Dipolar Relaxation in Functionalized Poly - ACS Publications

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Dipolar Relaxation in Functionalized Poly‑p‑phenylenes Bearing Ultrastrong Dipoles Perpendicular to the Backbone George Papamokos,† Jakob Wudarczyk,‡ Robert Graf,‡ Dieter Schollmeyer,§ Martin Baumgarten,‡ Klaus Müllen,*,‡ and George Floudas*,†,‡ †

Department of Physics, University of Ioannina, 45110 Ioannina, Greece Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128, Mainz, Germany § Institut für Organische Chemie, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany ‡

S Supporting Information *

ABSTRACT: Local polymer dynamics are studied in polymers bearing dipoles rigidly attached to the backbone. The compounds are based on cyano-substituted dihydrobenzimidazoles bearing ultrastrong dipole moments (∼12 D per repeat unit) incorporated in a poly-p-phenylene backbone, giving rise to polymers with rigid dipoles perpendicular to the chain. They belong to type B polymers according to the Stockmayer classification. They are ideal model systems for studying rotational isomers in the gas phase and the self-assembly and local dynamics in the solid state. Gas phase calculations (DFT) provided the dipole moments, the energetic barriers, and the backbone conformation as a function of the dipole strength and dipole separation. Calculated dipole moments show an odd− even effect as a function of dipole separation. Specific rotational isomers that maximize the dipole moment are obtained. In the solid state, dielectric spectroscopy and site-specific NMR techniques revealed that packing through intermolecular forces such as van der Waals, π−π, and dipole−dipole interactions dictates the dynamics. Dielectric spectroscopy further identified two modes, both with Arrhenius temperature dependence and activation energies of 20−23 kcal/mol. Combined results attribute the faster process to a libration motion of the highly polar group reorienting only the nonplanar five-membered ring and the slower process to larger amplitude and/or correlated motions of the polar groups. These dynamic results are in agreement with structural investigations (X-ray diffraction) demonstrating that type B polymers in the bulk have rigid backbones.

I. INTRODUCTION

Local polymer dynamics can best be studied in systems bearing strong dipoles rigidly attached to the backbone. This can be realized by addition of electron-withdrawing cyano groups on the one side and electron-donating amino groups on the opposite side of a benzene unit in a poly-p-phenylene. Recently, we have shown that hexasubstituted benzenes can have dipole moments in excess of 10 D.9 These compounds constitute the smallest neutral molecular species bearing the largest dipoles known today. In contrast to Braunsteins quinoid zwitterions10 forming hydrogen-bonded networks, 11 the methylation of the dihydrobenzimidazoles excludes the noncovalent bonding and thus displays the “pure” dipole effect. The polymerization of para-brominated dicyano-dihydrobenzimidazole monomers gives rise to polymers with rigid dipoles perpendicular to the chain. These can be considered as model type B polymers in studying rotameric transitions in the gas phase. Furthermore, the self-assembly and local dynamics in the solid state can be explored. The structure of the paper is as follows. We first provide the synthetic details of the two model polymers P1 and P2 bearing the same dipole but having a different backbone (P2 has an additional phenylene ring between the dipolar benzene units).

1

Long ago Stockmayer classified polymers according to the position of the polar groups in their repeat unit into three types with (A) dipoles parallel to the backbone, (B) dipoles rigidly attached to the backbone and perpendicular to the chain direction, and (C) dipoles located on a flexible side group. The dynamics of amorphous polymer chains with emphasis on longrange motions (Rouse,2 Zimm,3 and reptation4) that control the mechanical response of type A polymers is well investigated. On the other hand, local dynamics associated with dipoles perpendicular to the backbone (of the type B) is much less explored. The latter can comprise librational motions up to full rotameric transitions of individual dipoles or more concerted motions of a number of dipoles. The signature of such motions is best reflected in the dielectric response of the system.5,6 The scarce studies on this type of molecule reflect on the inability to synthesize polymer backbones with perpendicular dipoles rigidly attached to the backbone. Some earlier efforts have concentrated on polymers with dipoles as side groups, like poly(p-chlorostyrene).1 Yet, the latter neither can be considered as rigid nor have high dipole moments. Poly(vinylidene fluoride) (PVDF), on the other hand,7,8 bearing a stronger dipole, crystallizes in several different lattices, and this precludes an investigation of the dipolar dynamics. © XXXX American Chemical Society

Received: January 29, 2018 Revised: April 14, 2018

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DOI: 10.1021/acs.macromol.8b00215 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules Scheme 1. Synthesis of Dipolar Monomer Units and Polymers

SPhos afforded the formation of the terphenyl 4 in 63% yield. The chloro substituents further allowed the polymerization under Yamamoto conditions (P1) and Suzuki conditions (P2), but the resulting oligomers revealed low molecular weights (P1: Mn = 4.8 kDa and P2: Mn = 3.8 kDa) since chloro substituents show a lower reactivity in cross-coupling reactions, especially in Suzuki condensations.13 MALDI spectra unveiled signals for polymers up to 20 repeating units for P1 and signals up to 8 repeating units for P2 (see Figures S10 and S11). However, a detailed look at the spectra, with the aid of the MALDI spectrum of the monomer unit 4 (see Figure S9), shows fragmentation of an alkyl chain under illumination with laser light. Synthesis of 4,7-Dibromo-2,2-diheptyl-1,3-dimethyl-2,3-dihydro1H-benzo[d]imidazole-5,6-dicarbonitrile (3). 4,7-Dibromo-2,2-diheptyl-2,3-dihydro-1H-benzo[d]imidazole-5,6-dicarbonitrile9 (2) (1.30 g, 2.479 mmol) was dissolved in dry 150 mL of acetone under an inert gas atmosphere. After addition of potassium carbonate (2.74 g, 10.91 mmol, 8 equiv) and methyl iodide (1.548 g, 19.83 mmol, 4.4 equiv), the solution was stirred under reflux overnight. The reaction was monitored via thin layer chromatography, and 2−4 equiv of methyl iodide was added to achieve completion of the methylation. After each addition the solution was stirred for an additional 24 h. The mixture was cooled to room temperature and subsequently poured into 300 mL of DCM. After extraction with water three times and one time with brine, the organic phase was dried with sodium sulfate and filtered, and the solvents were evaporated. The crude product was purified via column chromatography (hexane/THF, v:v 1:6) and washed with small amounts of methanol to yield a cannary-yellow crystalline solid in 75% of theory (1.023 g, 1.852 mmol). 1H NMR: δ (300 MHz, CD2Cl2) = 0.87 (m, 6H), 1.13−1.35 (m, 20H), 1.65 (m, 4H), 3.16 (s, 6H). 13C NMR: δ (300 MHz, THF-d8) = 14.44, 23.31, 23.56, 30.16, 30.26, 30.68, 32.87, 36.12, 92.37, 94.03, 111.94, 116.36, 143.54. FD-MS: m/z = 552.0 (calcd 552.4). HRMS (ESI): 551.1395 (MNa+). Calcd for C25H36N4Br2Na: 551.1385. Melting point: 146 °C.

This step is followed by a computational study in the gas phase that provides the dipole moments, the energetic barriers, and the backbone conformation as a function of the dipole strength and dipole separation. The conformational patterns in a series of compounds with optimized structures that resulted in a maximization of the dipole moment are discussed. This procedure, although synthetically challenging, is computationally feasible. Subsequently, we study their self-assembly and show that it is very sensitive to the presence of an extra phenylene group in the repeat unit of P2 and possibly to the number of repeat units. As a result, P2 crystallizes whereas P1 exhibits a rigid-amorphous structure. Lastly, we investigate the bulk dipolar dynamics of P1 with dielectric spectroscopy (DS) and different solid-state NMR techniques. DS identifies two dielectrically active processes both with Arrhenius temperature dependence. Heteronuclear solid-state NMR provides the geometry of relaxing units at the frequency corresponding to the fast process. DS and NMR reveal a dynamically rigid polymer with only some librational motion of the dipolar group at ambient temperature. These results are discussed in terms of a relatively rigid backbone. The study thus suggests that type B polymers have some unique structural and dynamic features not common to type A and type C polymers.

II. EXPERIMENTAL SECTION Synthesis. Starting from 4,5-diamino-3,6-dibromophthalonitrile (1), solubilizing alkyl chains were added via ring closure reaction of two amino groups with a dimethoxyalkane to yield dihydrobenzimidazole (2) in 81% as shown in our previous publication.9 Substitution of the remaining amino protons with methyl groups using methyl iodide increased the dipole moment and prevented the formation of intra- or intermolecular hydrogen bonding (e.g., with solvent molecules). The following cross-coupling reaction of 4,7-dibromo2,2-diheptyl-1,3-dimethyl-2,3-dihydro-1H-benz[d]imidazole-5,6-dicarbonitrile (3) to terphenyl 4 was challenging due to the steric hindrance of the bromo substituents with cyano and methyl groups, which also did not allow direct polymerization of 4 via Yamamoto, Suzuki, or Stille polycondensation. Only palladium-catalyzed Suzuki crosscoupling under Buchwald conditions12 with 1.9 equiv of p-chlorosubstituted phenylboronic acids per bromine and the additional use of

Synthesis of 4,7-Bis(4-chlorophenyl)-2,2-diheptyl-1,3-dimethyl2,3-dihydro-1H-benzo[d]imidazole-5,6-dicarbonitrile (4). 4,7-DibroB


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Macromolecules mo-2,2-diheptyl-1,3-dimethyl-2,3-dihydro-1H-benzo[d]imidazole-5,6dicarbonitrile (3, 1.358 mmol) and 4-(chlorophenyl)boronic acid (806 mg, 5.159 mmol, 3.8 equiv) were dissolved in 40 mL of dry toluene in a flame-dried Schlenk flask. After degassing with argon for 30 min, 4.61 g (21.7 mmol, 16 equiv) of potassium phosphate, 112 mg (0.272 mmol, 0.2 equiv) of SPhos, and 62.2 mg (68 mmol, 0.05 equiv) of Pd2(dba)3 were added, and the mixture was stirred under an inert gas atmosphere for 48 h at 100 °C. After cooling to room temperature, the mixture was diluted with 300 mL of DCM and extracted with water three times. The organic phase was dried with sodium sulfate and filtered, and the solvents were evaporated. The crude product was purified via column chromatography (ethyl acetate/hexane, v:v 1:10) and recycling GPC (chloroform). The title product was obtained in a yield of 26% as a yellow solid (220 mg, 0.357 mmol). 1H NMR: δ (300 MHz, THF-d8) = 0.89 (m, 6H), 1.13−1.35 (m, 20H), 1.56 (t, J = 6.5 Hz, 4H), 2.23 (s, 6H), 7.33 (d, J = 8.4 Hz, 4H), 7.46 (d, J = 8.4 Hz, 4H). 13C NMR: δ (300 MHz, THF-d8) =. FD-MS: m/z = 617.1 (calcd 615.7). HRMS (ESI): 615.3031 (MNa+). Calcd for C37H45N4Cl2: 615.3021. Melting point: 159 °C.

Crystallographic data and structure refinement of compounds 2, 3, and 4, 13C NMR spectra of 3, 4, P1, P2, and MALDI-ToF of 4, P1, P2 are provided in the Supporting Information. X-ray Scattering. Wide-angle X-ray scattering (WAXS) measurements were made using Cu Kα radiation (Rigaku MicroMax 007 X-ray generator, Osmic Confocal Max-Flux curved multilayer optics). Samples of 2 mm thickness were hot pressed at 453 K under vacuum and slowly cooled to ambient temperature. 2D scattering patterns were recorded on a Mar345 image plate at a sample-to-detector distance of 34.8 cm. Radial intensity distributions are presented as a function of the modulus of the scattering vector q = (4π/λ) sin(2θ/2), where 2θ is the scattering angle. Temperature-dependent WAXS measurements were performed on heating and subsequent cooling, in the range from 303 K to 423 K in 10 K steps. For P2, temperature-dependent measurements were made from 303 to 443 K in 10 K steps. Dielectric Spectroscopy (DS). The sample cell consisted of two electrodes, 20 mm in diameter and a thickness of 50 μm. Dielectric measurements were executed at different temperatures in the range from 253.15 to 423.15 K, at atmospheric pressure, and for frequencies in the range from 1 × 10−2 to 1 × 106 Hz using a Novocontrol Alpha frequency analyzer with an active sample head. Samples were prepared as homogeneous films by hot-pressing at 433 K under vacuum. The complex dielectric permittivity, ε* = ε′ − iε″, where ε′ is the real and ε″ is the imaginary part, is a function of frequency ω, temperature T, and in general pressure P, ε* = ε*(ω,T,P).14,15 In the analysis of the DS spectra we have used the empirical equation of Havriliak and Negami (HN)16

Synthesis of Poly[4,7-di([1,1′-biphenyl]-4-yl)-2,2-diheptyl-1,3-dimethyl-2,3-dihydro-1H-benzo[d]imidazole-5,6-dicarbonitrile] (P1). Under the inert gas atmosphere of a glovebox, 228 mg (0.812 mmol, 2.5 equiv) of bis(1,5-cyclooctadiene)nickel(0), 129 mg (0.812 mmol, 2.5 equiv) of 2,2′-bipyridine, and 200 mg (0.325 mmol) of 4,7bis(4-chlorophenyl)-2,2-diheptyl-1,3-dimethyl-2,3-dihydro-1H-benzo[d]imidazole-5,6-dicarbonitrile (4) were dissolved in 16 mL of dry THF in a 32 mL microwave vial. After the addition of 143 mg (0.162 mL, 0.812 mmol) of cyclocotadiene, the mixture was kept dark and treated in the microwave at 90 °C for 3.5 h. After cooling to room temperature, the black-brownish suspension was carefully precipitated in a 5:1 mixture of concentrated hydrochloric acid in methanol. The solid was filtered off and extracted with acetone, ethyl acetate, and chloroform. The product was obtained from the chloroform fraction as a yellow-greenish solid in 90% yield (160 mg) 1H NMR: δ (300 MHz, CD2Cl2) = 0.86−0.96 (m, 6H), 1.18−1.39 (m, 20 H), 1.51−1.76 (m, 4H) 2.32 (s, 6H), 7.44−7.58 (m, 4H), 7.79−7.91 (m, 4H). GPC in DMF at 333 K vs polystyrene standard: Mn: 3.84 kg/mol, Mw: 6.84 kg/ mol; PDI: 1.73.

* (ω , T ) = ε∞(T ) + εHN

σ (T ) Δε(T ) + 0 [1 + (iωτHN(T ))m ]n iεf ω

(1)

where τHN(T,P) is the characteristic relaxation time, Δε(T,P) = ε0(T,P) − ε∞(T,P) is the relaxation strength of the process under investigation, m and n (with limits 0 < m, mn ≤ 1) describe respectively the symmetrical and unsymmetrical broadening of the distribution of relaxation times, σ0 is the dc conductivity, and εf is the permittivity of the free space. In the fitting procedure, we have used the ε″ values at every temperature, and in some cases the ε′ data were also referred to as a consistency check. From, τHN the relaxation time at maximum loss, τmax, was obtained analytically following

⎛ πm ⎞ 1/ m⎛ πmn ⎞ τmax = τHN sin−1/ m⎜ ⎟ ⎟ sin ⎜ ⎝ 2(1 + n) ⎠ ⎝ 2(1 + n) ⎠

(2)

In the temperature range where two relaxation processes contribute to ε* there are two ways of representing the data. The first one, followed here, is based on a summation of two HN functions and assumes statistical independence in the frequency domain. The second one, proposed by Williams and Watts, is a molecular theory for the dipole moment time-correlation function Cμ(t) (also known as the “Williams ansatz”). Solid-State NMR. In order to analyze the local packing and assign the different 1H and 13C NMR signals in the solid state, NMR spectroscopy measurements have been performed with a Bruker Avance III console operating at 850 MHz 1H Larmor frequency in the temperature range between 323 and 403 K at 25 kHz magic angle spinning (MAS) frequency. Measurements were performed using a commercial MAS double resonance probe supporting 2.5 mm MAS rotors. Frictional heating of the NMR samplesdue to the fast MAS conditionswas calibrated utilizing the temperature-dependent 207Pb chemical shift of lead nitrate. In order to probe the segmental dynamics, solid-state NMR spectra were recorded using the 13C−1H rotor-encoded polarization transfer heteronuclear dipolar order (REPT-HDOR) techniques.17 These experiments, performed on a Bruker Avance III system operating at 700 MHz 1H Larmor frequency,

Synthesis of Poly(4-([1,1′:4′,1″-terphenyl]-4-yl)-2,2-diheptyl-1,3dimethyl-2,3-dihydro-1H-benzo[d]imidazole-5,6-dicarbonitrile) (P2). 121 mg (0.197 mmol) of 4,7-bis(4-chlorophenyl)-2,2-diheptyl1,3-dimethyl-2,3-dihydro-1H-benzo[d]imidazole-5,6-dicarbonitrile (4) and 32.7 mg (0.197 mmol) of benzene-1,4-diboronic acid were dissolved in dry toluene under an argon atmosphere. After degassing with argon for 30 min, 210 mg (0.985 mmol, 5 equiv) of potassium phosphate, 16 mg (0.394 mmol, 0.2 equiv) of SPhos, and 9 mg (0.01 mmol, 0.05 equiv) of Pd2(dba)3 were added, and the mixture was stirred at 100 °C for 72 h under an argon atmosphere. After cooling to room temperature, the oligomer was precipitated from methanol. The crude product was then filtered off and extracted with acetone, ethyl acetate, and chloroform. The product was obtained as a yellowgreenish solid from chloroform fraction in 25% yield (30 mg, 0.0483 mmol). 1H NMR: δ (300 MHz, CD2Cl2) = 0.86−0.96 (m, 6H), 1.14− 1.38 (m, 20 H), 1.53−1.66 (m, 4H), 2.32 (s, 6H), 7.45−7.56 (m, 4H), 7.78−7.97 (m, 4H). GPC in DMF at 333 K vs polystyrene standard: Mn: 4.8 kg/mol, Mw: 5.7 kg/mol; PDI: 1.19. C


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Macromolecules employed 25.0 kHz MAS spinning frequencies and 240.0 μs REPTHDOR recoupling times, yielding site-specific 13C−1H dipole−dipole couplings (DDCs). Differential Scanning Calorimetry (DSC). The thermal properties were investigated with a Q2000 (TA Instruments) differential scanning calorimeter (DSC). Thermograms were obtained during the second cooling and heating runs with a rate of 10 K/min within the temperature range from 173 to 473 K. The DSC traces of P1 and P2 are shown in Figure S16. The instrument was calibrated for best performance on the specific temperature range and heating/cooling rate. The calibration sequence included a baseline calibration for the determination of the time constants and capacitances of the sample and reference sensor using a sapphire standard, an enthalpy and temperature calibration for the correction of thermal resistance using indium as standard (ΔH = 28.71 J/g, Tm = 428.8 K), and a heat capacity calibration with a sapphire standard. The DSC curve of P1 showed no evidence for crystallization/melting whereas P2 was crystalline (melting temperature = 457.2 K; heat of fusion = 53 J/g). Computational Methods. All molecules presented in Figures 1 and 2 were subjected to full unconstrained optimization with tight optimization criteria (RMS force criterion was set to 1 × 10−5) and a 99.590 grid to achieve smooth convergence. The DFT-ωB97X-D level of theory18 was employed and the 6-31+G(d,p) basis set.19 The ωB97X-D long-range corrected (LC) hybrid density functional includes empirical atom−atom dispersion corrections and shows the best performance for the prediction of properties of π-conjugated oligomers.20 The rotational barriers were employed at the DFTB3LYP21−24 and 6-31G(d,p) basis set. The stationary points found were confirmed to be true minima by subsequent frequency calculations. For all molecules the Gaussian09 software package25 was employed. Potential energy scan for the dimer D1 and Cartesian coordinates of all molecules in Figure 1 are given in the Supporting Information.

III. RESULTS AND DISCUSSION We discuss first the results from DFT calculations on the intramolecular rotational barriers and the associated dipole moments followed by the results from dielectric spectroscopy, NMR, and X-rays on the solid-state dynamics and structure. DFT Calculations of Dipole Moments. The optimized geometries of all molecules under study and the calculated dipole moments are shown in Figure 1. The figure depicts the 2,2-diheptyl-1,3-dimethyl-2,3-dihydro-1H-benzo[d]imidazole5,6-dicarbonitrile (here called M0), the corresponding monomer to compound 4 without the Cl substitution (called M1), and the corresponding M2 together with the dimers D1 and D2. M0 (Figure 1a) carries a high dipole moment (12.2 D), and this value is not affected by the addition of a phenyl ring to M1. Upon addition of one more phenyl ring (M2) the origin of the dipole moment vector is laterally translated (Figure 1b,c). Depending on the relative orientation of dipole vectors and the energetic barriers involved, the overall dipole moment in D1 and D2 can adopt a range of values from multiples of the monomer dipole moment to zero value. Starting from an initially parallel and coplanar orientation of the repeat units in D1 (Figure 1d), the resulting dipole moment is 17.3 D (ωB97X-D). Evidently, parallel arrangements are not achieved, the dipole moment vectors are not coplanar, and as a result the magnitude of dipole moment is not doubled. Alternatively, starting from an initially antiparallel coplanar conformation of the two repeat units in D1, having a zero total dipole moment, the following optimization results in a dipole moment of 4.4 D (ωB97X-D/6-31+G(d,p)) (Figure 1e) revealing that dipoles are not coplanar. Note that although dipole moment vectors are always vertical to the polymer axis, their directions can vary with respect to the ring planes. For D2,

Figure 1. Optimized structures and calculated dipole moments (debye) of molecules under study. All optimized structures shown here are reported at the DFT-ωB97X-D level of theory and 631+G(d,p) basis set. Blue arrows represent dipole moment vectors and are not proportional to their magnitudes: (a) M0, (b) M1, (c) M2, (d) D1 (dimer of M1) after optimization; its initial (input) geometry adopted a parallel and coplanar orientation with both dipole moment vectors of each monomer directed up (up−up orientation). The two rectangles in panel d include the D1 polymer axis from different views: axis almost vertical to the page plane and axis coplanar to the page plane. The same axial representation follows for panels e, f, and g. (e) D1 after optimization; its initial (input) geometry adopted an antiparallel and coplanar orientation with the dipole moment vector of one monomer directed up and the other one directed down (up− down orientation) (f), (g) D2 (dimer of M2) after optimization in up−up (f) and up−down (g) orientation. (h) Pictorial representation of the D1 dihedral angles d1, d2, and d3. (i) Pictorial representation of the D2 dihedral angles d4, d5, d6, and d7.

starting from an initially parallel and coplanar orientation of the repeat units (Figure 1f) the optimized structure shows a smaller deviation from parallelism, and the resulting dipole moment now is higher: 22.2 D (ωB97X-D/6-31+G(d,p)). On the other hand, the optimized structure for an initially antiparallel coplanar conformation of the two repeats for D2 (Figure 1g) results into a perfect antiparallel coplanar conformation for the D


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molecules shown in Figure 2, abbreviated as D1, D2, D3, and D4 with molecules D1 and D2 being the dimers shown already in Figure 1. Molecules D3 and D4 were constructed by adding one more and two more phenyl rings between the repeat units of molecule D1, respectively, as shown in Figure S13a. The molecules were optimized starting from initially parallel and antiparallel orientations. From the results shown in Figure 2a, series D, a pattern that maximizes the dipole moment vector is revealed. The number (n) of phenyl rings between the dipoles, i.e., in the “spacer”, must follow the equation n = 2k + 1, where k ∈ N; hence n must be an odd number. Here, the number k can adopt the zero value in the absence of steric hindrance. Moreover, the dihedral angles between the phenylene rings must vary as g+, g−. An odd number of rings ensures that (2k + 1)g+ = (2k + 1)g−. Additionally, this conditional pattern demands a parallel orientation. If, on the other hand, the orientation between the two dipoles is antiparallel, the same condition can result in a zero dipole moment (Figure 2b, series D, n = 3). Effect of Dipole Strength. It must be mentioned that for molecules of series D there is steric hindrance for these phenyl rings adjacent to the group bearing the dipole (M0 unit). In order to explore the effect of dipole strength, we constructed three additional series of molecules. First, starting from the D series, we replaced the cyano groups with ethynyl groups, and a new set of four molecules abbreviated as CCB1 up to CCB4 was generated (Figure S13b). Steric hindering was further reduced by adopting simple poly phenylene rings carrying cyano groups as shown in Figure S13c (abbreviated as CNn, n = 1−5) and fluoro groups (Figure S13d abbreviated as Fn, n = 1− 5, n denoting the number of phenyl rings between the dipoles). All molecules were built in initially parallel and antiparallel orientations (in Figure S13 only conformations with initially parallel orientation are shown). In total, 35 new optimizations took place including the monomers of CCB (3.9 D), CN (7.4 D), and F (2.8 D). The results (Figure 2a, series CCB, CN, F) fully corroborate the pattern revealed previously. In general, for molecules with initially a parallel orientation there is an odd− even effect in the dipole moment with an odd number of phenylene rings between the dipoles, resulting in the higher dipole moment. For the CN series of molecules and n = 1 the initially parallel orientation after optimization ended in a conformation far from a parallel arrangement (the dihedral angle between the dipoles was 110°) with a resulting dipole moment of 8 D (instead of 14 D). This can be explained since upon substitution the rotational barriers of biphenyl are dramatically increased due to steric effects. Interestingly, for an initially antiparallel orientation and an even number of rings (an even number of rings satisfies the condition: g+ = 2k + 1 and g− = 2k where k ∈ N, ≠ 0) a dipole moment is always present. Moreover, steric hindrance further increases the dipole moment of the dimer (Figure 2b, series D, CCB, and CN, n = 2, 4). In conclusion, a polymer bearing dipoles perpendicular to the backbone obtains a maximum value of dipole moment perpendicular to the polymer axis, when the following criteria are met: (1) A monomer carrying a dipole moment perpendicular to the backbone. The stronger the dipole moment of the monomer and the higher the degree of polymerization in the polymer, the higher the resulting dipole moment. (2) Dipoles must be oriented parallel to each other. Deviation from parallel arrangement, defined as the dihedral angle between the two dipoles, must be at minimum to obtain

Figure 2. Calculated dipole moments as a function of the number of phenylene rings between the dipoles initially in parallel (a) and antiparallel (b) orientation for the shown molecules (right). The number (n) of phenyl rings between the dipolar units is also indicated. Molecules were optimized employing DFT-ωB97X-D level of theory and 6-31+G(d,p) basis set.

two repeat units, and the dipole moment is now close to zero, i.e., 0.2 D (ωB97X-D). The rotational barriers about inter-ring bonds as predicted form the potential energy scan for D1 are reported in Figure S12. The calculated energies for the two conformers of D1 (Figure 1d,e) and D2 (Figure 1f,g) reveal that the antiparallel orientation has a somewhat lower energy for both levels of theory. The highest barriers are of the order of ∼4−5 kcal/mol. Evidently, the value of the dipole moment for such monomers/ dimers can be tuned by the small rotational barriers in the gas phase. Whether this is still possible in the solid state will be examined below with respect to the DS and NMR results. Computational Structural Aspects. The pictorial representation of the dihedral angles d1, d2, d3 and d4, d5, d6, d7 is given in Figures 1h and Figure 1i for D1 and D2, respectively. The DFT- ωB97X-D/6-31+G(d,p) optimized values of the dihedral angles for (a) D1 (initially parallel and coplanar) shown in Figure 1d are d1 = 76, d2 = −46, d3 = 75 and (b) D1 (initially antiparallel and coplanar) shown in Figure 1e are d1 = 93, d2 = −42, d3 = −70. The DFT- ωB97X-D/6-31+G(d,p) optimized values of the dihedral angles for (c) D2 (initially parallel and coplanar) shown in Figure 1f are d4 = 67, d5 = −43, d6 = 42, d7 = −85 and (d) D2 (initially antiparallel and coplanar) shown in Figure 1g are d4 = 86, d5 = −43, d6 = 42, d7 = −86. The backbone axis does not follow a straight line as shown in Figure 1d−g (two black rectangles at the bottom for each case) because of steric hindrance stemming from the methyl groups attached to the nitrogen atoms of the fivemembered rings. These nitrogen atoms adopt a trigonalpyramidal geometry, and the ring is not planar per se. As a result, the backbone conformation is banana- and worm-like for the parallel and antiparallel conformations, respectively. These findings will be discussed in light of the structural investigation below. It will also appear that the nonplanarity of the fivemembered rings has consequences on the dynamics (DS and NMR). Effect of Dipole Separation. In a subsequent step, we explored the effect of spacer between two repeat units bearing a high dipole moment. This is synthetically challenging yet computationally feasible. To this end, we constructed a series of E


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Figure 3. (a) WAXS curves obtained from P1 shown for different temperatures on heating and subsequent cooling. (b) Intensity contour plots. The arrows indicate heating and cooling runs. (c) Diffraction pattern at 423 K. Arrows indicate position of peaks corresponding to intermolecular and intramolecular distances and π−π stacking. (d) Temperature dependence of the corresponding distances.

Notably, the latter peak has a correlation length ξ ∼ 9 nm as extracted from the peak width, Δq (ξ = 2π/Δq), suggesting that the whole chain is correlated intramolecularly. This suggests a rather rigid configuration of the backbone in P1. On the other hand, P2 is crystalline with several intense reflections. The correlation length extracted from the peak width, Δq, corresponding to the first intense reflection, now amounts to ∼105 nm, i.e., much higher than in P1. Furthermore, the P2 WAXS patterns are anisotropic (Figure S15), revealing some degree of chain orientation. Subsequently, we discuss mainly the dynamics in the rigid-amorphous polymer P1. Dynamics. The rotameric transitions of dipoles are best reflected in the dielectric relaxation of chains containing dipoles oriented perpendicular to the backbone. In addition, dielectric spectroscopy is sensitive even to small-amplitude fluctuations (librations) of dipoles in the solid state. Figure 4 provides the dielectric permittivity and loss curves of the rigid-amorphous P1 at some temperatures. It depicts two broad processes: a faster process of low dielectric strength followed by a slower process with a higher strength. The temperature dependence of the dielectric strength, Δε, and of the shape parameters is shown in Figure 5. It depicts processes with a broad distribution of relaxation times especially from the low-frequency part of the distribution. In addition, the slower process carries most of the dielectric strength. Information on the dipole−dipole orientation correlations within the functionalized poly-p-phenylenes can be extracted by studying the dielectric strength of the slower process. The static dielectric permittivity of polar liquids with short-range interactions between molecules has been the subject of the Kirkwood−Fröhlich theory.12 The theory considers an infinite

additivity of dipole vectors. (3) Calculated dipole moments show an odd−even effect as a function of the phenylene rings used as spacers between the dipolar units. For an initially parallel orientation the dipole moment is maximized for an odd number of phenylene rings. Under this premise the dihedral angles between phenylene rings satisfy n(g+) = n(g−). (4) Upon an initially antiparallel orientation and an even number of phenylene rings between the dipolar units a dipole moment is always obtained, the value of which can be maximized by steric effects. This is true provided that in the polymer dihedral angles between three consecutive dipoles now follow the g+ = g− pattern. If this criterion is not satisfied, cancellation between dipole vectors can occur. A pictorial representation of a trimer where adjacent dipoles are set initially antiparallel is given in Figure S14. Self-Assembly. In the gas phase the relatively small rotational barriers allow for rotameric “transitions” between different conformers. However, in the solid state rotational barriers can increase as a result of intermolecular interactions and possibly increasing steric hindrance. These dynamic features may also reflect on the structure. The self-assembly in the two polymers, P1 and P2, studied by X-ray diffraction is discussed respectively in Figure 3 and Figure S15. The diffraction pattern of P1, shown in Figure 3a, consists of several broad reflections that are characteristic neither of an amorphous polymer nor of a typically crystalline polymer. From the analysis of the temperature dependence of the positions of the most intense peaks (Figure 3d) we assign the first peak to interchain distances (with a thermal expansion coefficient of 2.4 × 10−4 K−1) and the second peak, that is nearly independent of temperature, to intramolecular distances. F


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The relaxation times at maximum loss of the two processes in P1 are depicted in the usual activation representation (Figure 6). The figure depicts two dielectrically active processes with

Figure 4. Dielectric permittivity and loss curves of P1 shown at some selected temperatures. Solid lines represent the result of a fit to a summation of two Havriliak−Negami processes in addition to conductivity and electrode polarization contributions from lower temperatures. Dash-dotted and dashed lines indicate the faster and slower processes, respectively, at 323.15 K.

Figure 6. Arrhenius relaxation map for the faster (squares) and slower (circles) processes. The horizontal gray area depicts the characteristic frequency range of the NMR experiment probing dipolar couplings.

similar temperature dependence of their relaxation times. The relaxation times of the faster and slower processes conform to an Arrhenius temperature dependence according to

continuum of dielectric permittivity, ε′S, and within this a spherical region containing N elementary dipoles that are treated explicitly. Then the dielectric permittivity can be expressed as μ2 N 1 Δε = ε′S − ε∞ = Fg 3ε0 kBT V

⎛ E ⎞ ⎟ τ = τ0 exp⎜ ⎝ RT ⎠

(4)

with τ0 = 2 × 10−16 s and an activation energy, E, of 20 ± 1 kcal/mol for the faster process, and with τ0 = 6 × 10−14 s and an activation energy of 23.3 ± 0.2 kcal/mol for the slower process. Both dependencies are at variance from a stronger Tdependence (i.e., of the Vogel−Fulcher−Tammann type) found in amorphous polymers associated with the freezing of segmental dynamics at the liquid-to-glass temperature (Tg). The Arrhenius τ(T) dependence and the absence of a Tg in the DSC traces of compound P1 are suggestive of rather localized dipolar dynamics. Furthermore, the obtained activation energies are much higher than the activation barriers found in the gas phase (DFT). Clearly, rotameric transitions accessible in the gas phase are suppressed in the solid state. The rotational dynamics of polymer chains containing dipoles oriented perpendicular to the backbone has been treated theoretically. The theory considered an extension of Glauber’s model for the time-dependent statistics of the Ising chain.26 The model employs an infinitely long array of equally spaced, rigid, permanent electric dipoles oriented at right angles

(3)

Here, F = ε′S(ε∞ + 2)2/(3(2ε′S + ε∞)) is the local field, N/V is the number density of dipoles expressed as (ρ/M)NA, where ρ is the mass density (here we employ ρ ∼ 1.158 g/cm3, corresponding to the crystal structure of compound 4, Table S9) and M is the molar mass, μ is the dipole moment, and g is the Kirkwood−Fröhlich dipole orientation correlation function. The latter is defined as the ratio of the mean-squared dipole moment measured in a dense system divided by the same quantity obtained in a noninteracting case, i.e., in the gas phase, g = μ2/μgas2. Knowledge of the gas phase dipole moments (DFT) results in the dipole orientation correlation function for the slower dielectric process (TΔε ∼ 350 K, using μgas = 4.4 D) with g ∼ 0.3. This value is suggestive of a destructive interference of dipoles with an antiparallel orientation. This is in agreement with the DFT results that have shown that the conformer with the lowest energy corresponds to the one with the antiparallel orientation of dipoles.

Figure 5. Temperature dependence of the dielectric strength corrected for the temperature, TΔε (left), and of the HN parameters, m (filled symbols) and mn (open symbols), corresponding to the faster (red) and slower (blue) processes. G


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Macromolecules to a linear axis and with rotational freedom (e.g., rotamers).27,28 The theory further explored the effects of chain curvature and of a finite chain length. Following Glauber, interactions within the chain were included by means of a time-dependent angular correlation function. Interactions of dipoles with the surrounding (solution or in bulk) were introduced by a thermal bath. The model predictions were based on three important simplifications: (i) interactions between adjacent dipoles were based on a 2-fold potential, (ii) interactions were considered only between adjacent chain elements, and (iii) concerted motions involving the simultaneous reorientation of two or more chain elements were excluded. Cross-correlation terms were found to dominate the dielectric response. Under these assumptions the model predicts a bimodal and asymmetric dielectric function. The fast time scale relates to the time required to establish the equilibrium angular correlation function for the rotators within the chain. This time scale depends on the potential function for the interaction between neighboring rotamers and on the temperature. The slower time scale reflects motion of correlated chain segments. The actual time scale depends on the average size of the correlated unit and on the viscosity. These theoretical predictions are in agreement with the bimodal dielectric function found in experiment; however, the theory does not provide explicit expressions for the temperature dependence of relaxation times for the two modes. More information on the geometry of molecular motions associated with the dynamic processes can be obtained from solid-state NMR experiments. The 1H MAS NMR spectra of P1 recorded at variable temperatures (Figure 7) suggest high

dipole coupling constant for a static 1H−13C spin pair of 21.0 kHz using the relation S=

1 (3 cos2 θCH(t ) − 1) 2

=

⟨DCH(t )⟩t DCH,static

(5)

The results from this investigation are included in Figure 7 at 323 and 393 K. At both temperatures there is a gradient of mobility, from very mobile C−H bonds at the methyl and outer methylene positions to nearly immobile phenylene groups in the backbone. Notably, even at 393 K, there is very little mobility of the phenylene rings. These groups, since they do not carry a dipole moment, are invisible in DS. On the other hand, both the 1H MAS spectra and the site-specific heteronuclear rotor-encoded dipolar sideband patterns suggest some local molecular fluctuation of the N-methyl sites at the nonplanar five-membered rings. Therefore, considering both the NMR and DS results together, we can attribute the faster DS process to a librational motion of the highly polar 2,2diheptyl-1,3-dimethyl-2,3-dihydro-1H-benzo[d]imidazole-5,6dicarbonitrile group reorienting only the nonplanar fivemembered ring. The slower DS process, bearing the highest dielectric strength (Figure 5), may be associated with larger amplitude motions and/or correlated motions of the polar groups. This process will shift into the NMR frequency window (shown in gray in Figure 6) only at very high temperatures not accessible to our NMR equipment. Overall, molecular packing determines the dynamics in polyp-phenylenes bearing ultrastrong dipoles perpendicular to the backbone. Although DFT calculations in the gas phase of the dimers suggested rather low rotational barriers with conformers (rotamers) that are accessible at ambient temperature, in the solid state the combined results from the NMR and DS experiments have shown otherwise. In the solid state, it is the packing through intermolecular forces such as van der Waals, π−π, and dipole−dipole interactions, the latter from dipoles with antiparallel orientations that dictate the dynamics. DS and solid-state NMR techniques revealed a dynamically rigid polymer P1 with only some librational motion of the dipolar group at ambient temperature. In addition, DS identified a slower process which carries most of the dielectric strength associated with larger amplitude motions and/or possibly correlated motions of the polar groups. These “dynamic” results are in excellent agreement with the structural investigation that demonstrated a relatively rigid backbone.

Figure 7. (left) 1H MAS spectra at 850 MHz 1H Larmor and 25 kHz MAS spinning frequency shown at two temperatures. (right) Sitespecific local order parameters obtained from dipolar sideband patterns at two temperatures: T = 323 K (in black) and T = 393 K (in red).

IV. CONCLUSION The synthesis of polymers bearing strong dipoles perpendicular to the chain enabled the first investigation of the dynamics of type B polymers in the gas and solid state respectively by DFT calculations and DS−1H NMR. The computational study revealed that these molecular structures can be fine-tuned as to maximize their dipole moment. The choice of the repeat unit, the degree of polymerization, the selection of a substituent that imposesthrough steric effectsa specific dihedral angle, the sign (g+ or g−) of the dihedrals between the phenylene rings, and the number of phenylene rings separating the dipolar units constitute a fine molecular rheostat that can engineer type B polymers with ultrastrong dipole moments. Calculated dipole moments show an odd−even effect as a function of rings between the dipolar units. The highest barriers encountered in DFT were 4−5 kcal/mol.

rigidity with only very weak thermal fluctuations up to T = 403 K. Only at the highest temperatures accessible to the NMR equipment is some line narrowing due to molecular mobility of the N-methyl moiety observed. In order to gain more information on the molecular mobility, we have recorded a series of site-specific heteronuclear rotor-encoded dipolar sideband patterns, using the rotor-encoded polarization transfer (REPT-HDOR) technique.29,30 In this kind of experiment, the local molecular motion is monitored through the effective 1 H−13C dipole−dipole coupling (DCH), corresponding to the time-averaged value of the anisotropic heteronuclear dipolar Hamiltonian, which spatial part is described by a second-order Legendre polynomial. The measured dipole−dipole couplings can be related to an effective order parameter using the dipole− H


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(8) Sy, J. W.; Mijovic, J. Reorientational dynamics of poly(vinylidene fluoride)/poly(methyl methacrylate) blends by broad-band dielectric relaxation spectroscopy. Macromolecules 2000, 33, 933. (9) Wudarczyk, J.; Papamokos, G.; Margaritis, V.; Schollmeyer, D.; Hinkel, F.; Baumgarten, M.; Floudas, G.; Müllen, K. Hexasubstituted benzenes with ultrastrong dipole moments. Angew. Chem., Int. Ed. 2016, 55, 3220. (10) Xiao, J.; Zhang, Z.; Wu, D.; Routaboul, L.; Braunstein, P.; Doudin, B.; Losovyj, Y. B.; Kizilkaya, O.; Rosa, L. G.; Borca, C. N.; Gruverman, A.; Dowben, P. A. The Interface bonding and orientation of a quinonoid zwitterion. Phys. Chem. Chem. Phys. 2010, 12, 10329− 10340. (11) Siri, O.; Braunstein, P. Unprecedented zwitterion in quinonoid chemistry. Chem. Commun. 2002, 208−209. (12) Barder, T. E.; Walker, S. D.; Martinelli, J. R.; Buchwald, S. L. Catalysts for Suzuki−Miyaura coupling processes: scope and studies of the effect of ligand structure. J. Am. Chem. Soc. 2005, 127, 4685−4696. (13) Littke, A. F.; Fu, G. C. Palladium-catalyzed coupling reactions of aryl chlorides. Angew. Chem., Int. Ed. 2002, 41, 4176−4211. (14) Kremer, F.; Schoenhals, A. Broadband Dielectric Spectroscopy; Springer-Verlag: Berlin, 2002. (15) Floudas, G.; Paluch, M.; Grzybowski, A.; Ngai, K. L. In Molecular Dynamics of Glass-Forming Systems; Springer: Berlin, 2011. (16) Havriliak, S.; Negami, S. A complex plane representation of dielectric and mechanical relaxation processes in some polymers. Polymer 1967, 8, 161. (17) Saalwächter, K.; Graf, R.; Spiess, H. W. Recoupled polarizationtransfer methods for solid-state1H-13C heteronuclear correlations in the limit of fast MAS. J. Magn. Reson. 2001, 148, 398−418. (18) Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615. (19) Ditchfield, R.; Hehre, W. J.; Pople, J. A. Self-consistent molecular-orbital methods. ix. An extended gaussian-type basis for molecular-orbital studies of organic molecules. J. Chem. Phys. 1971, 54, 724. (20) Salzner, U.; Aydin, A. Improved prediction of properties of πconjugated oligomers with range-separated hybrid density functionals. J. Chem. Theory Comput. 2011, 7, 2568. (21) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648. (22) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785. (23) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 1980, 58, 1200. (24) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 1994, 98, 11623. (25) Gaussian 09, Revision A.02: Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian, Inc.: Wallingford, CT, 2016. (26) Glauber, R. J. Time-dependent statistics of the ising model. J. Math. Phys. 1963, 4, 294.

In the solid state there is a 5-fold increase in the barriers, and as a consequence full rotameric transitions between rotational isomers are suppressed. Dielectric spectroscopy further identified two modes both with Arrhenius temperature dependence and activation energies of 20−23 kcal/mol. Results from DS and site-specific NMR techniques taken together attribute the faster process to a libration motion of the highly polar group reorienting only the nonplanar five-membered ring and the slower process to larger amplitude and/or correlated motions of the polar groups. These “dynamic” results are in excellent agreement with the structural investigation that demonstrated a relatively rigid backbone. Overall, type B polymers are structurally rigid and have unusually sluggish dynamics.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00215. NMR spectra, high-resolution mass spectroscopy, MALDI-ToF spectra, GPC results, details of DFT calculations, and WAXS results of P2 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: gfl[email protected] (G.F.). *E-mail: [email protected] (K.M.). ORCID

Jakob Wudarczyk: 0000-0003-1214-5277 Klaus Müllen: 0000-0001-6630-8786 George Floudas: 0000-0003-4629-3817 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The computations in this paper were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University. We thank Prof. T. Kaxiras for the cluster availability and for several suggestions.

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REFERENCES

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