Local Chain Alignment via Nematic Ordering Reduces Chain

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

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Local Chain Alignment via Nematic Ordering Reduces Chain Entanglement in Conjugated Polymers Renxuan Xie,† Melissa P. Aplan,† Nicholas J. Caggiano,† Albree R. Weisen,† Tang Su,‡ Christian Müller,§ Mo Segad,∥ Ralph H. Colby,*,†,‡,∥ and Enrique D. Gomez*,†,‡,∥ †

Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 41296 Göteborg, Sweden ∥ The Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States Macromolecules Downloaded from pubs.acs.org by UNIV OF OTAGO on 12/15/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: Chain entanglements govern the dynamics of polymers and will therefore affect the processability and kinetics of ordering; it follows that through these parameters chain dynamics can also affect charge transport in conjugated polymers. The effect of nematic coupling on chain entanglements is probed by linear viscoelastic measurements on poly[N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2thienyl-2′,1′,3′-benzothiadiazole)] (PCDTBT) and poly((9,9-dioctylfluorene-2,7-diyl)-alt-(4,7-di(thiophene-2-yl)-2,1,3-benzothiadiazole)-5′,5″-diyl) (PFTBT) with varying molecular weights. We first verify the existence of nematic phases in both PFTBT and PCDTBT and identify nematic−isotropic transition temperatures, TIN, between 260 and 300 °C through a combination of differential scanning calorimetry, polarized optical microscopy, temperature-dependent X-ray scattering, and rheology. In addition, both PCDTBT and PFTBT show a glass transition temperature (Tg) and TIN, whereas only PFTBT has a melting temperature Tm of 260 °C. Comparing the molecular weight dependence of TIN with theoretical predictions of nematic phases in conjugated polymers yields the nematic coupling constant, α = (550 ± 80 K)/T + (2.1 ± 0.1), and the long-chain limit TIN as 350 ± 10 °C for PFTBT. The entanglement molecular weight (Me) in the isotropic phase is extracted to be 11 ± 1 kg/mol for PFTBT and 22 ± 2 kg/mol for PCDTBT by modeling the linear viscoelastic response. Entanglements are significantly reduced through the isotropic-to-nematic transition, leading to a 10-fold increase in Me for PFTBT and a 15-fold increase for PCDTBT in the nematic phase.

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Thus, measurements of the glass transition temperature,12−14 tie-chain density,7,15 and entanglement molecular weight16 are crucial to eventually connect the chemical structure to macroscopic properties. Furthermore, entanglements restrict chain diffusion, thereby affecting the polymer response to processing conditions. The diffusion coefficient of entangled flexible chains scales with the reciprocal square of the chain length, whereas the diffusion coefficient of unentangled Rouse chains scales with the reciprocal of chain length, suggesting more constrained chain motion once chains entangle.17 Efforts to enhance crystallization or phase separation in multicomponent systems through solvent or thermal annealing will therefore be limited by the molecular weight in a way that is connected to the entanglement strand length. In addition, depending on the kinetics of crystallization, chains may or may not have enough time to reptate out of existing entanglements in the melt before

INTRODUCTION Conjugated polymers often possess a unique set of properties that are ideal for flexible and stretchable electronics. One promising possibility is that of highly stretchable conductors,1−3 where the modulus likely needs to be on the order of 1 MPa or lower so that it can be easily deformed under stress. But below the glass transition temperature, the moduli of conjugated polymers are ∼1 GPa.4 At higher temperatures, the modulus decreases to ∼10 MPa if the morphology is dominated by crystals interconnected by tie chains in a semicrystalline structure.4 Above the melting temperature or the glass transition temperature for noncrystalline polymers, the entropic elasticity of entangled polymer chains leads to a modulus of ∼1 MPa if the chain length significantly exceeds the entanglement strand.4 Although there have been many reports that measure the moduli of conjugated polymers by tensile tests,5−9 buckling tests of thin films,5,10,11 and oscillatory shear rheometry,12 the lack of knowledge regarding the intercrystalline structure (tie chains) and chain dynamics (glass transition and chain entanglements) precludes the prediction of mechanical properties of conjugated polymers. © XXXX American Chemical Society

Received: August 26, 2018 Revised: November 8, 2018

A

DOI: 10.1021/acs.macromol.8b01840 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules assembling on a crystalline lattice.18 As crystals grow, chain entanglements (including both transient and permanently trapped entanglements) reside between nearby crystals, affecting the final crystal size and crystallinity, and ultimately affect the probability of forming tie chains. In this way, chain entanglements can affect tie-chain densities and potentially macroscopic charge conduction. Despite the importance of chain entanglements in conjugated polymers, there are few attempts in the literature to measure the entanglement strand length. On the basis of the molecular-weight dependence of specific viscosity in dilute solution for regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT), a molecular weight of 35 kg/mol is found to demark the transition between two power law exponents.7 The authors attributed this molecular weight as two times the entanglement molecular weight.7 But at dilute concentrations near 0.1 wt % that are far below the overlap concentration, only isolated chains are expected. As such, the entanglement molecular weight identified in solution needs to be scaled by the polymer concentration, leading to unphysical values for the entanglement molecular weight below that of the monomer repeat unit. Other work based on molecular dynamics simulations has predicted the entanglement length of P3HT to be 50 to 60 monomers (i.e., 8 to 10 kg/mol).19 In principle, the entanglement length can be derived from the rubbery plateau modulus in the melt state by linear viscoelastic rheology.17 But liquid-crystalline phases (e.g., nematic and smectic phases), which are ubiquitous in conjugated polymers,20−22 should affect the rheological response and thereby potentially confound measurements of the entanglement moduli. Specifically, although the weakly first-order nature of the nematic− isotropic transition has been unequivocally proven by the small discontinuities of order parameter,23 enthalpy, and specific volume,24 many efforts are still being devoted to understand and quantify the strength of the nematic interaction;25−27 however, no studies relate this to chain entanglement yet. So, we adapt our previous definition of the nematic coupling constant as an interaction strength parameter that controls the aligning potential energy, which is a part of the dimensionless Helmholtz free-energy formulation (i.e., F/kT),20 to quantify the nematic coupling parameter from experimentally measured nematic−isotropic temperatures for polymers of various molecular weights. The effect of nematic ordering on the chain entanglement is then elucidated with rheological characterization on multiple molecular weights of conjugated polymers. In this work, we quantify the entanglement molecular weight of two conjugated polymers in their isotropic phase with accessible liquid-crystalline phases, poly[N-9′-heptadecanyl2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole)] (PCDTBT) and poly((9,9-dioctylfluorene)-2,7-diyl-alt[4,7-bis(thiophen-5-yl)-2,1,3-benzothiadiazole]-2′,2″-diyl) (PFTBT). As shown by polarized optical microscopy, X-ray scattering, and rheology, PCDTBT and PFTBT both exhibit thermotropic nematic phases, whereas only PFTBT can crystallize. The temperature-dependent nematic coupling constant, α(T), is estimated for PFTBT based on the molecular-weight dependence of the nematic−isotropic transition temperature. Entanglement molecular weights for both PFTBT and PCDTBT are obtained by fitting the melt rheology data in the isotropic phase with a tube (reptation) model for loosely-entangled linear polymers (tube diameter > Kuhn length). When the polymers access the nematic phase

such that chains become locally aligned, chain entanglements drop by approximately 10-fold, evidenced by the shortening of the rubbery plateau, when compared with the isotropic phase. We thus explore the role of nematic order on entanglement moduli and macroscopic mechanical properties.

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MATERIALS AND METHODS

Synthesis and Molecular-Weight Distribution. PFTBT and PCDTBT with chemical structures shown in Figure 1a,b were synthesized by a Suzuki polycondensation reaction. PCDTBT and various molecular weights of PFTBT were made by controlling the molar ratio of monomers, 9-(9-heptadecanyl)-9H-carbazole-2,7diboronic acid bis(pinacol) ester (CD) or 9,9-dioctylfluorene-2,7-

Figure 1. Chemical structure of (a) PFTBT and (b) PCDTBT. (c) Molecular-weight distributions of PFTBTs and PCDTBT obtained by high-temperature 1,2,4-trichlorobenzene GPC at 150 °C using universal calibration that relies on refractive index and viscometer detectors. diboronic acid bis(1,3-propanediol) ester (F) and 4,7-bis(2-bromo-5thienly)-2,1,3-benzothiadiazole (TBT). According to the Carothers equation, the number-average molecular weight (Mn) can be

Table 1. Characterization of PFTBTs and PCDTBT Based on GPC with Universal Calibration and Prediction by Carothers Equation polymer predicted Mn (kg/mol)a Mn (kg/mol) Đ = Mw/Mn Mw (kg/mol)

PFTBT 1 PFTBT 2 PFTBT 3

PFTBT 4 PCDTBT

2.4

4.8

11.0

15.5

10.0

7.9 5.53 44.2

9.3 3.93 36.5

11.7 4.50 52.6

16.0 4.23 67.8

13.7 3.72 51.1

a

Prediction by Carothers equation assuming complete reaction of the limiting reagent monomer and linear chains.

B


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Macromolecules predicted by the molar ratio of monomers as summarized in Table 1. All batches were synthesized by the same published procedure,12 adjusting only the amount of TBT added to control the molecular weight. Four different molecular weights of PFTBT from low to high were labeled as PFTBT 1, PFTBT 2, PFTBT 3, and PFTBT 4. Hightemperature gel permeation chromatography (GPC) (model: Agilent PL-GPC 220) coupled to a sample preparation system (model: Agilent PL-SP 260VS) at 150 °C in 1,2,4-tricholorobenzene was used to determine the molecular-weight distribution of PFTBTs and PCDTBT after complete dissolution overnight and filtering. This high-temperature GPC is equipped with a refractive index detector that measures the mass concentration and a viscometer detector that measures the specific viscosity as a function of the elution time. Thus the molecular-weight distributions for PFTBTs and PCDTBT are determined by the universal calibration method. But in Table 1, the predicted Mn values by the Carothers equation for PFTBT 1 and PFTBT 2 appear to be significantly smaller than GPC results. Nevertheless, we speculate that their true molecular weights might be substantially larger than both methods, as discussed later in the Chain Entanglement in the Isotropic Phase section. This may be caused by specific polymer adsorption onto the packing particles in the GPC column. In Figure 1c, all PFTBTs show large dispersities with bimodal distribution, whereas PCDTBT also shows large dispersity but with unimodal distribution. Weight-average molecular weight (Mw) and dispersities (Đ) are summarized in Table 1. Differential Scanning Calorimetry. PFTBT and PCDTBT are very similar in their repeat unit structure, except for the point where the side chains were attached, and this might be the reason why PFTBT can crystallize and melt at the characteristic temperatures, whereas PCDTBT remains completely noncrystalline at all temperatures. This is clearly shown by a combination of techniques in the next section, including differential scanning calorimetry (DSC), temperature-dependent wide-angle X-ray scattering, and rheology. Specifically, polymer samples for DSC were sealed in aluminum hermetic pans inside a nitrogen-filled glovebox (H2O < 1 ppm and O2 < 10 ppm). The heat flow data were then measured by a TA Instruments Q2000 DSC under a N2 environment by scanning from 50 to 300 °C at a rate of 20 °C/min after isothermal annealing at 194 °C for 30 min, during which PFTBT did crystallize and PCDTBT remained noncrystalline. Rheometry. Samples for shear melt rheology required molding into bubble-free pucks with thickness of roughly 1 mm and diameter of 8 mm. To avoid thermal degradation, samples were molded inside a nitrogen-filled glovebox. Heating samples to 290 °C (above any melting temperatures of all of our polymers) under vacuum eliminated air bubbles. Then, ∼1 MPa of pressure was sufficient to compress samples into pucks. Molded polymer pucks were placed between two 8 mm diameter aluminum parallel plates in a straincontrolled ARES-LS rheometer (Rheometric Scientific) and then melted to ensure good contacts by first heating to 300 °C within a nitrogen-purged oven. Isothermal frequency sweep results were first collected with strain amplitude between 0.01 and 0.1 from 300 to 200 °C (−10 °C increment). A strain sweep was run to ensure that the isothermal frequency results were within the linear region, where the shear moduli are independent of the strain amplitude. PFTBTs were then isothermally crystallized at 195 °C for 30 min before the reversibility of the nematic−isotropic transition was checked by ramping temperatures from 195 to 320 °C and back at a fixed frequency of 1 rad/s. Because of the noncrystalline nature of PCDTBT, the isothermal frequency sweep was extended to 90 °C (using 3 mm diameter and 4.5 mm tall aluminum parallel plates below 130 °C to reduce transducer compliance effects) and then followed by a cyclic temperature ramp between 200 and 300 °C. To detect the abrupt transition in entanglement from the isotropic to nematic phase, a multiwave temperature ramp test was implemented for PFTBT 2 from 300 to 240 °C at 2 °C/min with a fundamental frequency of 1 rad/s and harmonics of 2, 4, 7, 14, 27, 52, and 100. This multiwave test allowed data collection at several frequencies simultaneously, which is much faster than a conventional frequency sweep test. It was

done by combining independent strain waves with different frequencies and amplitudes according to the Boltzmann superposition principle.28 X-ray Scattering. The temperature-dependent wide-angle X-ray scattering (WAXS) for both PFTBT and PCDTBT was performed on a Xeuss Xenocs 2.0 apparatus. Temperature was controlled by a Linkam HFSX350 hot stage with maximum operating temperature of 350 °C and was calibrated against an external thermometer. Samples were directly cut from a molded rheology puck into a smaller disk with diameter of 5 mm and thickness of 0.7 mm. The polymer disk was sealed in a melt cell (provided by Linkam) between Kapton windows inside a nitrogen-filled glovebox and then directly attached to the Linkam hot stage. The X-ray beam was generated by a Genix 3D copper source with a wavelength of 1.542 Å and was focused by two sets of scatterless slits to a spot size of 0.8 × 0.8 mm. Sample-todetector distance was set as 153 mm by bringing the detector close to the sample chamber and with the help of an arm extension adapter for the hot stage. The 2D scattering patterns were collected on a hybrid photon counting detector (Dectris Pilatus 3R 200 K-A) and then radially averaged to generate a 1D isotropic scattering profile. Beam stop and other detector null signals were masked and excluded from the sample signal. During the temperature-dependent WAXS experiment, the sample was equilibrated at each temperature for 10 min, followed by a collection time of 10 min. The structural anisotropy of large amplitude oscillatory shear (LAOS) PCDTBT was also examined by 2D wide-angle X-ray scattering at room temperature. The LAOS sample puck was first quenched to room temperature, removed from the plates, and mounted onto the WAXS sample holder. Then, starting at the center of the puck and moving out to the puck edge, 2D WAXS data were collected at different distances away from the center, corresponding to different local strain amplitudes. Finally, to quantify the extent of anisotropy, relative intensity as a function of the azimuthal angle was compared at the interchain backbone spacing for different positions on the sample puck. Optical Microscopy. Polarized optical microscopy (POM) samples were spin-coated from 20 mg/mL of polymer/1,2dichlorobenzene solution at 90 °C at 800 rpm onto a heated quartz substrate. The sample was then placed in a vacuum-tight and nitrogen-filled Instec hot stage for optical imaging by an Olympus BX53 apparatus. Images were acquired both with and without crossed polarizers at temperatures from 40 to 320 °C (+5 °C increment) using a 20× objective lens. Samples were first annealed in the isotropic phase at 300 °C for 5 min to erase any spin-coating history and then cooled to 40 °C, followed by reheating to determine the melting point and the nematic-to-isotropic transition temperature. Temperature control of the Instec hot stage was calibrated with an external thermometer. The intensity of the image was integrated by ImageJ software at each temperature.

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RESULTS Thermal Transitions of PFTBT and PCDTBT. Liquidcrystalline phases are expected in many conjugated polymers because of their stiff backbones. Nematic ordering, which occurs when chains are locally aligned in one direction, is most common. In this section, PFTBT and PCDTBT are proven to form a nematic phase with an accessible isotropic-to-nematic transition temperature (TIN) via a combination of DSC, POM, temperature-dependent WAXS, and linear shear rheology. As the temperature is increased, PFTBT transitions from a glassy state, to semicrystalline, then liquid crystalline, and finally to an isotropic phase. PCDTBT exhibits similar behavior, except without a crystalline phase, forming a nematic glass on cooling. Figure 2 shows second heating scans from DSC for both PCDTBT and PFTBT. As is common for conjugated polymers, features other than crystal melting are subtle and can be challenging to assign. The step changes in heat flow at ∼130 °C are the glass transition temperatures for PCDTBT C


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absorption and focus only on the change in birefringence, the corrected transmitted intensity ratio was calculated as the ratio of normalized intensity under crossed polarizers over that without crossed polarizers, similarly to previously reported methods.29 The derivative of the corrected transmitted intensity ratio is also plotted to highlight the thermal transition temperatures of PFTBT 1. The two separate peaks in the derivative at 245 and 270 °C for PFTBT 1 in Figure 3b correspond to melting and liquid-crystal-to-isotropic transitions, respectively. The small step change in heat flow by DSC in Figure 2 at 293 °C for PFTBT 2 is also identified as the nematic-to-isotropic transition temperature. More details regarding the crystallization of PFTBT and its effect on Tg can be found in previous work.12 Interestingly, PCDTBT does not show any sign of crystallization or melting, and the signature of the nematicto-isotropic transition for PCDTBT at 274 °C by DSC is also much weaker than that of PFTBT 2 (Figure 2). Polarized optical micrographs in Figure 3c show the disappearance of liquid-crystalline texture, as PCDTBT changes from nematic to isotropic at 300 °C. This transition temperature (i.e., TIN) for PCDTBT is identified to be 275 °C as the peak of the derivative of the transmitted intensity with respect to temperature in Figure 3d. DSC and POM show good agreement in locating TIN for PCDTBT. We speculate that perhaps the sp3-hybridized carbon atom, where dioctyl side chains directly attach to fluorene units for PFTBT, may favor a tetrahedral configuration with respect to the backbone and therefore a higher chance of packing on a crystalline lattice when compared with PCDTBT. Alternatively, because the side chains in PCDTBT can rotate freely about the C−N bond, the side chains can introduce more disorder (when compared with PFTBT) at a molecular level that apparently suppresses crystallization.

Figure 2. Second heating scans of PFTBT 2 and PCDTBT at 20 °C/ min after isothermal annealing at 194 °C for 30 min. The glasstransition temperatures (Tg = 133 °C for PFTBT 2 and 129 °C for PCDTBT), nematic-to-isotropic transition temperatures (TIN = 293 °C for PFTBT 2 and 274 °C for PCDTBT), and melting temperature (Tm = 267 °C for PFTBT 2) are identified accordingly on the plot. Data are vertically shifted for clarity.

and PFTBT; the location is confirmed by rheology as discussed in previous work.12 Exothermic cold crystallization peaks are visible around 194 °C (∼70 °C above its Tg), and a sharp endotherm at 267 °C indicates melting of semicrystalline PFTBT 2 into another phase, which is later identified as the nematic phase by WAXS and rheology. Optical micrographs of the semicrystalline state, the liquidcrystalline state, and the isotropic state under crossed polarizers for PFTBT are shown in Figure 3a. The substantial change in color absorption of the polymer is associated with the melting transition, and the disappearance of the “sparkling” texture marks the liquid-crystal-to-isotropic transition. The transmitted intensity of the micrograph was first integrated and normalized to the value at the highest temperature in the isotropic phase. Then, to subtract out the change in color

Figure 3. Optical micrographs under crossed polarizers taken for (a) PFTBT 1 at semicrystalline (150 °C), nematic (250 °C), and isotropic states (290 °C) and for (c) PCDTBT at nematic (150 and 200 °C) and isotropic states (300 °C). Normalized transmitted intensity either with or without crossed polarizers (CPs) as a function of temperature for (b) PFTBT 1 and (d) PCDTBT. Corrected normalized intensity (hollow circles) and its derivative (solid circles) are also shown. Thicker parts of cast films (aggregates or dust particles) appear as the black spots surrounded with a brighter region in both PFTBT and PCDTBT under crossed polarizers. D


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Figure 4. Temperature-dependent wide-angle X-ray scattering of (a) PFTBT 2 and (b) PCDTBT.

Figure 5. Temperature dependence of complex viscosity (η*), storage modulus (G′), and loss modulus (G′′) of (a) PFTBT 2 and (b) PCDTBT at frequency of 1 rad/s and ramp rate of 2 °C/min under oscillatory shear verifies the reversibility of the nematic−isotropic transition.

Table 2. Summary of TIN Values for PFTBT 2 and PCDTBT Obtained from Different Methods, with Heating Rate in Parentheses PFTBT 2 PCDTBT

DSC (°C)

POM (°C)

WAXS (°C)

rheology (°C)

293 ± 1 (20 °C/min) 274 ± 1 (20 °C/min)

271 ± 5 275 ± 5

276 ± 5 276 ± 5

280 ± 5 (2 °C/min) 265 ± 5 (2 °C/min)

a

a

Value for PFTBT 1.

both DSC and POM. In the isotropic phase, only two amorphous halos at around 0.4 and 1.3 Å−1 remain, representing the broad distributions of spacing across the side chains or between backbones, respectively. PCDTBT also displays similar amorphous halos at 300 °C in the isotropic phase (Figure 4b). As temperature decreases below 281 °C, a weak peak emerges at ∼0.4 Å −1 , corresponding to the isotropic-to-nematic transition that closely matches the observations in both DSC and POM. As temperature further decreases, the densification gradually decreases the nematic spacing between the polymer backbones, resulting in larger q for the peak. The nematic peak at 0.4 Å−1 becomes more prominent as temperature decreases until the glass transition (Tg = 129 °C), where further ordering is arrested due to the lack of chain motion. In addition, PCDTBT only exhibits the nematic ordering peak at ∼0.4 Å−1 at lower temperatures and no sign of sharp crystalline diffraction peaks, agreeing with the absence of any melting endotherm by DSC and the sole transition process that is observed by POM. The nematic−isotropic transition for both PFTBT and PCDTBT is further examined by oscillatory shear linear viscoelasticity. In Figure 5, under heating, both PCDTBT and

The type of liquid-crystalline phase for both PFTBT and PCDTBT is identified by X-ray scattering and linear viscoelasticity from melt rheology. 1D WAXS profiles in Figure 4 show a series of peaks indicative of crystalline and nematic peaks for PFTBT and PCDTBT. The crystalline peaks for PFTBT 2 in Figure 4a, after isothermal crystallization at 195 °C for 30 min, persist up to 262 °C, above which the crystal melts into the nematic phase, agreeing closely with Tm of 267 °C by DSC. Labeling each diffraction peak with corresponding crystalline planes is beyond the scope of this work, but the strongest intensity peak at ∼0.4 Å−1 is likely the (100) peak, which corresponds to the spacing between polymer backbones across the side chains. As the temperature increases, thermal expansion of PFTBT causes this peak to shift to slightly lower q, and the intensity of crystalline peaks to decrease due to the gradual loss of crystalline order as Tm is approached. Between 267 and 271 °C, PFTBT shows nematic ordering, where only one periodic spacing between the backbones exists, giving an estimated distance of 14 Å. At even higher temperatures, this peak completely disappears, indicating the full loss of nematic ordering of PFTBT, in agreement with the nematic-to-isotropic transition observed in E


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Macromolecules PFTBT show similar temperature dependence of viscosity and moduli, which can be classified into three regions: (1) the nematic region where viscosity decreases with increasing temperature for Tm < T < 275 °C for PFTBT 2 and T < 260 °C for PCDTBT; (2) the biphasic region where viscosity increases with increasing temperature, that is, 275 < T < 290 °C for PFTBT 2 and 260 < T < 275 °C for PCDTBT; and (3) the isotropic region where viscosity again decreases with increasing temperature, T > 290 °C for PFTBT 2 and T > 275 °C for PCDTBT. Specifically, the apparent increase in complex viscosity (roughly doubled in this case) in the biphasic region is a well-known rheological signature during the nematic-toisotropic transition for various main-chain liquid-crystalline polymers30−36 but not for side-chain liquid-crystalline polymers.37−40 Consequently, the increase in viscosity with temperature in the biphase indicates that the backbones form a nematic phase. In addition, the reversibility of this phase transition is verified by cooling below 300 °C for PFTBT and PCDTBT, eliminating the possibility of chemical degradation via crosslinking as the cause of the increase in viscosity under heating. The only other example that shows reversible thermal stiffening is realized in a specially engineered polymers/ nanoparticle composite system.41 In this composite, the dynamic coupling between the low-Tg polymer matrix and the high-Tg polymer that is previously adsorbed onto silica nanoparticles can be thermally activated, leading to drastic mechanical stiffening upon heating.41 Instead, here the nematic phase has lower average viscosity than that of randomly oriented polymer melts in the isotropic phase due to the faster diffusion along the backbone direction because of nematic ordering.42 The 15 K temperature window of the biphasic region could be associated with the large dispersity of PFTBT 2 and PCDTBT (dispersity index ∼4), because lowermolecular-weight fractions may transform into the isotropic phase before higher-molecular-weight fractions. TIN values obtained by DSC, POM, WAXS, and rheology are compared in Table 2. Reasonable agreement between the different techniques is observed, especially for PCDTBT, and some discrepancy is expected due to differences in heating rate, instrument sensitivity, and molecular weight. The uncertainties of TIN are represented by the temperature step sizes of DSC, POM, and WAXS and by the biphasic region for values obtained from rheological measurements. In addition, the POM study is carried out on the lowest-molecular-weight batch of PFTBT 1 only, whereas other studies are done on PFTBT 2. Large amplitude oscillatory shear (LAOS) in the nematic phase at 250 °C was also implemented to achieve macroscopic alignment probed by ex situ 2D WAXS, thus providing further proof of the nematic phase in PCDTBT. Because of the relatively high Tg of 129 °C and lack of crystallization, the macroscopically aligned morphology is preserved by quenching immediately after LAOS in the nematic phase (Figure S1). By taking advantage of the parallel plate geometry, the extent of anisotropy is examined as a function of local strain amplitude ranging from 0.05 near the center to 0.95 near the edge of a LAOS PCDTBT sample. As shown in Figure 6a, macroscopic alignment is only observed above the critical shear strain amplitude of 0.5. In other words, in the context of spin-coated conjugated polymer films with thicknesses of ∼100 nm, thin films need to be deformed by at least 50 nm tangential to the top surface to align chains in the nematic phase. The 2D

Figure 6. (a) Schematic showing the beam direction for 2D WAXS experiments on large-amplitude oscillatory sheared PCDTBT (250 °C, 1 rad/s, 100% strain for 30 min). 2D WAXS images were obtained at five different positions within the sample puck, corresponding to different local strain amplitudes (γ), as labeled from 0.05 to 0.95. (b) Relative intensity as a function of azimuthal angle (ψ) at q = 0.4 Å−1 shows an increase in anisotropy with local strain, with strong anisotropy for strain amplitude exceeding 0.5.

WAXS pattern exhibits strongly anisotropic intensity in the horizontal direction that is perpendicular to the vertical shear direction for both amorphous halos, which correspond to interchain spacing across side chains (at q ≈ 0.4 Å−1) and between backbones (at q ≈ 1.3 Å−1). This implies that chains are highly aligned parallel to the shear direction. To quantify the extent of anisotropy, scattering intensity is averaged within the range 0.25 < q < 0.45 Å−1 and plotted as a function of azimuthal angle in Figure 6b. The bigger difference between peak and valley intensities indicates stronger anisotropy or larger extent of chain alignment. So, large amplitude oscillatory shear above a critical strain amplitude of 0.5 at 250 °C can promote chain alignment, consistent with a nematic phase in PCDTBT. We quantify the effect of molecular weight on the nematic− isotropic transition temperature for PFTBT using oscillatory shear experiments at the same frequency under cooling from the isotropic to the nematic phase at 2 °C/min, leading to a wider nematic phase window than seen in heating. The isotropic-to-nematic transition temperatures (TIN) probed by rheology for PFTBTs with different molecular weights are shown in Figure 7a. Under cooling, the complex viscosities for all PFTBTs decrease significantly when transforming from the isotropic (or biphasic region) to the nematic phase, and the TIN is located as the temperature that shows a local minimum F


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Figure 7. (a) Isotropic-to-nematic temperature (TIN) is identified as the local minimum of complex viscosity under cooling at 2 °C/min and 1 rad/s for different molecular weights of PFTBTs. (b) Number-average degree of polymerization (N) dependence of TIN is fitted by eq 1 such that TIN in the long-chain limit is extrapolated to 350 °C for PFTBT.

can be extracted by fitting the experimental data. Thus we obtain the nematic coupling constant for PFTBT as

in complex viscosity. The isotropic phase is not fully reached within the experimental temperature limit for the two higher molecular weight PFTBTs (PFTBT 3 and PFTBT 4). Any temperature higher than 320 °C, even in a nitrogen-filled oven, might lead to significant degradation of the alkyl side chains. These TIN values located by rheology range from 260 to 300 °C for PFTBT, which are in reasonable agreement with previously reported values43 from noncrystalline PFTBTs from DSC and POM; although, discrepancies exist, perhaps due to differences in molecular-weight characterization methods, such as extracting molecular weights from GPC relative to polystyrene standards versus using the universal calibration. To quantify the strength of nematic interactions in PFTBT, we model the molecular-weight dependence of TIN in semiflexible polymers. We locate the critical nematic coupling constant (αc) at TIN, where a given semiflexible polymer undergoes the nematic−isotropic transition, using previously reported αc(lp, N) as a function of both the persistence length (lp) and the chain length (N) obtained from self-consistent field theory calculations.20 For PFTBT, lp of 5.6 nm is estimated by the freely rotating model44 and should be independent of temperature, as previously demonstrated.20 Thus, αc = 1.54/N + 3.0 describes the chain-length dependence of αc. In the long-chain limit (i.e., N ≫ 1), αc reaches an asymptotic value of 3.0 for PFTBT, whereas in the monomer limit (i.e., N = 1), it reduces to 4.54, in agreement with the Maier−Saupe theory for small-molecule rigid rods.20 We then assume that the nematic coupling constant α(T) takes the form of A/T + B previously used by Olsen et al.45 and treat A and B as fitting parameters. This temperature dependence is analogous to that of the Flory−Huggins interaction parameter χ for polymer blends, where the temperature-independent term B has been interpreted as the entropic contribution (here, for nematic formation) and the temperature-dependent term A/T could arise from enthalpic interactions. As a consequence, a relationship between TIN and N can be established by setting α(T) = αc(lp = 5.6 nm, N) at the nematic−isotropic phase boundary, TIN, for PFTBT as follows α(T = TIN) =

α(T ) = (550 ± 80 K)/T + (2.1 ± 0.1) for PFTBT

(2)

where the errors of the fitting parameters are propagated from the standard errors of the slope and the y intercept of the fitted line. For PFTBT, the positive signs for A and B terms may suggest that both the enthalpic and the entropic terms lower the free energy on forming the nematic phase, as expected. The non-negligible presence of the temperature-dependent term (A) perhaps suggests that π−π stacking is enhanced in the nematic relative to the isotropic phase for this class of materials. Furthermore, in the long-chain limit, TIN,∞ is extrapolated to be (350 ± 10) °C. We compare nematic coupling constants for PFTBT with those of other conjugated polymers by recalculating α(T) from the reported dependence of TIN with N (summarized in Figure S2a of the Supporting Information) and our prediction of αc(lp, N).20 The values for poly(2,5-di(2′-ethylhexyloxy)-1,4phenylenevinylene) (DEH-PPV), poly(3-dodecylthiophene2,5-diyl) (P3DDT), and poly(3-ethylhexylthiophene-2,5-diyl) (P3EHT) using persistence lengths of 11 nm for DEH-PPV and 3 nm for P3DDT and P3EHT (equivalent to that of P3HT),46 are given as21,45 α = (92 ± 15 K)/T + (0.50 ± 0.13) for DEH‐PPV

(3)

α = (477 ± 55 K)/T + (0.43 ± 0.03) for P3DDT

(4)

α = (340 ± 23 K)/T + (0.58 ± 0.04) for P3EHT

(5)

We also compare with α(T) for P3HT predicted from simulations run between 600 K and 700 K20 α = (1550 ± 190 K)/T − (1.63 ± 0.30) from simulations for P3HT

(6)

PFTBT appears to have the strongest nematic coupling strength between 300 and 600 K among other conjugated polymers, as shown in Figure S2b of the Supporting Information. All experimentally derived values for the temperature-independent term B are positive, although the value for P3HT from simulations is negative. We expect that the sign of B should be positive such that even at the high-temperature limit the nematic coupling interaction should still exist due to the excluded volume effect of rod-like chain segments. As a consequence, we speculate that the negative sign reported for P3HT might be a consequence of errors associated with the

A 1.54 + B = αc(lp = 5.6 nm, N ) = + 3.0 TIN N (1)

Equation 1 expects a linear relationship between 1/TIN and 1/N, as observed in Figure 7b (i.e., 1/TIN vs 1/N), from which the temperature-dependent and temperature-independent terms of the nematic coupling constant, namely, A and B, G


Article

Macromolecules limited temperature range (600 K to 700 K) studied in simulations. Indeed, the value for A when fitting simulations results to A/T+B is rather large; an overestimate of A would result in poor estimates of B, such as negative values. The temperature dependence of α shown in eq 2 for PFTBT is derived using N from the universal calibration in GPC. As discussed below, we can also extract molecular weights for PFTBT 1 and PFTBT 2 by modeling the viscoelastic response in the isotropic phase using a Branch-on-Branch (BoB) model. Using these molecular weights, we provide a second estimate of α(T) for PFTBT as α(T ) = (123 ± 18 K)/T + (2.8 ± 0.1)

(7)

Although the temperature dependence of the nematic coupling constant shown in eq 7 is weaker than when the molecular weight from the GPC universal calibration is used, α is nevertheless higher than that reported for other conjugated polymers. Further efforts to accurately measure molecular weights of conjugated polymers, such as through static light scattering equipped with a near-infrared laser (i.e., outside the absorption range of PFTBT and PCDTBT solutions), are warranted to validate estimates of α(T). Chain Entanglement in the Isotropic Phase. The concept of chain entanglement originates from the topological constraints imposed by neighboring chains in a flexible polymer liquid. Despite the significant development on the theoretical treatment of “tightly entangled” semiflexible polymers,47−49 experimental verification is lacking. As shown in Figure 8, semiflexible polymers, such as PFTBT and PCDTBT with estimated persistence lengths of ∼5.6 nm using the freely rotating chain model,44,50 display a typical linear viscoelastic response in the isotropic phase of entangled polymer melts with high dispersity. At high frequency, elasticity dominates, such that storage modulus (G′) > loss modulus (G′′), because of topological constraints from the surrounding chains (the rubbery plateau). As the frequency decreases (or at longer time scales), G′′ and G′ cross and then enter the viscous region (G′ < G′′), where many chains have escaped from entanglements. Other high-molecular-weight conjugated polymers, such as regiorandom poly(3-alkylthiophenes),12,51 have also shown clear entanglement plateaus at temperatures above Tg and with molecular weight well above their entanglement molecular weight (Me). To extrapolate Me of linear chains with high dispersity, the master curve is first constructed at a reference temperature of 300 °C using both horizontal shift factors (aT) and vertical shift factors (bT) and then compared with the BoB model developed by Read and Das.52 BoB requires inputs of Me, the Rouse time of an entanglement strand (τe), monomer molecular weight, melt density, and the absolute molecular weight distribution. Melt densities (ρ) are estimated to be 1.2 g/cm3 for both PFTBT and PCDTBT at 300 °C from the sample volume (sample thickness between two 8 mm diameter parallel plates) and the sample mass. The shape of the molecular weight distribution is input as a list of 80 monodisperse linear components and their corresponding weight fractions obtained from GPC, whereas the weightaverage molecular weight (Mw) is treated as a fitting parameter by shifting the entire distribution. We suspect that Mw is underestimated because of the poor match between the viscoelastic data and BoB prediction using Mw determined from the universal calibration, as shown in Figure S3 of the Supporting Information. As a consequence, we fit Me, τe, and

Figure 8. (a) Predictions from the BoB model for the master curve of PFTBT 2 in its isotropic phase at a reference temperature of 300 °C by varying Me while fixing Mw = 115 kg/mol and the shape of the molecular weight distribution and (b) varying Mw while fixing Me = 11 kg/mol and the shape of the molecular-weight distribution. (c) Master curves of PFTBT 1, PFTBT 2, and PCDTBT at the same Tref of 300 °C with the best BoB prediction (fitting parameters shown in Table 3).

Mw, but the shape of the entire molecular-weight distribution remains fixed, and we assume that only linear chains are present to compare to BoB predictions. Figure 8a,b shows attempts to fit to BoB by adjusting Me and Mw, respectively. Roughly, Me controls the crossover modulus level, whereas the ratio, Mw/Me, determines the width of the rubbery plateau, and τe only shifts the whole curve on the log frequency axis. The best fit for PFTBT 2 is achieved with Me = 11 kg/mol and Mw = 115 kg/mol (about a factor of three larger than Mw from universal calibration in Table 1); a H


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Macromolecules

Although comparing BoB predictions to rheology data for PFTBT and PCDTBT suggests the molecular weight is underestimated by GPC even when the universal calibration is used, BoB predictions using the absolute Mw obtained by static light scattering for regiorandom P3HTs are found to nicely describe viscoelastic data (Figure S5 of the Supporting Information). Thus, underestimation of Mw by universal calibration appears specific to PFTBT and PCDTBT. We propose that the disagreement in molecular weight between the GPC universal calibration and BoB fits to rheology data does not necessarily suggest a general failure of the universal calibration but instead perhaps highlights other issues, such as polymer adsorption onto the GPC columns or aggregates that are filtered out during sample preparation because of its relatively poor solubility. Indeed, PFTBT and PCDTBT are less soluble than regiorandom P3HT. Effect of Nematic Phase on Entanglements. When cooling from the isotropic to nematic phase, the rubbery plateau region appears to shorten drastically for PFTBT 2 and PCDTBT, as shown in Figure 9. The entanglement plateau width decreases from between 100 and 1 rad/s to between 100 and 10 rad/s, and the time−temperature superposition (tTs) fails completely at the two temperatures shown because of the clear mismatch in tan(δ) after horizontal frequency shifts, as expected when crossing TIN.

significant mismatch between the BoB prediction and the master curve is observed for 15% or greater deviation in either Me or Mw. By implementing the same analysis method for PFTBT 1 and PCDTBT, both PFTBTs show nearly the same Me (or plateau modulus, Ge = ρRT/Me), as expected, whereas a much larger Me = 22 kg/mol is observed for the isotropic phase of PCDTBT in Figure 8c. The difference in τe between PFTBT 1 and PFTBT 2 can be explained by the difference in their glass transition temperature, as shown in Figure S4 of the Supporting Information. The fitted parameters for BoB are summarized in Table 3. Furthermore, the number of Kuhn Table 3. BoB Fit Parameters for PFTBTs and PCDTBT in the Isotropic Phase at Tref = 300 °C

PFTBT 1 PFTBT 2 PCDTBT

Ge,iso (MPa)a

Me,iso (kg/mol)

Mw by BoB (kg/mol)

τe,iso (s)

0.56 ± 0.06 0.52 ± 0.05 0.26 ± 0.03

10 ± 1 11 ± 1 22 ± 2

135 ± 15 115 ± 15 200 ± 20

1.0 × 10−4 6.0 × 10−4 4.3 × 10−4

a

Ge,iso is directly calculated from Me.

segments within an entanglement strand for PFTBT and PCDTBT is calculated to be 6 and 10, respectively, which is indeed much larger than unity, suggesting that the tube model should be applicable to these conjugated polymers.

Figure 9. (a) Frequency sweep results of PFTBT 2 at 270 °C (in the nematic phase) and at 295 °C (in the isotropic phase) show the effect of nematic ordering on chain entanglements. (b) Frequency sweeps of PCDTBT at 250 °C (in the nematic phase) and at 270 °C (in the isotropic phase). (c) Temperature dependence of the G′, G′′ crossover frequency (ωc), which represents the lower frequency boundary of the entanglement plateau and is obtained by multiwave temperature ramp test from 300 to 240 °C at 2 °C/min at a frequency of 1 rad/s and harmonics of 2, 4, 7, 14, 27, 52, and 100 for PFTBT 2. Black symbols represent the directly measured crossover frequency within the probed region, namely, between 1 and 100 rad/s. Gray symbols represent the extrapolated crossover frequencies based on the second-order interpolation fit to measured multiwave frequency data. The change in the entanglement plateau width is caused by the isotropic-to-nematic transition. I


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Figure 10. (a) Master curves of G′, G′′, and tan(δ) with Tref = 300 °C and (b) horizontal shift factors, aT, and vertical shift factors, bT, in the isotropic phase (red) and the nematic phase (blue) for molten PFTBT 2. Time−temperature superposition (tTs) fails for PFTBT 2 between 285 and 270 °C (not shown) because this is the biphasic region and below 230 °C (not shown) due to crystallization. (c) Master curves with Tref = 300 °C and (d) shift factors in the isotropic phase (red) and the nematic phase (blue) for molten PFTBT 1. tTs fails for PFTBT 1 between 270 and 250 °C (not shown) because this is the biphasic region and below 190 °C (not shown) due to crystallization. The dashed lines in panels b and d are Arrhenius fits to extrapolate activation energies in both the nematic (111 ± 10 kJ/mol for PFTBT 1 and 96 ± 10 kJ/mol for PFTBT 2) and the isotropic phases (203 ± 12 kJ/mol for PFTBT 1 and 211 ± 10 kJ/mol for PFTBT 2).

main-chain nematic polymers. We propose that conjugated polymers, such as PFTBT and PCDTBT, serve as model systems for studies of entanglements in semiflexible polymers. This is further demonstrated next with the construction of master curves in both nematic and isotropic phases. To highlight how entanglement appears to differ in PFTBT and PCDTBT, master curves and the corresponding shift factors aT at a reference temperature of 300 °C are constructed in the nematic and isotropic phases, separately, in Figures 10 and 11. Because of the biphasic nature between nematic and isotropic phases, tTs in this region fails; therefore, those data are excluded from the master curves. In Figures 10b,d and 11b, aT for both PFTBT and PCDTBT in the isotropic phase follows the typical Arrhenius relationship, with extrapolated activation energies of 210 ± 10 kJ/mol for both PFTBTs and 160 ± 8 kJ/mol for PCDTBT. In Figure 11c, because PCDTBT is not crystalline (verified previously by DSC and WAXS) the master curve of a nematic glass is constructed and well described by the Williams−Landel−Ferry (WLF)

To elucidate this change in the width of the entanglement plateau, the G′ and G′′ crossover frequency, ωc, which represents the lower frequency boundary of the plateau or the reciprocal of reptation time scale, is obtained as a function of temperature in Figure 9c using a multiwave temperature ramp test. As PFTBT 2 cools from 300 °C, the rubbery plateau extends to a lower ωc, as expected until 285 °C, where ωc starts to increase by more than one order of magnitude when further cooled to 270 °C. We attribute this drastic increase in ωc (or shortening in entanglement plateau width) for PFTBT 2 to the biphasic region of the isotropic to nematic transition, which is verified by its rheological signature in complex viscosity (Figure 7), POM (Figure 3), and temperature-dependent WAXS (Figure 4). Finally, at lower temperatures, deep in the nematic phase ( Diso > D⊥,42,58 it is likely that the diffusion coefficient for the nematic phase on average might still be larger than that for the isotropic phase, leading to a larger tube diameter on average (dt,nem) and a larger effective Me as observed for PFTBT and PCDTBT. In summary, the existence of a nematic phase in both PCDTBT and PFTBT and the noncrystalline nature of PCDTBT have been demonstrated by a combination of DSC, POM, temperature-dependent X-ray scattering, and linear viscoelastic rheology. Their nematic-to-isotropic transitions have shown unique signatures with these methods, including a small endothermic change in heat flow, decrease in birefringence (or normalized transmitted intensity ratio), disappearance of the nematic ordering scattering peak, and increase in viscosity upon heating. Furthermore, the macroscopic alignment of PCDTBT by LAOS in its nematic phase is verified by the emergence of an anisotropic WAXS pattern for local strain amplitude exceeding 0.5. A TIN for the single molecular weight of PCDTBT studied is identified at 272 ± 5 °C, whereas for PFTBT, TIN ranges from 260 to 300 °C depending on the molecular weight. The molecular-weight dependence of TIN for PFTBT is modeled nicely by a theoretical prediction of nematic phases in conjugated polymers,20 such that the high-molecular-weight limit of TIN is extrapolated to be (350 ± 10) °C and the nematic coupling constant is determined to be α(T) = (550 ± 80 K)/T + (2.1 ± 0.1). The nematic coupling constant of PFTBT appears to be larger than that of other conjugated polymers such as P3HT, P3DDT, P3EHT, and DEH-PPV, suggesting stronger nematic

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge the financial support of the National Science Foundation DMREF program under grant number DMR1629006. We thank Anders Mårtensson for the help with GPC measurements and Scott Milner for insightful comments. We also thank Pat Mather for helpful discussions regarding characterization of liquid crystals.

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REFERENCES

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Local Chain Alignment via Nematic Ordering Reduces Chain

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