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PROGRESS REPORT

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Connecting the Mechanical and Conductive Properties of Conjugated Polymers

Renxuan Xie, Ralph H. Colby, and Enrique D. Gomez*

DOI: 10.1002/aelm.201700356

1. Introduction

The continued drive toward wearable electronics will require deformability as never before.[1,2] Significant recent advances have demonstrated the potential for stretchable electronics in artificial skin and wearable biometrics by integrating rigid devices with flexible substrates such as polydimethylsiloxane

Both the mechanical deformability and electronic conductivity of conjugated polymers play important roles in the development of wearable and stretchable electronics. Despite the recent progress and emphasis on achieving highly stretchable and conductive devices, the correlation between the mechanical and conductive properties is poorly understood and remains mostly empir-ical. The future of flexible electronics relies on the ability to predict and tune the mechanical and conductive properties such that the molecular design of conjugated polymers can be optimized for various applications. Instead of seeking a direct correlation between mechanical and conductive properties, this Progress Report proposes to examine the common microstructural origin for mechanical performance and charge transport in conjugated polymers. Measurements of microstructural information, such as persistence length, chain entanglement, glass transition, liquid crystalline phase transition, and intercrystalline morphology, are desperately needed in the field of conjugated polymers in order to establish connections with both the mechanical/con-ductive properties and the chemical structures. Conventional experimental methods in the field of flexible polymer physics, such as linear viscoelastic rheometry, open up new avenues for characterizing these microstructural parameters, thereby providing a path toward predicting and designing the molecular structure of conjugated polymers with desired mechanical and conductive properties.

Flexible Electronics

R. Xie, Prof. E. D. GomezDepartment of Chemical EngineeringThe Pennsylvania State UniversityUniversity ParkPA 16802, USAE-mail: [email protected]. R. H. ColbyDepartment of Materials Science and EngineeringThe Pennsylvania State UniversityUniversity ParkPA 16802, USA

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/aelm.201700356.

(PDMS), polyethylene terephthalate, and polyimide.[2–4] Conjugated polymers may fill a need beyond substrates as deformable semiconductors, because of their delocal-ized π orbitals along a covalently linked backbone that allows electron or hole con-duction within a stretchable network.[4–6] As materials with more efficient charge transport have been introduced, empirical trends linking stiffness and charge trans-port performance have also arisen.[7,8]

To first order, stiffer backbone struc-tures that impose longer conjugation lengths lead to fast intrachain charge mobilities along the backbone, which, in turn, can lead to macroscopic enhance-ment of transport but possibly more rigid behavior as well.[9] Aiming to achieve both highly flexible and conductive properties, one simple solution to circumvent this trade-off is to blend flexible insulating polymers with semiconducting polymers; nevertheless, the chemical dissimilarity between the polymers might cause mac-roscopic phase separation and deteriorated performance in devices over time.[10] Simi-larly, blends of regiorandom (RRa) iso-mers that are amorphous with low charge

mobilities and regioregular (RR) counterparts of the same polymer with high charge transport efficacy, such as in blends of regiorandom and regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT),[11] lead to remarkable materials with high performance and flexibility. Unfortunately, blending of materials with con-trolled isomerism has not been demonstrated as a general approach beyond P3HT.

Alternatively, some efforts have attempted to incorporate var-ious flexible moieties either as a soft block in a block copolymer structure[12,13] or as grafted flexible side chains[13,14] of a brush architecture to improve the overall flexibility of the film without sacrificing charge transport. The addition of small amounts of plasticizers (≈2 vol%) to active layers can also lower the mod-ulus significantly without compromising on device perfor-mance, and has been demonstrated for polymer–fullerene solar cells.[15,16] These examples highlight the potential to develop new materials with the tremendous synthetic versatility of poly-meric semiconductors.

The mechanical properties of conjugated poly-mers have been quantified in terms of the tensile mod-ulus, elongation to failure, and tensile strength. Beyond these

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parameters, opportunities lie in elucidating fundamental insights into charge transport with mechanical measure-ments. For example, rheological measurements and dynamic mechanical analysis (DMA) can map phase behavior and reveal the complex microstructure of semicrystalline or liquid crystal-line polymers. Recent work has demonstrated that oscillatory shear rheology can clearly delineate the glass transition tem-perature (Tg) as a function of molecular weight of conjugated polymers such as regiorandom P3HT, regioregular P3HT, and poly((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-bis(thiophen-5-yl)-2,1,3-benzothiadiazole]-2′,2″-diyl) (PFTBT).[17] Both a side chain Tg ≈ −100 °C and a backbone Tg ≈ 10 °C were clearly identified for P3HT, while PFTBT shows only one Tg at 144 °C. As a con-sequence, the modulus at 20 °C of PFTBT is 700 MPa and far exceeds that of regioregular P3HT (≈150 MPa). Because chain motion depends on the temperature relative to Tg, these meas-urements are crucial for predicting morphological stability and for optimizing thermal or solvent annealing protocols that aim to enhance performance in electronic devices.

Despite recent progress, many opportunities for new insights exist. Although in principle rheology yields signatures of the liquid-crystal-to-isotropic clearing transition tempera-ture (Tc), this approach for mapping the phase behavior has not been applied to conjugated polymers. The number of tie chains bridging crystals governs the semicrystalline modulus and is hypothesized to limit charge conduction, but no current estimates of tie chain densities exist for conjugated polymers. Entanglements, characterized in terms of the entanglement molecular weight (Me) that is obtained from the plateau modulus in the amorphous liquid phase, have also not been examined for conjugated polymers. We propose that Tg, Tc, Me, and tie chain density can be obtained from rheology, and that they are the missing links between molecular parameters such as the persistence length, packing length and side chain volume fraction, and macroscopic mechanical and conductive properties.

In this Progress Report, we focus on connecting mechanical and conductive properties of conjugated polymers with micro-structural insights gained by linear viscoelastic measurements. We begin with recent progress on mechanical measurements of conjugated polymers as thin films (thickness ≤ 100 nm) and as bulk samples. Then, we highlight several microstruc-tural parameters that may directly impact charge transport and discuss the effectiveness and the challenges of characterizing these parameters through rheology. We also summarize cur-rent empirical correlations trying to connect mechanical and conductive properties of conjugated polymers. Finally, we close with an outlook that emphasizes the opportunities in applying tools from polymer physics, such as rheology, to the field of conjugated polymers.

2. Measurements of Mechanical Properties of Conjugated Polymers

Characterization of the mechanical properties of conju-gated polymers can be classified into either thin-film or bulk measurements. Figure 1 highlights two methods to measure the modulus for polymer thin films, buckling of films on

Renxuan Xie received his B.S. in both chemical engi-neering and materials science and engineering from the University of Minnesota at Twin Cities with a background on the linear viscoelastic properties of co-continuous polymer blends and chewing gum. He is currently a Ph.D. candidate in the Chemical Engineering Program at the

Pennsylvania State University under the guidance of Prof. Enrique D. Gomez and Prof. Ralph H. Colby. His research focuses on understanding the polymer physics of conju-gated polymers and their structure–property relationships.

Ralph H. Colby is a Professor of Materials Science and Engineering at the Pennsylvania State University. Dr. Colby was a Fulbright Scholar in New Zealand in 2005 and a Leverhulme Visiting Professor at Imperial College, London in 2012. His current research focuses on polyelectrolytes and ionomers, flow-induced crystallization of

semicrystalline polymer melts, characterization of semiflexible polymers, and solutions of native cellulose in ionic liquids.

Enrique D. Gomez is an Associate Professor of Chemical Engineering at the Pennsylvania State University. He received a B.S. in Chemical Engineering from the University of Florida and a Ph.D. in Chemical Engineering from the University of California, Berkeley. He then spent a little over a year as a postdoc-

toral research associate at Princeton University, after which he joined the faculty at the Pennsylvania State University in August of 2009. His research activities focus on under-standing how structure at various length scales affects macroscopic properties of soft condensed matter.

elastomers,[11,16,18,19] and tensile tests on water.[6,20,21] Three separate experiments determine the plane-strain modulus, the yield strain, and the fracture strain of thin films.[21,22] A thin film is prepared on top of a soft and compliant elastomer, such





as cured PDMS. After applying a small compressive strain (typ-ically less than 2% strain),[18] wrinkles appear on the thin film. The plane-strain modulus of the film is extracted by comparing the wrinkle wavelength and film thickness using[22]

E E d

h13

1 2f

f2

s

s2

3

ν ν π−=

−

(1)

where Ef and Es are the plane strain moduli of the film and the substrate, respectively, νf and νs are the Poisson’s ratios of the film and substrate, respectively, d is the wavelength of the buckled film, and h is the film thickness. By increasing and then releasing strain on the film-coated PDMS substrate in a cyclical manner, eventually plastic deformation occurs and wrinkles remain after the strain release, indicating the yield strain of the thin film.[21] The crack-onset strain can also be estimated as the strain at which the pinholes and voids start to appear in the film under tension.[21] Tensile tests on water use a hydrophobic conjugated polymer thin film, floating on top of water. PDMS is used to grip the ends of the film, and tension is applied at a slow strain rate until the film ruptures.[6] Details of the experimental setup can be found elsewhere.[20] The resulting stress–strain curves show an elastic response at

low strain, a yield point, strain hardening/plastic deformation, and the fracture point, as expected for polymers.

Comparing the tensile modulus, the yield stress, and the strain to fracture obtained by both methods shown in Figure 1c for regioregular P3HTs, it is apparent that low-molecular-weight polymers have a lower strain at fracture. Most likely, the lack of tie/bridging chains or entanglements connecting the crystals for low-molecular-weight chains (Mn = 15 kDa by gel permeation chromatography (GPC) relative to polystyrene (PS) standards likely overestimates actual molecular weight[23]) makes those films brittle. Quantitatively, however, the strain at fracture differs dramatically, as shown in Figure 1c, especially for the higher-molecular-weight P3HTs. Film roughness, voids within films, and different strain modes/rates could lead to problems and dif-ferences in stress–strain curves between these two methods.[21] Because both fracture strain and fracture stress increase with molecular weight, high-molecular-weight polymers are vital for good mechanical properties, as is true for all polymers.

Although DMA is typically done on bulk samples, DMA under tension has been recently demonstrated for conjugated polymer thin films by reinforcing the polymer with either a stainless steel “materials pocket,”[24] woven glass fibers,[25] or thin polyimide substrate[26] before loading. Films are either


Figure 1. Comparison of two common mechanical measurement techniques for thin films of conjugated polymers: a) tensile test on water and b) compressional buckling test on a PDMS elastomer. Regioregular P3HTs with different molecular weights are shown as an example. Reproduced with permission.[21] Copyright 2017, American Chemical Society. c) The molecular weight dependence of the fracture strain and fracture stress obtained by these two methods for regioregular P3HTs. Data from the literature.[21]




directly enclosed by the stainless steel pocket, deposited on thin polyimide substrate, or solvent cast onto the woven glass fibers that are at 45° with respect to the tensile direction, so that the tensile load is mostly on the polymer film rather than the glass fibers, as shown for poly[2,3-bis(3-octyloxyphenyl)quinoxaline-5,8-diyl-alt-thiophene-2,5-diyl] in Figure 2.[25] The phase angle (δ) is defined as between the applied oscillatory strain and the measured oscillatory stress, such that tan (δ) can be plotted versus frequency or temperature. As a consequence, this DMA thin-film test offers higher sensitivity than conventional differ-ential scanning calorimetry (DSC) to probe thermal transitions, such as melting and glass transitions for the backbone or for side chains. Figure 2 shows clear local maxima of tan(δ) that are signatures of thermal transitions; in this case, the authors attribute the transition near 0 °C to the glass transition of the side chains, and the transition near 100 °C to the backbone Tg. We further discuss using DMA to extract Tg from conjugated polymers in Section 3.1.

Nevertheless, due to the undefined sample geometry for both loading techniques in thin-film DMA, absolute values for the modulus cannot be extracted. Without accurate moduli, thermal transitions are harder to identify, as glass transitions, side chain melting, melting, or smectic-to-isotropic transi-tions of conjugated polymers all exhibit local maxima in tan(δ). While the nematic-to-isotropic transition does not exhibit such a signature in tan(δ), it is easily detected by the unusual obser-vation of viscosity increasing with temperature, as detailed in Section 3.2.

Some methods, such as nanoindentation[27] or scanning probe microscopy,[28] do not rely on thin-film geometries, although they measure mechanical properties near a free sur-face. As a result, the measured modulus depends on both the indentation depth and the film thickness; the origin of these dependences is still under debate, with artifacts, true material response, or surface–probe interactions as possible candidates. Specifically, the modulus of a thin film is observed to reach the bulk value only when the indentation depth is relatively large.[29] For spin-coated polymer films with thicknesses below a few hundreds of nanometers, the apparent modulus is consid-erably higher than the bulk value, possibly due to a stiffening effect from a rigid substrate,[30] interactions between probe and polymer,[31] or strongly stretched chains in spin-coated films.

Only recently, this substrate stiffening effect has been separated from the thickness dependence of the modulus with extensive finite element simulations.[32] Overall, it remains challenging to interpret values for the modulus of polymer thin films obtained from nanoindentation, although recent progress suggests a growing role for this emerging technique.

Because conjugated polymers are often used as thin-film active layers in electronic devices, one might assume that mechanical testing in thin-film geometries is needed. The glass transition of polymer thin films has been shown to differ by as much as 50° from the bulk in some cases.[33] But, the tensile moduli extracted from buckling experiments for poly-styrene are found to be independent of film thickness from 30 to 250 nm, and agree well with bulk values.[22] Tensile tests on water for Au thin films show roughly a 15% lower modulus as the thickness decreases below 100 nm.[6,20] As such, we propose that bulk measurements can yield important insights into the properties of conjugated polymers, especially if the morphology of bulk samples is comparable to that of thin films.

Conventional mechanical tests of bulk samples, such as tensile tests, are usually carried out by first melt compressing polymer powders into “tapes” or “dog bone” shapes.[34] In Figure 3a, bulk tensile tests on regioregular P3HTs exhibit the expected dependence on molecular weight similar to that of the thin-film tensile test on water. Nevertheless, bulk tensile tests require much more material (at least 300 mg) than thin-film methods (≈5 mg), and both require replicate runs for good sta-tistics, particularly for stress and strain at failure.

One approach to minimize the sample requirement is to use 3 mm diameter disks in rotational shear rheometry. This requires ≈15 mg of material and is very reproducible. Sam-ples can be molded inside a glove box to remove all bubbles and minimize degradation as shown in Figure 3b. At tem-peratures deep into the glassy region, the critical shear strain for the linear region usually is less than 0.005, requiring fine motor control to achieve a good sinusoidal wave with a strain amplitude of only 0.001 at the perimeter of the 3 mm diam-eter plates. An extremely sensitive transducer is required to measure the small torque response from the sample at high temperatures where the terminal regime is achieved. Figure 3c shows the complex moduli that vary between 100 Pa and


Figure 2. Thin-film DMA for conjugated polymers. Solution-cast conjugated polymer films are reinforced by woven glass fibers.[25] This approach is more sensitive for glass transition temperatures (Tg and sub-Tg) of conjugated polymers than DSC, but accurate modulus values cannot be extracted due to a poorly defined sample geometry. Reproduced with permission.[25] Copyright 2017, American Chemical Society.




1 GPa for about 30 orders of magnitude in frequency for a regiorandom P3HT using time–temperature superposition of data taken between −120 and 250 °C with a reference tempera-ture of 0 °C; data were acquired using a Rheometric Scientific ARES-LS.[17]

Shear rheology is expected to play a significant role in mapping the phase behavior of conjugated polymers. The various thermal transitions found in conjugated polymers, such as the glass transition, melting of the backbone or side chains, and liquid crystal to isotropic transitions, confound data obtained through techniques such as DSC or polarized optical microscopy. For instance, reported values for the glass transition temperature vary significantly from −14 to 140 °C for P3HT.[24,35] Linear viscoelastic rheology can distinguish among the various thermal transitions based on a combina-tion of the value for complex modulus and the temperature,

time, and frequency dependence. By fitting the temperature dependence of the shift factors with two known models (i.e., Williams–Landel–Ferry equation[36] and Arrhenius equation) in Figure 3d, more microstructural insights regarding the glass transition process of P3HT can be extracted, including the Vogel temperature at which the liquid state free volume extrapolates to zero, activation energy for the Arrhenius alkyl side chain relaxation below Tg, and even the glass fragility (or the sharpness of the glass transition).[17] As described in the following section, solid versus liquid response can be iden-tified from the magnitude of the storage and loss moduli and their frequency dependence; whether semicrystalline or not, polymer glasses usually have shear storage moduli (G′) between 0.5 and 3 GPa, and there are unique signatures in the modulus through liquid crystal to isotropic transitions as discussed in Section 3.2.


Figure 3. Examples of the tensile and the shear measurements of bulk samples for conjugated polymers. a) Uniaxial tensile test at room temperature for melt-pressed regioregular P3HT strips of different molecular weights. Reproduced with permission.[34] Copyright 2013, Elsevier. b) Schematic of a vacuum-assisted molding setup to obtain void-free and un-degraded P3HT disks (pictures shown with 3 mm diameter and 1 mm thickness) for shear rheology measurements. Example of the master curve of one regiorandom P3HT (RRa 3) with Mw = 101 kg mol−1 for c) storage (G′) and loss moduli (G″) at a reference temperature of 0 °C and d) frequency shift factors (aT) based on the time–temperature-superposition principle. RRa 4 is another batch of RRa P3HT with Mw = 110 kg mol−1 and 6 is a regioregular (RR) P3HT with Mw = 38.3 kg mol−1. Reproduced with permission.[17] Copyright 2017, American Chemical Society.




3. Microstructural Parameters and Corresponding Signatures in Mechanical Measurements

The mechanical properties of conjugated polymers are dictated by the glass transition temperature (Tg), the liquid-crystal- to-isotropic clearing transition temperature (Tc), the entan-glement molecular weight (Me), and the semicrystalline morphology (crystallinity and tie chain density). At low tempera-ture, the glassy modulus dominates, where most polymers have shear storage moduli ≈1 GPa.[37] At higher temperatures, above Tg, the polymer could crystallize, in which case the sample is a solid and the storage modulus should be higher than the loss modulus but much lower than GPa (typically, ≈100 MPa).[38] If a nematic phase is found after melting of the crystals, then the loss modulus should exceed the storage modulus, indicating a liquid-like response at low frequency, but the frequency depend-ence will depend on local order and defect density as opposed to the response of amorphous isotropic melts. The rheological response for a smectic phase should be a viscoelastic solid, showing a plateau storage modulus usually around 104 Pa[38] or lower in the low-frequency region. In the isotropic phase at even higher temperatures, the frequency dependence in the linear viscoelastic regime might be described by the classic tube reptation model if well above the entanglement molecular weight, at least for flexible polymer melts.[37,39] Thus, molec-ular parameters, such as the molecular weight, the persistence length, the packing length, and the nematic coupling constant, have an important role in dictating the mechanical response.

There is a lack of agreement in the literature for Tg of conju-gated polymers,[17,24,35,40–43] although recent work has likely set-tled this debate for P3HT by measuring Tg for regiorandom and regioregular polymers as a function of molecular weight using linear viscoelastic methods,[17] suggesting further rheometry experiments are needed for other conjugated polymers. But, debate on liquid crystal to isotropic transitions continues;[44–47] too few published results on Me currently exist;[34,48] and no estimates of tie chain densities are reported for conjugated polymers. Fortunately, all of these microstructural parameters have distinct mechanical/rheological signatures and are often supported by well-established theories in polymer physics.

3.1. Glass Transition

The glass transition is a temperature-activated process, such that below the characteristic temperature Tg, the segmental motion of the chain mostly ceases; above Tg, cooperative motion is allowed in the amorphous phase. For conjugated polymers, the glass transition process is important not only because of the drastic change in the shear storage modulus between ≈1 GPa (typically 0.5–3 GPa) below the Tg,[37] and ≈1 MPa for amorphous poly-mers or 100 MPa[38] for semicrystalline polymers above the Tg, but also because below Tg chain motion is kinetically arrested.

Various experimental techniques have been demonstrated for measuring Tg of conjugated polymers. Dielectric relaxa-tion spectroscopy[49] focuses on probing main-chain segmental relaxations, DMA usually in tensile mode[24,25,50] and linear viscoelastic oscillatory shear rheology[17] probe changes in mechanical properties, DSC[35] identifies signatures in changes

of heat capacity, and UV–vis absorption spectroscopy[43] can indicate abrupt changes in the thermal expansion coefficient. In all techniques, measurements are focused on signatures from amorphous chains even when polymers are semicrys-talline, as these are the only ones that contribute to the glass transition. A recent review by Müller includes a comprehensive summary and discussion of the various methods of measuring Tg for conjugated polymers.[41]

The mechanical signatures of Tg are commonly investigated by DMA or shear rheology, which measures the magnitude of


Figure 4. a) Loss modulus versus temperature for regiorandom P3ATs with different alkyl side chain lengths at a frequency of 10 rad s−1 and heating rate of 2 °C min−1. Curves are shifted vertically for clarity. Repro-duced with permission.[52] Copyright 2009, American Chemical Society. b) Glass transition temperatures of regiorandom P3ATs for both back-bone (Tα = Tg, green symbols) and side chain (TαPE, orange symbols) as a function of the side chain lengths (squares)[52] and the effect of molecular weight for P3HT (triangles).[17]




the complex modulus (accurate only for bulk samples) and the phase angle, δ, between the oscillating stress and the strain in either tensile or shear deformation. The applied strain ampli-tude is kept below 0.005 to stay within the linear response region, such that the measured stress increases linearly with the applied strain leading to strain-independent modulus. As poly-mers undergo the glass transition, the storage modulus (E′ for tensile or G′ for shear) decreases by one order of magnitude, while the loss modulus (E″ for tensile or G″ for shear) reaches a local maximum. The glass transition temperature (Tg) is defined by the local maximum in loss modulus representing the relaxa-tion process typically probed at a frequency of 1.0 rad s−1,[51] while the local maximum in tan(δ) (i.e., the ratio of E″/E′ or G″/G′) usually gives higher Tg values. Nevertheless, measuring Tg from DMA or rheology is more sensitive than with DSC; measurements of the Tg from thin films is possible using DMA as highlighted in Figure 2.

Studies of the glass transition of conjugated polymers through bulk DMA measurements have been mostly limited to the poly(3-alkylthiophene) family, perhaps due to the large amount of sample required. For instance, glass transition tem-peratures have been compared between RRa and RR poly(3-alkylthiophenes) (P3AT) as a function of the alkyl side chain length, ranging from butyl to dodecyl.[17,50,52,53] The glass tran-sition temperature of the backbone (Tα = Tg) for regiorandom P3AT decreases with longer alkyl side chains from butyl to decyl, and then increases slightly for dodecyl as shown in Figure 4.[52] The dodecyl side chain crystallization is thought to be responsible for hindering the backbone segmental motion and thereby increases Tg slightly, while the shorter side chains remain amorphous.[52] A recent study on the molecular weight

dependence of the glass transition temperatures for RRa P3HTs by rheology[52] is also compared with those for RRa P3HT in side chain length study by DMA[52] in Figure 4b, showing good agreement for the side chain glass transition (TαPE) but a slightly lower Tα. More details regarding the molecular weight dependence of P3HTs are discussed in the following section and in Section 3.3.

A systematic study on the molecular weight dependence of both RR and RRa P3HT was carried out using oscillatory shear rheometry using 15 mg of each material, as shown in Figure 5.[17] Table 1 shows the molecular weight and dispersity for the polymers used in Figure 5. Because Tg for polymers can vary by 10–20 °C with frequency,[54] a frequency of 10 rad s−1 was kept constant as the temperature varies. The temperature for the backbone (α process, near 0–20 °C) and the side chain (αPE process, near −80 to −90 °C) glass transition can be clearly distinguished based on the local maxima of G″. The difference in G″ values between RR P3HTs and RRa P3HTs also implies a different extent of microphase separation between side chains and backbones. The larger G″ for the αPE process in RR P3HT shown in Figure 5b could be attributed to stronger segrega-tion of side chains from backbones at the nanoscale. For both RR and RRa P3HT, the Flory–Fox equation[55] was used to describe the molecular weight effect on Tα (i.e., Tg) successfully, except for some deviations due to the semicrystalline structure (to be discussed in Section 3.3). The side chain glass transi-tion temperature, TαPE, is independent of molecular weight, as expected, and much of the polymer literature refers to this as a β relaxation.

3.2. Liquid Crystalline Phase Transition

Liquid crystallinity in conjugated polymers is hypothesized to be important to enhance long-range order and thereby enhance charge transport,[56] yet the liquid-crystal-to-isotropic transition, which is a weakly first-order tran-sition, is not always easy to identify. The


Figure 5. a) Storage modulus and b) loss modulus as function of temperature for various molecular weights of both regioregular (RR dashed curves) and regiorandom (RRa solid curves) P3HTs showing the side chain (αPE) and the backbone (α) glass transition processes, which are probed by small-amplitude oscillatory shear rheometry. 1–8 are eight batches of RR P3HTs with Mw ranging from 3.1 to 67.0 kg mol−1 and RRa 1–RRa 4 are RRa P3HTs with Mw ranging from 11.4 to 110 kg mol−1; see Table 1. Reproduced with permission.[17] Copyright 2017, American Chemical Society.

Table 1. Characteristics of regioregular and regiorandom P3HTs used in Figures 5 and 7.[17]

Polymer 1 2 3 4 5 6 7 8 RRa 1 RRa 2 RRa 3 RRa 4

Mwa) [kg mol−1] 3.1 6.7 16.7 20.7 29.5 38.3 50.9 67.0 11.4 25.2 101 110

Đ from GPC 1.14 1.26 1.15 1.35 1.22 1.78 1.84 1.83 2.06 2.04 2.42 2.45

a)Determined from static light scattering except for 1 and 2, those obtained from 1H NMR and GPC.




enthalpy change from the liquid crystal to the isotropic phase can be as large as 10 J g−1[44] for poly(2,5-bis(3-hexadecylth-iophen-2-yl)thieno[3,2-b]thiophene) (PBTTT) or as small as 0.3 J g−1 for RR P3HT[47] due to the dominating entropic con-tribution to the order parameter. Small molecule nematics have nematic-to-isotropic enthalpy changes of 1–7 J g−1.[57] Thus, methods beyond DSC have been employed to identify the liquid crystalline phase in conjugated polymers, such as optical microscopy under crossed polarizers,[42,58] polarized Raman spectroscopy,[59,60] and X-ray scattering.[45,61]

The unique advantages of probing mechanical signatures of the liquid crystal to isotropic transition are highlighted in Figure 6. The only reported example that takes advantage of changes in mechanical properties to map phase behavior is shown in Figure 6a for P3HT. DMA data at fixed frequencies of either 1.0 or 10 Hz show a small step decrease in both E′ and E″ at 246 °C above the melting temperature of 230 °C, and it was suggested by the authors to be a liquid-crystal-to-isotropic transition at 246 °C.[24] Nevertheless, detailed frequency sweeps are needed to verify the type of liquid crystalline phase. For a smectic phase, a storage plateau modulus should be apparent at low frequency, indicating either the layer spacing in the smectic phase or the defect texture of the unaligned smectic polymer.[62] Also, a constant power law with exponents of 0.3–0.6 for both G′ and G″ at high frequency is expected.[62,63]

Furthermore, thermotropic nematic-to-isotropic transitions have unique rheological signatures, as shown in Figure 6b.[64] As the temperature is increased and an isotropic phase is achieved, the complex viscosity or complex modulus increases, and upon cooling and recovery of nematic order, the viscosity or modulus drops. This reversible increase in viscosity with increasing temperature is unique, and can, therefore, be used to unequivocally identify nematic-to-isotropic transitions.

The microscopic origin for the lower viscosity in the nematic phase is hypothesized to be the enhanced chain dif-fusion coefficient (or less friction) along the aligned direction,

such that the randomly oriented chains in the isotropic phase will have a higher viscosity. Although the nematic forming polymer shown in Figure 6b is not conjugated, we expect that the same rheological signature should apply because of the same microscopic origin for the nematic phase. In addi-tion, polymers that form smectic phases usually show an elastic plateau (or nearly frequency-independent G′) at low frequency[57] and have higher modulus values than both the isotropic and the nematic phase. Therefore, the thermotropic liquid crystalline phases of polymers can be clearly identified and distinguished from other thermal transitions due to their unique temperature and frequency dependence in oscillatory shear rheology.

The formation of lyotropic liquid crystalline phases is an important tool to enhance order and charge transport in con-jugated polymers. For example, ordered aggregates in solu-tion can be used to impart or template enhanced long-range order in films cast from solution; this is usually done by aging solutions above their overlap concentration for days.[59,65] Cross-polarized optical microscopy and polarized Raman spectro-scopy are often used to monitor this process. An alternative way to promote stronger order within solutions of conjugated poly-mers is to apply continuous shear in the rheometer and achieve shear-induced crystallization, which is apparent by the orders of magnitude increase in viscosity within several hours.[66]

3.3. Chain Conformations and Microstructure in Semicrystalline Polymers

The microstructure in semicrystalline polymers is composed of crystal domains and amorphous phases that include loops, tie chains, and dangling ends. Depending on the molecular weight of the chain and the crystallization process, the crystal size, crystalline volume fraction (i.e., crystallinity), and density of tie chains can vary significantly. This complex morphology is


Figure 6. a) Example of identifying the liquid-crystal-to-isotropic transition temperature (246 °C shown on the inset) for P3HT by DMA—1.0 Hz: E′, black line; tan(δ), black squares. 10 Hz: E′, red dashed line; tan(δ), red triangles. Reproduced with permission.[24] Copyright 2011, American Chemical Society. b) A typical rheology signature for identifying the nematic-to-isotropic transition of a polymer (structure shown on the top) is the increase in complex viscosity upon heating (open symbols) for ramp rates of 0.1 K min−1 (◊) and 2.0 K min−1 (□), and this trend is fully reversible when cooling (filled sym-bols). Dashed line is the nematic-to-isotropic transition temperature from DSC. Reproduced with permission.[64] Copyright 1994, The Society of Rheology.




of long-standing interest to the polymer community because it dictates mechanical properties such as strain hardening during the cold drawing process for polyethylene.[67]

Charge transport in conjugated polymers is enabled due to strong π–π stacking, although intramolecular charge mobilities along planar backbones are expected to be higher than through intermolecular π–π stacks. Ordered domains can thus enhance transport by promoting interchain π–π stacking. Furthermore, charge transport through amorphous domains is suppressed due to disruptions in π–π stacking. In a semicrystalline mor-phology, charge conduction is hypothesized to be limited by the intercrystalline amorphous domains.[68] For example, pre-vious work has used a melt and quench approach to tune the crystallization kinetics of P3HT films with different crystalli-zation temperatures. Even when the crystallinity in the active layer is the same, charge mobilities from devices were higher when crystallization kinetics were faster, likely trapping more tie chains. Enhanced charge transport was indeed attributed to higher tie chain densities due to faster crystallization kinetics, although the tie chain density was not explicitly measured.[69]

Because of the relatively stiff backbone of the conjugated aro-matic structure compared to flexible polymers, chain folding, and tight loops at the crystal surface are less likely to occur, usually resulting in “extended micelle” morphologies. Based on Gambler's Ruin arguments, the probability of a tie chain for P3HT is more than two times higher than that when tight folds are possible.[70] The number of chain ends, entanglements, and tie chains is governed by the crystallite size, the molecular weight of the chain, the persistence length, and the packing length (p), which is given by

pM

R N2

0 AVρ≡

(2)

where M is the molecular weight, ⟨R2⟩0 is the mean-square end-to-end distance of the polymer chain, NAV is the Avoga-dro’s number, and ρ is the mass density. The packing length

essentially describes the shape of the chain and is a measure of the chain “thickness.”[71] Longer persistence length leads to stiffer chains and more contacts between chains (i.e., entan-glements) and lower entanglement molecular weight (Me).[72] Smaller packing lengths lead to smaller Me and more chain entanglements. Larger molecular weights increase both entan-glements per chain and tie chain density. In turn, entangle-ments and tie chains provide intercrystalline connectivity that is stress bearing, but we hypothesize that only tie chains can boost conductivity unless significant π–π stacking occurs among entangled chains.

Based on the above description of the semicrystalline mor-phology, the origin of the mechanical response has three main additive contributions: tie chains, a crystal filler effect, and entanglements, as shown schematically in Figure 7a. The effects of tie chains and their entanglements are expected to be analogous to crosslinked polymer networks.[73] If tie chains are stretched, the Krigbaum model can be used because it con-siders the effects of chain stretching through the inverse Lan-gevin equation and the crystallinity,[74] but more experimental characterization is needed to validate this model.

Detailed measurements of the glass transition temperature as a function of molecular weight suggest a significant amount of chain stretching in the amorphous region of semicrystalline conjugated polymers. As shown in Figure 7b, the backbone glass transition temperature Tα (i.e., Tg) is higher for RR P3HT than for RRa P3HT, even though the origin of the glass tran-sition can only be attributed to amorphous chains.[17] Because RR P3HT is semicrystalline and RRa P3HT is amorphous, we speculate that nanoscale confinement[76] of amorphous chains restricts segmental mobility and thereby elevates Tα (i.e., Tg). Furthermore, the abrupt transition in Tα for RR P3HT at Mn of 14 kg mol−1 suggests two regimes. Assuming a crystal-linity for RR P3HT of 50%,[70] a crystal thickness of 30 nm,[77] and long fibrils on a hexagonal lattice for simplicity, then the separation distance between crystals is about 10 nm. At the threshold molecular weight of 14 kg mol−1, the contour length


Figure 7. a) Schematic of the semicrystalline structure of conjugated polymers showing tie chains in red, entanglements in green, and filler effect in blue. Adapted with permission.[75] Copyright 2013, Nature Publishing Group. b) Molecular weight dependence of glass transition temperatures for both regioregular (RR) and regiorandom (RRa) P3HTs. Green symbols correspond to the backbone segmental relaxation temperature, Tα (i.e., Tg), and orange symbols represent the side chain relaxation temperature, TαPE. Open symbols refer to RR P3HTs and filled symbols refer to RRa P3HTs. For RR P3HT, an abrupt transition in the molecular weight dependence of Tα (i.e., Tg) occurs at Mn = 14 kg mol−1, suggesting that this is the molecular weight of intercrystalline tie chains. Reproduced with permission.[17] Copyright 2017, American Chemical Society.




is 34 nm, and the random walk end-to-end distance is 14 nm using a persistence length of 3 nm.[47,78,79] Thus, for tie chains incorporated into two crystals, it is reasonable to assume a modest degree of chain stretching. Furthermore, 14 kg mol−1 happens to also agree closely with 12 kg mol−1 at which chain folding is believed to occur for P3HT, according to successive self-nucleation and annealing measurements in DSC.[70] Inter-estingly, Figure 6b shows that higher-molecular-weight chains above 14 kg mol−1 lead to higher Tα (i.e., Tg) with a strong molecular weight dependence, which we attribute to a higher number density of tie chains as the molecular weight increases, assuming tie chains are stretched. Below 14 kg mol−1, the molecular weight dependence is weaker even than that of RRa P3HT, suggesting the rigid amorphous segments of chains con-fined by the crystal–amorphous interface and with one chain end within a crystal (dangling ends) are responsible for the ele-vated Tα (i.e., Tg) with respect to RRa P3HT.[17]

The effect of crystallites on the semicrystalline modulus can be estimated using the Halpin–Tsai composite theory[80] if the aspect ratios of the lamella, the crystallinity, the single crystal modulus, and the entanglement modulus are known. The single crystal modulus can be obtained from the crystal struc-ture and simulations. The entanglement effect on modulus can be experimentally measured from melt rheology if the conju-gated polymer is of high enough molecular weight to show a rubbery plateau above the melting temperature. Unfortunately, there are currently only two reports on the study of entangle-ments in conjugated polymers: the molecular weight depend-ence of the specific viscosity in dilute solutions[34] and molecular dynamics simulations of P3HT.[48] Thus, melt rheology studies are needed to quantify the entanglement molecular weight of conjugated polymers.

The entanglement plateau modulus can also be predicted from the local chain properties, such as the persistence length and the packing length.[81] Figure 8 shows the Graessley–Edwards plot[82] with dimensionless entanglement plateau modulus versus the dimensionless number density of Kuhn segments or equivalently the ratio of the Kuhn length (lK) and packing length (p). Everaers and co-workers have demonstrated excellent agreement between the experimental plateau moduli and the results from the primitive path analysis spanning across from the loosely entangled polymer melts (flexible with

/ ~ ( / )0 3B K

7/3G l k T l pN K ) to the tightly entangled polymer solutions (semiflexible with / ~ ( / )0 3

B K7/5G l k T l pN K ).[81] Conjugated polymers

with tunable persistence length and packing length based on the versatile backbone chemistry and side chain architecture should serve as the ideal candidates to validate this prediction, especially for the crossover region between the semiflexible and the flexible scaling regions. RRa P3HT with a persis-tence length of 3.0 nm[79,83] and the entanglement modulus of 7.54 × 105 Pa, extracted from Figure 3c,[17] is found to agree well with the universal scaling prediction as shown in Figure 8. The packing length is calculated to be 1.1 Å using Equation (2) based on the repeat unit length of 0.38 nm and Kuhn length of 6.0 nm for P3HT. This small packing length could be attributed to the easiness of packing from its planar chain structure, com-paring with other semiflexible polymers (e.g., polyetheretherk-etone, polycarbonate and polysulfone having packing length of 1.7 Å).[71,84]

Much of the ground work appears to be in place for detailed mechanical measurements to obtain tie chain densities, although quantitative estimates are currently lacking in the literature. Rheology is also likely to reveal crucial details about the con-nectivity in the semicrystalline structure. A stress relaxation test with an applied step strain shown in Figure 9a is more suitable to probe long time behavior of any slow relaxation process;[37] Figure 9a shows typical stress relaxation data for semicrystalline polymers, here isotactic polypropylene (iPP). A plateau value is not observed within the measured time frame. Instead, stress decays with a weak power law, as is often observed for semicrys-talline polymers, such as iPP and polyethylene. Various empirical models and theories[88,89] have been proposed over the years to describe the stress relaxation behavior of semicrystalline poly-mers, but these models do not provide a theoretical basis on how to locate the plateau modulus or estimate the number density of tie chains. Some have estimated the modulus from either the initial modulus[74] or the quasiequilibrium modulus at very long time beyond 104 s.[90] The origin of this extremely slow relaxation is hypothesized to be either the dynamic process of the constant crystallization and melting at the crystal–amorphous interface, or from slow defect diffusion within the connected crystal skeleton network structure. In either case, the long relaxation time sug-gests a percolated crystal morphology that would have different consequences on charge transport than the tie chain model high-lighted in Figure 6a, as discussed in the following sections.

Instead of crystals that are connected to each other only by tie chains, another possibility is a connected crystal morphology,


Figure 8. Dimensionless plateau moduli as a function of the dimen-sionless number density of Kuhn segments: experimental data versus predictions. Red symbols indicate experimental data for various loosely entangled polydiene, polyolefine, and polyacrylate melts and loosely entangled θ solutions of polystyrene and polybutadiene. Blue symbols represent the tightly entangled F-actin and fd-phage solutions. The green point is extracted from our previously reported data assuming lk = 2lp = 6.0 nm, p = 1.1 Å and 7.54 100 5GN = × Pa.[17] Colored lines represent theoretically derived power laws for tightly[85] and loosely entangled systems.[86] Black line represents the universal scaling predic-tion by Everaers and co-workers with slight modification to the fit for the loosely entangled region.[81] Adapted with permission.[87] Copyright 2008, American Institute of Physics.




as shown in the right panel of Figure 9b.[91] If this picture is correct, the tie chain density is not the crucial parameter for either the modulus or charge mobilities. Instead, longer crystal fibrils are directly connected to form a crystal network mor-phology, resulting in higher charge mobilities than crystals con-nected through amorphous phases by tie chains. Previous work has demonstrated that casting from 1,2,4-trichlorobenzene, as opposed to chlorobenzene, leads to longer conjugation lengths that span across connected crystal fibrils within the crystal net-work, as evidenced by analysis of UV–vis data with Spano’s model.[91] The longer crystal fibril structure is supported by strong anisotropic patterns in resonant soft X-ray scattering data for P3HT films cast from 1,2,4-trichlorobenzene.[91] Even when crystallinities were carefully controlled to be equal, longer conjugation lengths and anisotropic crystal structures lead to higher charge mobilities in thin-film transistors. Mechanical measurements are warranted to ascertain the nature of crystal connectivity within semicrystalline conjugated polymers.

In summary, various microstructural parameters for conju-gated polymers including the glass transition, liquid crystalline phases, and the intercrystalline morphology can be examined via their unique mechanical signatures in linear shear rhe-ology. This is a result of the common microstructural origin for mechanical properties and charge transport in conjugated polymers. Measurements of fundamental parameters, such as the persistence length, packing length, entanglement modulus, and glass transition temperature, will allow for new insights that could lead to new design concepts for flexible electronics from conjugated polymers.

4. Empirical Correlations between Mechanical Properties and Charge Transport

Despite the lack of concrete estimates of the aforementioned microstructural parameters, a few empirical correlations

between mechanical properties and charge transport have been demonstrated. For instance, early studies by Smith and co-workers applied mechanical drawing to create fibers of doped polyacetylene, and these show a linear correlation between the Young’s modulus and the electrical conductivity (Figure 10a).[7] The stronger uniaxial alignment of the chains achieved by mechanical drawing enhances the lateral packing of the crystal and the coherence length, resulting in both strain hardening and faster interchain charge transport. This correlation between the mechanical strength and the conductivity is also observed for drawn polyphenylene vinylene, including anisotropic con-ductivity and Young’s modulus between the drawn and the transverse directions.[92]

Delongchamp and co-workers have proposed another cor-relation for the polythiophene family (e.g., P3HT and PBTTT) by simplifying the semicrystalline morphology as a mixture of isolated crystals and an amorphous matrix.[8] Consequently, the overall mobility can be approximated by the rule of mixtures and the crystallinity, while the modulus is modeled, by the Halpin–Tsai composite theory,[80] as a function of both the crys-tallinity and the geometric parameter of the lamellae crystal,[8]

ξ, equal to the ratio of two times the length of the lamella over the height.[8] By eliminating the common parameter, namely crystallinity, a direct correlation between the mobility and the modulus is obtained. As the crystal lamellae geometric param-eter (or the crystal fibril dimension) increases, the correlation of the modulus with charge mobilities becomes nonlinear. Com-paring values for P3HT, as-cast PBTTT, and annealed PBTTT, a nonlinear correlation is observed with a relatively large lamella aspect ratio of 10 or higher, as shown in Figure 10b. Annealing PBTTT films in the liquid crystalline phase appears to change the lateral size of the lamellae and thereby increases both the modulus and the mobility significantly compared with that of the as-cast film.

These correlations between charge mobility and modulus should only apply to semicrystalline conjugated polymers, but


Figure 9. a) Example of the stress relaxation test for isostatic polypropylene shows the continuous slow relaxation without reaching a plateau modulus in the semicrystalline state, indicating the possible origin of this connected crystals morphology similar to the schematic drawn for P3HT thin films spin-coated from trichlorobenzene. Reproduced with permission.[89] Copyright 1995, Elsevier. b) Effect of solvent on the microstructure and the charge mobility of P3HT thin films spin-coated from either chlorobenzene or trichlorobenzene. High mobilities are attributed to an interconnected crystal morphology. Reproduced with permission.[91] Copyright 2016, American Chemical Society.





recent work has demonstrated nearly amorphous polymers with higher mobilities than highly crystalline PBTTT.[93,94] One possible explanation for these high mobilities suggests that highly planar and stiff backbones are resilient to alkyl side chain disorder,[93] leading to fast intrachain charge transport without the need of frequent interchain charge hopping via strong π–π stacking in a crystalline lattice. As a consequence, charge mobilities are no longer controlled by the crystallinity but instead correlated with the persistence length and packing length, which in turn affect both Tg and Tc, and result in drasti-cally different moduli.

Without a clear description of structural parameters of con-jugated polymers, modulus–mobility correlations for either semicrystalline or amorphous polymers will remain empirical. We propose that fundamental knowledge of the microstructural parameters including the intercrystalline morphology, Tg, Tc, and Me must be examined first, to establish relationships with molecular parameters, such as the persistence length and the packing length. Then, models connecting the chemical struc-ture, mechanical properties, and charge conduction can be developed.

5. Conclusions and Outlook

Despite recent progress in assessing mechanical properties of conjugated polymer thin films, such as the thin-film tensile test on water and the buckling method, there are many opportu-nities for new insights from mechanical measurements. This Progress Report highlights the need for fundamental polymer physics studies of conjugated polymers, as a prerequisite for predicting or establishing the correlation between mechanical and conductive properties. Conventional bulk mechanical tests, such as oscillatory shear rheology, open up the possibility of exploring various microstructural parameters for conjugated polymers, including the glass transition temperature, the liquid-crystal-to-isotropic transition temperature, chain entan-glement, and the intercrystalline morphology. Equipped with these microstructural parameters, one can then establish a

connection between the mechanical and the conductive prop-erties to formulate new design rules for stretchable electronics with high flexibility and efficient charge transport.

AcknowledgementsThe authors gratefully acknowledge the financial support of the National Science Foundation under grant number DMR-1629006.

Conflict of InterestThe authors declare no conflict of interest.

Keywordscharge transport, conjugated polymers, rheology

Received: July 31, 2017Revised: October 16, 2017

Published online: December 11, 2017

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