anhydrides (preparation of poly[6,9-dihydro-6,9-dioxobisbenzimidazo[2,1-b:1',2'- j]benzo[1mn]phenanthroline-2,12-diyl] - (BBB); and poly[17-oxo-7,10-benz[de]imidazo[4',5':5,6]-benzimidazo[2,1-a]isoquinoline-3,4:10,11-tetrayl)-10-carbonyl]) - BBL)^20,21. The coupling mechanism of electrochemical aromatic compounds with a perimidine unit in their structure through (electro) oxidation has recently been studied by our research group. It was found that the perimidine segment of perimidine-isoindolone^22,23, perimidine-pyrrole²⁴, and perimidine-naphthalene-carbazole²⁵ monomers (Fig. 1a) show evidence of a coupling process between the radical cations. This reaction creates stable dicationic bis-perimidine segments in the polymer that do not deprotonate when polarized over a wide range of potentials. Additionally, these investigations demonstrated the feasibility of creating two bonds between perimidine units to produce structures such as BBB using electrochemical techniques, for example, cyclic voltammetry (CV), differential pulse voltammetry (DPV), and chronoamperometry (CA). Therefore, the aim of this work was to present the electrochemical preparation of new π-conjugated polymer materials based on the perimidine unit, which exhibited a multi-redox nature and show ultra-low bandgap. The monomers were prepared in a one-step, straightforward synthesis, which was beneficial compared to chemical polymerization.

Electrochemistry

Electrochemical studies of prepared monomers 1 and 2 showed they were electroactive and underwent multiple redox processes, but reversible reduction processes could not be definitively stated due to low concentration of monomer in the solution (28 µM and 23 µM, respectively for 1 and 2). However, it was possible to conduct the appropriate studies on the anodic and anodic-cathodic waveforms, in which the electro-oxidation reaction was used to obtain layers of electroactive materials.

The study found that the oxidation of the monomers was linked to the oxidation of the perimidine unit, which is described in previous studies as coupling radical cations. The oxidation of monomers 1 and 2 was irreversible with max peaks at + 0.93V and + 0.86V, respectively. The products of the electro-oxidation were different depending on the electrode cycle, leading to varying chemical structures and electroactivity. Table S1 shows the potentials obtained in the anode and anode-cathode cycles and Fig. S3 shows the potential ranges of the three main fractions of products.

The oxidation of the studied monomers was related to the oxidation of the perimidine unit, which is described in previous studies as coupling radical cations^22–25. Also, the prepared monomers displayed irreversible oxidation with the max. at + 0.93 V for monomer 1 and + 0.86 V for monomer 2 (Fig. S2). Reports have shown that depending on the position of two perimidine units during electrocoupling, various fractions of products could be characterized by different electroactivity depending on the potential. The type of products can differ depending on the deposition in an anode or anode-cathode cycle due to the distinct organization of molecules on the electrode during the cathodic cycle, which involves n-type doping and can rearrange the material’s structure²⁶. Tab. S1 shows the potentials of materials obtained during the electro-oxidation of monomers 1 and 2 in the anode and anode-cathode cycles. In the anodic waveform, four fractions of products were observed for polymer 1 (p1), and three fractions for polymer 2 (p2). The products were divided into three main fractions. Fig. S3 shows the potential ranges of the fractions, from − 0.25 to 0.19 V for 1ox, 0.20 to 0.64 V for 2ox, and 0.65 to 1.15 V for 3ox; which were products of p1 and p2.

CA was employed at the monomer-oxidizing potentials to determine that the formation of 2ox fraction required an alternating potential. Fig. S4 shows that at a constant potential, the current intensity for the product polarization was comparable to the background (Fig. S4c), hence, 2ox product was not formed. However, during the electrodeposition process, by sweeping the potential from 0.9 to 0.7 V, 2ox fraction was obtained (Fig. S4d). Therefore, 2ox fraction was a mixture of decoupled products, in which its preparation required a lower potential after reaching the monomer’s oxidation peak.

During the electro-oxidation of the anodic-cathodic waveform, a widening of the current response and two reduction peaks for each of the material was observed (for p1 at -1.52 and − 2.00 V; for p2 at -0.98 and − 1.44 V). These are marked in Fig. 1 as red1 and red2. The presence of these two reduction peaks proved that the redox couples derived from the monomers were maintained (Fig. S2). The reduction of both materials and monomers was comparable to the electroactivity of BBL polymer²⁷, which consists of isomeric units of compound 1. The redox process in BBL is reversible and contains two single electron transfer steps at the potentials of -1.14 and − 1.48 V vs. Fc/Fc^+ 28. A two-stage reduction was also observed with pyrrolo[3,4-m]phthaloperinedione (for p1) and [3, 8]phenanthrolinedione (for p2) cores. 1red and 2red peaks that corresponded to these processes were broadened due to the development of various types of products and non-covalent interactions between the material segments in the solid.

Sweeping the potential in a wide range (Fig. S5) did not degrade or dissolve the materials, which proved their stability. During the anodic-cathodic waveform, materials with higher current responses were always obtained that did not disappear in the subsequent sweep cycles, hence, the electropolymerization method, which included the potential sweep in the reduction region, was better. In addition, an increased current intensity was detected compared to the background for the obtained materials. This suggested the conductivity of the materials over the entire range of the potential sweep. In the case of p2, the boundary between the reduction and oxidation regions was invisible (Fig. S3), which was considered as the electrochemical energy gap of the material close or equal to zero. The same gap for p1 was equal to 0.44 V. Main issues arose during the development of further structural studies due to the low concentration of monomers 1 and 2, making it impossible to obtain a sufficient amount of p1 and p2 materials to peruse further research techniques. Therefore, to explain the structure of the obtained materials, we decided to use quantum chemical calculations, which will be presented later in the article.

Quantum chemical calculations

Quantum chemical calculations were utilized to determine the energies and localization of molecular orbitals for the syn- and anti-isomers present in monomers 1 and 2. Density Functional Theory (DFT) was employed to obtain information regarding the expected redox potentials and the preferred reactivity sites of these systems (Tab. S2). These calculations were supplemented with localizations of spin densities for the appropriate radical ionic states (Tab. S3). HOMO (Highest Occupied Molecular Orbital) was located mainly on the perimidine units for all calculated monomers and the energies values were − 5.33 eV for monomer 1 and − 5.11 eV for monomer 2. The energy and localization of orbitals are the same for syn- and anti-isomers, meaning their properties should be similar during experiments. The energy value of HOMO-1 was lower than that of HOMO (-5.47 eV for monomer 1 and − 5.40 eV for monomer 2). This suggested the ‘electronic communication’ of the two terminal perimidine units by aromatic cores. Additionally, it led to partial delocalization of the orbitals and extension of the charge throughout the molecule. LUMO (Lowest Unoccupied Molecular Orbital) was located mainly on the aromatic core units (pyrrolo[3,4-m]phthaloperinedione and [3, 8]phenanthrolinedione) and partially delocalized towards the oxygens in the molecule. The energy values of these orbitals were − 2.94 eV for monomer 1 and − 3.06 eV for monomer 2.

Based on the calculated localization of electron spin density for excited forms, we proposed the position of the covalent connection in the electro-oxidation products. All calculated radical cations showed that the spin was located mainly on the four carbon positions 1, 3, 4, and 6 and nitrogen atoms (Tab. S3). The entire spin of both radical cations and diradical dications was located on the perimidine units. Hence, the spin of the radical anions and diradical dianions was located on the aromatic central unit e.g., pyrrolo[3,4-m]phthaloperinedione and [3, 8]phenanthrolinedione.

To facilitate the calculations, some assumptions and simplifications were used. The syn- and anti-isomers of monomer 2 were only calculated. Three main groups of products were categorized (Fig. 2) - protonated bis-perimidine (Tab. S4), semi-ladder bis-perimidine (Tab. S5); and ladder bis-perimidine (Tab. S6). Additional mers (n = 4 or 8) were computed with only 4 possible structures of ladder bis-perimidine products (Tab. S8 and S9). Intermolecular interactions and supporting electrolyte ions were ignored. The calculated HOMO value for monomer 2 was − 5.11 eV, which was compared with the calculated energies of the orbitals for electro-oxidation products. Additionally, a difference of 1 eV corresponded to a difference of 1 V for CV and DPV measurements²⁹.

Based on the calculations performed for the possible electro-oxidation products, we proposed a series of products obtained during the electropolymerization of monomer 2 (Fig. 3). Firstly, during the recombination of perimidine radical cations, the simplest connection was the protonated bond in the dication segment, which was previously described as 1ox fraction. The calculated LUMO value of this type of connection was between − 4.44 and − 4.65 eV. The oxidation potential of monomer 2 was 0.84 V, so the calculated values for the products of fraction 1ox should have a potential of 0.17 V. The electrochemical response for fraction 1ox was in the range of -0.2 to 0.2 V for DPV measurement and it is most probably a set of redox reactions for bis-perimidine junctions in the form of dications. During the previous calculations of bis-perimidine dications, it was found that some bonds, such as 1,1’ or 1,6’, were more stable due to the possibility of possessing hydrogen bond interactions inside the molecule. The products stabilized in this way did not undergo any further oxidation reaction^23,25.

2ox and 3ox fractions were products of deprotonation of bis-perimidine dications to neutral bonds of semi-ladder and ladder bis-perimidines, respectively. According to the calculations, these fractions should be related to 2ox and 3ox at potentials 0.36 and 0.91 V, respectively. In this case, the calculations were consistent with DPV measurement results. To test our theory of the generation of ladder connections in 2ox fraction, electrochemical analysis of perylene was conducted due to ladder dimers being derivatives of perylene (Fig. S6). The oxidation potential of perylene was 0.55 eV, which confirmed the presence of a perylene unit in p2 material, found in 2ox fraction. Additionally, the current response assigned to 3ox may be caused by the oxidation of perimidine terminal units and monomers included in the material structure.

In the reduction region (below 0 V) current responses on DPV curve starting from − 0.4 V were observed. These were generated during the reduction of neutral dimers and larger oligomers with semi-ladder and ladder perimidines. During the calculations, it was found that the reduction of longer oligomers should occur at higher potentials compared to the monomer, owing to the energy value of LUMO orbital larger oligomers becoming lower. Additional signals below − 1 V originated from the reduction of the monomer occluded in the polymer structure, the terminal units, and from further stages of the reduction of the oligomers.

The calculations showed that with each additional monomer unit in the polymer chain, the band gap decreases to a limit of 0.93 eV, as shown by fitting the trend function for the calculated oligomers (Fig. S7). The geometry and values of the boundary orbitals were calculated in a pure solvent, ignoring intermolecular interactions.

Also, calculations for neutral ladder oligomers of 2, 4, and 8 monomer units were performed. The calculations showed that with each additional monomer unit in the polymer chain, the band gap decreases to a limit of 0.93 eV, as shown by fitting the trend function for the calculated oligomers (Fig. S7). The geometry and values of the boundary orbitals were calculated in a pure solvent, ignoring intermolecular interactions. In a condensed system, hydrogen or π-electron interactions (such as π-stacking) may occur, which stabilized the structure and reduced the band gap of the material^30–32.

Mechanism of electropolymerization

p1 and p2 polymers were produced via electropolymerization of perimidine units. These materials arose due to the recombination reactions of perimidine radical cations, generated by the application of an oxidizing potential. As shown above, the spin density of radical cations was concentrated at positions 1, 3, 4, and 6. Hence, bonding at these perimidine positions was possible. The bond at position 1 was in a non-protonated form due to the stabilization of the proton with the nearby amide group. Binding through the remaining positions stemmed from the formation of deprotonated bis-perimidine segment first (semi-ladder segments). In the subsequent oxidation cycles, a certain amount of semi-ladder segments could condense into a ladder, which is especially favored by the planarity of the monomer and product structure (Fig. 3).

The deposition reactions of p1 and p2 are shown in Fig. S8 and Fig. S9, respectively. In the anodic-cathodic wave, p1 showed an additional orientation of the molecules after the application of low potential and the formation of π-stacking interactions that stabilized the polymer structure. In the case of p2, deposition in an anodic-cathodic waveform promoted the radical anions to react upon the application of reducing potentials. The correct orientation of the oligomer segments caused the formation of covalent bonds between the naphthalene units, resulting in the stiffening of the polymer structure and increased stability of the material during cyclic polarization, compared to p1. This phenomenon was previously observed for isoindole isomers containing a perimidine unit¹⁷.

Electrochemical properties of p2 material

Notably, p1 material was not stable during prolonged polarization at both reducing and oxidizing potentials. Its low stability, compared to p2, was possibly due to the considerably smaller amount of interactions between planar pyrrolo[3,4-m]phthaloperinedione central units. In addition, p2 during the reduction process formed covalent bonds between the [3, 8]phenanthrolinedione cores. Therefore, we will present in this work further research only for p2 material.

The bandgap value for p2 material was impossible to determine using CV Cardona’s method³⁴, because, according to calculations, it had an energy gap below zero (Fig. S10). By measuring the admittance of p2 material, the electrochemical band gap of the material deposited during 10, 20, and 30 cycles were determined (Fig. 4). The admittance measurement revealed that with an increasing number of deposition cycles, the value of LUMO orbital energy for the material decreased, while HOMO energy remained unchanged. The decreasing LUMO value with each deposition cycle tightened the band gap to the value of 0.14 eV for the 30th cycle layer.

To gain a better understanding of the doping behavior, p2 material was studied using electrochemical impedance spectroscopy (EIS) for 10 and 20 cycles of deposition. This technique allows for the analysis of complex electrode processes and has previously been used to describe polarization-induced ion antiport³⁵ as well as the determination of the conductivity type of semiconducting materials³⁶. We proposed an equivalent circuit describing the polymer film under polarization, which is shown in Fig. 5. The circuit was not processable due to an infinite number of parameters, hence a simplified approach was employed. The circuit described charge relaxation, meaning the propagation of the charge from the polymer-electrode to the polymer-solution interface. Each R-C branch stood for a charge transfer process, which was defined by its rate and sensitivity to the potential change.

The introduction of a time-dependent element in the equivalent circuit for impedance measurement allowed for the characterization of p2 films for 10 and 20 deposition cycles (Fig. 6). The processes that occur in the thin and thick films were the same, but observation of the processes was much more pronounced in the case of the thicker film (20 cycles of deposition). The fastest processes characterized by a time-constant below 50 µs (Fig. 6, b fast) were not present in this material. However, processes for a medium and slow time-constant above 0.1 ms were detected. The impedance measurements revealed that two electrochemical processes occur in p2 polymer with a time-constant above 10 ms. These processes were caused by the dedoping of the polymer, i.e., the migration of counter ions from the material to the electrolyte due to the changed polarization of the working electrode. They occurred at potentials of c.a. -0.75 and 0.3 V (Fig. 6b slow). Other processes were considered as oxidation or reduction of individual segments of the material, which was accompanied by the migration of electrolyte ions into the material (doping). Therefore, p2 was mainly a redox polymer. However, high charging currents of the material, especially in the range from − 0.6 to -0.2 V, indicated conductivity along the polymer chain and intermolecular conductivity. Most likely, the conductivity in this range increased due to trapped counter ions in the material’s structure.

The presented study has shown that it was possible to obtain new monomers from cheap, easily available precursors by a simple condensation reaction. In this work we used much simpler monomers with two reactive perimidine units. The obtained monomers, which were a mixture of non-separable isomers, were subjected to oxidative polymerization under potentiodynamic and potentiostatic conditions. The effect of both methods was similar and controlled oxidation coupling of perimine units was performed, followed by deprotonation of new bonds at a lower potential to obtain as many deprotonated single (partial-ladder segment) and double junctions (ladder segments) in the polymers. Importantly, extremely stable protonated bonds existed in the bonding population between the mers, i.e., at least with one carbon C1 closest to the amino group, which stabilized the protonated bonds in the polymer by hydrogen interaction. Yields of electropolymerization of 1 and 2 were different and perimidinobenzophenanthroline polymer p2 precipitated more efficiently from the solution. The production of higher mass polymers may be influenced by the efficiency of maintaining intermediate products on the electrode’s surroundings to induce subsequent reactions. Intermolecular interactions between both soluble oligomers and atoms of the electrode material may be important. Using electrochemical measurements and quantum-chemical calculations, we proposed the presence of specified bonds in the insoluble polymer. The electroactive segments during electrooxidation were mainly products identified as protonated, semi-ladder, and ladder bis-perimidines. Additionally, during the reduction process, the electroactive segments were determined as pyrrolo[3,4-m]phthaloperinedione and [3, 8]phenanthrolinedione cores. Perimidinobenzophenanthroline polymer p2 was stable over a wide potential range. Its calculated energy gap was based on admittance measurements and reached the value of 0.14 eV with a conductivity related to the redox reaction of protonated segments, migration of doping ions, and p_z electron delocalization. The results showed that the transfer of all types of carriers ran along the polymer chain, but the intermolecular transfer was also extremely important, promoting the narrowing of E_g value.

Synthesis of monomers 1 and 2

Monomers 1 and 2 were prepared via the condensation reaction of aromatic dianhydrides with 1,8-diaminonaphthalene. A detailed description of the reaction, purification method, and characterization of the structure are presented in Supplementary Information.

Electropolymerization and electrochemical analysis

CV and DPV were determined using a CH Instruments Electrochemical Analyzer, model 620. All analyses were carried out on compound 1 or 2 saturated solutions (28 µM and 23 µM, respectively), which were prepared in anhydrous dichloromethane (DCM). In all cases, tetrabutylammonium tetrafluoroborate (Bu₄NBF₄, 0.1 M) was used as the supporting electrolyte. The solutions were prepared directly in the electrolytic cell, under an Ar atmosphere, and the weighted quantity of Bu₄NBF₄ was added to the filtered solution of monomers 1 or 2 in DCM. Then, Ar was bubbled through the solution for 15 min. The experiments were carried out at 25°C, and the experimental setup included a single electrochemical cell with three electrodes: a platinum disc (area = 1 mm²) as the working electrode (WE), platinum coil as the counter electrode, and a silver electrode as the Ag/Ag⁺ pseudoreference electrode, which was previously calibrated with ferrocene (Fc/Fc⁺). Materials p1 and p2 were deposited on the platinum disc electrodes by cyclic electro-oxidation within the potential range covering the first oxidation peak. The cyclic voltammograms were obtained at the potential scanning rate of 100 mV/s. For stability measurements and DPV of films, WE with deposited material (p1 or p2) was washed with anhydrous DCM and the experiments were conducted in the solution of the supporting electrolyte.

Impedance spectroscopy measurements were carried out using a BioLogic SP-150 potentiostat with a built-in frequency response analyzer. The material was deposited onto the electrode using DCM solution containing 23 µM of monomer 2 in Bu₄NBF₄ 0.1 M over 10 cycles (“thick film”) in the potential range of -1.69 to + 1.01 V (vs. Fc/Fc⁺). Before the impedance measurement, the film was stabilized with 5 more cycles at the same potential range as for depositing, and in the supporting electrolyte solution. The impedance measurement of the resulting film was carried out in DCM solution containing Bu₄NBF₄ 0.1 M, in the potential range of -1.79 to + 1.11 V. Impedance spectra were obtained in 1 MHz^− 1 Hz frequency range with 3 points per decade in the logarithmic scale (the total number of frequencies in one spectrum was 19). Analysis of electrochemical impedance spectra, determination of equivalent circuit parameters, and other calculation procedures were processed using Microsoft Excel 2013.

IMPEDNCE CALCULATIONS

The admittance of the circuit presented in Fig. 5 (a) was

$$Y=\sum _{i=1}^{n}\frac{1}{{R}_{i}-j\frac{1}{\omega {C}_{i}}}=\sum _{i=1}^{n}\frac{{1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.}{1-j\frac{1}{\omega {R}_{i}{C}_{i}}}$$

The product R_iC_i of the resistor and capacitor connected in series is known in physics as a relaxation time-constant, usually assigned as τ. This parameter characterized the rate of the current exponential drop (current relaxation) when the capacitor was connected to a power source via a resistor. Then

$$Y=\sum _{i=1}^{n}\frac{{1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.}{1-j\frac{1}{\omega {\tau }_{i}}}=\sum _{i=1}^{n}\left(\frac{{1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.}{1+\frac{1}{{\left(\omega {\tau }_{i}\right)}^{2}}}+j\frac{1}{\omega {\tau }_{i}}\frac{{1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.}{1+\frac{1}{{\left(\omega {\tau }_{i}\right)}^{2}}}\right)$$

When ω_i∙τ_i > > 1 was assumed. Then the impact of the i-th process into the total admittance was

$${Y}_{i}=\frac{{1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.}{1+\frac{1}{{\left(\omega {\tau }_{i}\right)}^{2}}}+j\frac{1}{\omega {\tau }_{i}}\frac{{1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.}{1+\frac{1}{{\left(\omega {\tau }_{i}\right)}^{2}}}\approx {1ex}{$1$}\!\left/ \!{-1ex}{${R}_{i}$}\right.$$

In the opposite case, when ω_i∙τ_i < < 1:

$${Y}_{i}=0$$

Thus, the imaginary component of a process with time-constant τ_i was evident in the system impedance only at the frequency of ω ≈ 1/τ_i. Moving from this value to lower frequencies decreased the admittance to 0. Increasing the frequency caused the disappearance of the imaginary component and only 1/R_i remains. It was confirmed that fragmentary analysis of experimental spectra was possible using a three-element equivalent circuit (Fig. 2, right). If the frequency range covered by the considered fragment was narrow enough, then it was assumed that measured R_s and C described a single process, whereas R_p stood for all the processes where the relaxation was not observed in this range, due to the conditions ω_i∙τ_i < < 1 and ω_i∙τ_i > > 1.

Then, every relaxation process was characterized by two parameters: its intensity 1/R_i expressed in the units of conductivity and its rate expressed in the units of time as a time constant. The two polymer layer was analyzed using this method. The results are shown in Fig. 6.

Quantum chemical calculations

For calculations, DFT was used with B3LYP³⁷ hybrid functional combined with 6-31G(d) basis set. For all optimized structures, the frequency calculations were systematically achieved (at the same level of theory) to confirm the minimum nature of the optimized geometries. All calculations in this work were performed using the ORCA 4.1.1³⁸ package programs. Input files and molecular orbital plots were prepared with Gabedit 2.4.7 software³⁹. The Conductor-like Polarizable Continuum Model (CPCM) was used to examine the effect of solvent on the calculated structures⁴⁰.

Acknowledgments:

Authors acknowledge the Polish National Science Centre (NCN) (project No 2021/41/B/ST5/03221). This research was also supported by the Polish Budget Founds for Scientific Research in 2022 as a core funding for R&D activities in the Silesian University of Technology – funding for young researchers (grant No. 04/040/BKM21/0161), and Excellence Initiative – Research University at the Silesian University of Technology in Gliwice (grant No. 32/014/RGJ22/2007).

Contribution:

Patryk Janasik: synthesis of the monomers, cyclic voltammetry, spectroelectrochemistry investigations, DFT calculations, and manuscript preparation; Pavel Chulkin: electrochemical impedance spectroscopy measurements and data workup; Malgorzata Czichy: writing, reviewing, and editing of the manuscript; Mieczyslaw Lapkowski: original idea, conceptualization, and supervision of the project.

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Novel multiredox π-conjugated perimidine polymers with ultra-low band gap

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Introduction

Results

Electrochemistry

Quantum chemical calculations

Mechanism of electropolymerization

Electrochemical properties of p2 material

Discussion

Methods

Synthesis of monomers 1 and 2

Electropolymerization and electrochemical analysis

IMPEDNCE CALCULATIONS

Quantum chemical calculations

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