Correlating Crack Onset Strain and Cohesive Fracture Energy in

The molecular structure of each polymer is provided in Figure 1 and include ... The elastic modulus of glass was taken as 70 GPa and Poisson's ratio a...
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Correlating Crack Onset Strain and Cohesive Fracture Energy in Polymer Semiconductor Films Nrup Balar and Brendan T. O’Connor* Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States S Supporting Information *

ABSTRACT: Polymer semiconductors are an attractive material system for flexible and stretchable electronic devices owing to their potentially favorable mechanical attributes. Establishing the thermomechanical behavior of polymer semiconductors is thus an important consideration to ensure successful operation in these applications. One of the most common mechanical characterization methods for these materials is to manipulate the thin films while on an elastomer substrate. A primary measurement with this approach is the film’s crack onset strain (COS), a measure of ductility. It is simple and effective; however, it is a highly qualitative view of film mechanical stability, particularly in flexible device applications. Alternatively, cohesive fracture energy (Gc) provides a direct quantitative measure of the mechanical integrity of the film. While fracture energy provides important insight into mechanical stability, it typically requires a more complex measurement method than the film on elastomer tests. Here, we compare the COS using film on elastomer testing, with cohesive fracture energy measured using four-point bending for a range of polymer semiconductor films. The polymers considered have a range of molecular structures and molecular packing characteristics providing a broad representative sample set. The values of Gc ranged from 0.4 to 18 J/m2 while COS ranged from 2% to over 100%. We show that COS of the films can be correlated with Gc providing support that COS is a valuable measurement to probe the mechanical toughness of polymer semiconductor films. We also discuss the physical characteristics each measurement highlights and the complementary nature of these measurements.

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elastomer (FOE) method.16,17 This is primarily used to determine the elastic modulus and COS of the film9,12,15 and can also provide other characteristics such as fracture strength in some cases.18 COS provides an important perspective of film ductility and is a direct probe of stretchability.2 However, the relationship between COS and mechanical failure of flexible organic electronic devices under various loading conditions has not been well established. Alternatively, there are more advanced mechanical measurements to probe key properties including tensile tests of films floating on water,19 nanoindentation measurements,20 and four-point bending (FPB) and double-beam cantilever (DCB) testing.4,13,14 FPB and DCB tests in particular provide a direct measurement of the adhesive or cohesive fracture energy of the film, which are fundamental metrics that capture the likelihood of failure of flexible devices under given loading conditions. For example, it has been shown that fracture energy is directly related to the minimum radius of curvature of multilayer films prior to failure.8 While fracture energy provides a quantitative probe of mechanical failure, the measurement is more complex than

INTRODUCTION Polymer semiconductors are promising materials for a range of applications such as photovoltaic devices, thin film transistors, and displays. A unique advantage of polymers over inorganic semiconductors is that they have favorable mechanical characteristics for realizing flexible and stretchable devices.1−3 Such devices require that the films are able to withstand large strains encountered during device manufacturing and operation.4−7 Thus, characterizing the thermomechanical behavior of polymer semiconductors is an important consideration to ensure mechanical stability.4,8,9 Mechanical properties of interest typically include storage and loss modulus, yield strain, crack onset strain (COS), adhesive fracture energy, and cohesive fracture energy, among others.4,9−11 There have been numerous reports on conjugated polymers and polymer blends that have shown that these properties can vary widely and are dependent on a number of molecular and morphological features.9,12−15 In most organic electronic applications, the polymer semiconductors films are less than 200 nm thick and thus encounter challenges when attempting to measure their mechanical behavior.16 Nevertheless, a number of measurement methods have been established to characterize these thin films. One of the simplest measurement approaches is to probe the thin film while on an elastomer substrate, referred to as film on © XXXX American Chemical Society

Received: June 16, 2017 Revised: October 9, 2017

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DOI: 10.1021/acs.macromol.7b01282 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules COS measurements and requires more sophisticated test equipment. Here, we compare the COS measured using the FOE method to cohesive fracture energy (Gc) measured using FPB for a variety of conjugated polymers showing that a clear correlation exists between these properties. The relationship between COS and Gc has been previously studied in a number of thin brittle films on supporting substrates.21−27 It was shown that there is a direct relationship between COS and Gc for elastic films on elastic or elastic−plastic substrates.21−23 This relationship was derived using linear elastic fracture mechanics (LEFM) with a finite fracture mechanics perspective.21,22 While the derivation of this relationship is based on LEFM, it has been extended to inelastic thin films,25 discussed in more detail below. Here, we consider a variety of polymer semiconductors with widely varying ductility. We show that for this family of polymers there remains a correlation between COS and Gc that extends to large applied strains and films that show varying fracture behavior. Establishing a correlation between Gc and COS for polymer semiconductors allows the simple COS measurement to inform the expected critical stresses that would lead to film fracture in a device. A comparison of the measurements also highlights the film characteristics that each measurement is uniquely capable of probing and the complementary information they are able to provide. Combined, these measurements provide greater insight into the origins of mechanical integrity of polymer semiconductor thin films.

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EXPERIMENTAL DETAILS

Polymer Semiconductors. Six different high performance polymer semiconductors were studied, chosen for their various molecular structures and known variation in ductility. These polymers are commonly used in thin films transistor and photovoltaic device applications. The molecular structure of each polymer is provided in Figure 1 and include PTB7-Th, P(NDI2OD-T2), P3HT, pBTTT, PCDTPT, and DPP-DTT. Two P3HT variants were considered that consisted of different molecular weights and regioregularity. This includes P3HT with weight-averaged molecular weight (Mw) of 57 kg/ mol, dispersity (ĐM) of 2.4, and regioregularity of 91−93% from Reike Metals and P3HT with Mw = 135 kg/mol, ĐM = 2.5, and regioregularity >98% from Sigma-Aldrich. We will use the terms LMw-P3HT for the material from Reike Metals and HMw-P3HT for the material from Sigma-Aldrich. pBTTT was procured from Solarmer with Mw > 12 kg/mol and ĐM = 1.8. P(NDI2OD-T2) was purchased from Polyera with Mw = 178 kg/mol and ĐM = 3.7. PTB7-Th (Mw = 140 kg/mol, ĐM = 2−3), PCDTPT (Mw = 76 kg/mol, ĐM = 2.5), and DPP-DTT (Mw = 86 kg/mol) were procured from 1-Material. Information on the glass transition temperature of the polymers is provided in the Supporting Information. All polymer films considered are tested at a temperature below their Tg when known except for P3HT, which has a Tg of approximately 15 °C.28 Film Preparation. All substrates were cleaned by sonication for 15 min in deionized (DI) water, acetone, and isopropanol, followed by UV-ozone treatment for 15 min, rinsing with DI-water, and drying under N2 gas flow. Neat polymer films were spun-cast on silicon and indium tin oxide (ITO) coated glass substrates precoated with poly(3,4-ethylenedioxythiophene) polystyrenesulfonate (PEDOT:PSS), formulation AI4083 from Heraeus Materials. Polymer films of different thicknesses were produced, within the range of ∼50 to ∼300 nm, by varying the solvent, the solution concentration, and the spin-cast speed. Details on the processing conditions are provided in the Supporting Information (Table S1). PEDOT:PSS films were cast at 5000 rpm for 60 s and annealed at 120 °C for 20 min in air, which resulted in 30 nm thick film. All film thicknesses were measured using variable angle spectroscopic ellipsometry (J.A. Woollam M2000).

Figure 1. Molecular structures of the polymers considered. Mechanical Characterization. Cohesive fracture energy can be measured using a variety of methods. Here we use FPB as it has been one of the most commonly used approaches to analyze thin film organic semiconductors.29 Specimen preparation started with a 50 mm × 50 mm × 1.1 mm ITO coated glass used as the substrate. A PEDOT:PSS film was spun-cast onto the ITO followed by spin-casting the polymer semiconductor film. The PEDOT:PSS layer assists in promoting cohesive fracture of the polymer semiconductor film.30 Following the polymer semiconductor layer, 20 nm Ca and 100 nm Al were thermally evaporated at ∼10−7 mbar on top of the polymer film. The prepared stack was then covered with a glass slide that was adhered to the stack using a brittle epoxy (EPO-TEK, 353-ND). The epoxy was cured at 80 °C for 1 h. The metal film provides a barrier to possible epoxy diffusion into the polymer layer. The material stack with the high work function PEDOT:PSS and low work function Ca layer also mimics common organic optoelectronic device structure and is a specimen stack previously used in FPB tests.4,13,14 The prepared sandwich structure was diced into smaller test specimens of size 50 mm × 5 mm using a high speed dicing saw (Disco Co., DAD 321). This was done by cutting trenches into the glass on both sides of the sample at a depth of 4/5 the glass thickness. This approach is used to prevent the cooling water of the dicing saw from interacting with the hydrophilic PEDOT:PSS. Edges of the stack were also sealed with B

DOI: 10.1021/acs.macromol.7b01282 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules epoxy. Specimens of size 50 mm × 5 mm were cleaved from the prenotched sandwich. On these specimens, a notch to initiate precrack was made with a depth of approximately 4/5 the glass thickness. The notch was created on the glass coated with ITO. The FPB specimen along with the film stack is illustrated in Figure 2a. The fracture energy

observed under an optical microscope while being strained, and the strain at which the first cracks were observed was identified as the COS, as illustrated in Figure 2b. All measurements were conducted in air at room temperature.

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RESULTS AND DISCUSSION Cohesive Fracture Energy. The Gc of the polymers were measured over a range of thicknesses, with results given in Figure 3. A linear fit is applied to the fracture energy with

Figure 2. (a) Illustration of four-point bending specimen and loading conditions, with the film stack provided on the left. (b) Illustration of film on elastomer crack onset strain measurement. was measured using the delamination test system (DTS Co.). The substrate was loaded under the fixture at the displacement rate of 0.8 μm/s with outer pin distance of 40 mm and inner pin distance of 17 mm or 22 mm. Cohesive fracture energy was calculated by31

Gc =

Figure 3. Cohesive fracture energy of the polymer films with variation in film thickness. A linear fit is applied to the data for each polymer type. Fracture energies at each thickness were measured from a minimum of six test specimens. Uncertainties were taken as 1 standard deviation of the mean.

21Pc 2L2 16b2h3E ̅

(1)

where Pc is the critical load, b the width, and h is the half thickness of the test specimen. L is the distance between the inner and the outer pins, and E̅ is the plane strain elastic modulus of the glass substrate. The elastic modulus of glass was taken as 70 GPa and Poisson’s ratio as 0.24. The fracture energy is calculated from the load−displacements curves, following a previously reported approach.4,14 Example load− displacement curves for the four-point bend specimens are given in Figure S1a. Cohesive failure was visible for all the systems studied, which was identified by the polymer film visually observed on both sides of the fracture. The fractured interfaces were also scanned using atomic force microscopy (AFM), and the measured surfaces were indicative of cohesive fracture. For FOE tests, polymer films were first spin-coated on a PEDOT:PSS film to achieve consistent film morphology between the FOE and FPB measurements. After casting the films on PEDOT:PSS coated glass, they were transferred to a polydimethylsiloxane (PDMS) elastomer substrate through a water transfer method.16 Once the film was on the PDMS, its elastic modulus was measured using a buckling based method described in detail elsewhere.16 Here, the elastic modulus is given by

⎛ λ ⎞3 Ef = 3Es⎜ B ⎟ ⎝ 2πt ⎠

thickness as a guide to the eye and to highlight the thickness dependence. The polymers with the lowest fracture energy (pBTTT, PCDTPT) do not have significant thickness dependences, consistent with brittle failure. The majority of the polymers, PTB7-Th, LMw-P3HT, DPP-DTT, and N2200, had Gc between 3.0 and 6.5 J/m2. Of these polymers, PTB7-TH had the largest thickness dependence followed by P(NDI2ODT2), LMw-P3HT, and DPP-DTT. Finally, the HMw-P3HT had the largest variation in Gc with thickness and for thick films had a substantially higher Gc of 17 J/m2 compared to the other polymers considered. To gain insight into the fracture behavior, the fractured surface topography was measured by AFM. Characteristic surfaces for each polymer type are compared in Figure 4. pBTTT was observed to have a highly planar surface indicative of its brittle nature and well-defined terraced microstructure.33 PCDTPT, DPP-DTT, and PTB7-Th had a similar fracture surface with small nodule features that extended away from the fracture surface. This may be attributed to crazes forming at the crack tip due to the expected molecular entanglements associated with their large Mw and fracture taking place below their glass transition temperatures. Of these polymers, PCDTPT had the lowest measured fracture energy. This can be attributed to the stiff backbone and greater crystallinity, which would have the effect of increasing the persistence length of the chains, and possibly reducing entanglements, leading to a smaller plastic zone around the crack tip. In the FPB test, the load vs displacement behavior of PCDTPT films exhibited a sawtooth pattern (Figure S1b) which is often associated with

(2)

where λB is the buckling wavelength, t is the film thickness, and E̅ is the plane strain modulus. E̅ = E/(1 − v2) where ν is the Poisson’s ratio. The Poisson’s ratio of all semiconductor films was taken as 0.35, and for PDMS it was taken as 0.5.32 The elastic modulus of a strip of PDMS was measured using a conventional tensile test approach. The elastic modulus was calculated from the slope of stress−strain curve in the limit of 15% strain. The COS of the polymer films were determined by straining the film in tension while on the elastomer at an approximate strain rate of 2%/s. The film preparation followed the same procedure as the buckling measurements, but the film-elastomer stack is placed in tension rather than compression.15 The film was C

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Figure 4. AFM height images of the fractured film surfaces resulting from four-point bending tests. The films measured include (a) 290 nm thick pBTTT, (b) 185 nm thick PCDTPT, (c) 165 nm thick DPP-DTT, (d) 156 nm thick PTB7-Th, (e) 88 nm thick P(NDI2OD-T2), (f) 222 nm thick LMw-P3HT, and (g) 177 nm thick HMw-P3HT. Scan size was 10 μm × 10 μm for all films, and the RMS roughness is provided below each image.

stick−slip behavior during fracture, indicative of an elastic strain buildup, during crack arrest, prior to a forward crack jump.34,35 The fractured surfaces of PCDTPT, DPP-DTT, and PTB7Th films of similar thickness were measured by AFM, with images given in Figure 4. The measured fracture surface roughness of these films is found to increase with measured fracture energy. The AFM image for P(NDI2OD-T2) was from a thinner film than the other polymers considered and thus has a corresponding low surface roughness. The fracture surface roughness increased with film thickness as observed for PCDTPT and P(NDI2OD-T2), shown in Figure S2. The P(NDI2OD-T2) films also showed features of crazing. Finally, the fracture of HMw-P3HT resulted in a fracture interface with much higher roughness than that of LMw-P3HT. The larger Mw polymer results in increased chain entanglements which resist pull out and transfers the stress to neighboring chains, increasing the size of the plastic zone and making the film tougher.14 The entanglements contribute to a large plastic zone and lead to a significant thickness dependence of Gc, as observed for HMw-P3HT. This is associated with the plastic zone being constrained by the top and bottom substrates, such that thinner films will limit the size of the plastic zone leading to lower Gc. The large plastic zone also results in the rough fracture surface observed by AFM. This is consistent with previous reports of fracture energy in P3HT−fullerene bulk heterojunction films where a strong Mw dependence on Gc was observed along with a greater thickness dependence with increasing P3HT Mw.14 This Mw dependence is also consistent with the other polymers being considered, with the higher Mw PTB7-Th and P(NDI2OD-T2) having a greater thickness dependence than the lower Mw P3HT, DPP-DTT, and PCDTPT. The higher Mw suggests increased entanglements; however, it should be noted that entanglements will depend more specifically on the chain length, polymer backbone stiffness, and processing conditions. Elastic Modulus. The elastic modulus of the films with various thicknesses is given in Figure 5a. The elastic modulus varied from 0.05 GPa for DPP-DTT to 0.4 GPa for PTB7-Th. The majority of the polymers did not have a significant thickness dependence, similar to previous reports.15,16 The exception to this was PTB7-Th and P(NDI2OD-T2), which showed an increase in stiffness with film thickness. Changes in elastic modulus have been shown to drop for ultrathin films

Figure 5. (a) Elastic modulus and (b) crack onset strain of the polymer films with variation in film thickness. A linear fit is applied to the graphs for each polymer type. Both properties at each thickness were measured from a minimum of three films. Uncertainties were taken as 1 standard deviation of the mean.

tested below their bulk glass transition temperature due to surface confinement effects; however, this is usually found for thicknesses less than 50 nm.37,38 Thus, we do not attribute the change in modulus of PTB7-Th and P(NDI2OD-T2) to confinement effects. Alternatively, there may be a change in film D

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Comparison of Mechanical Characteristics. A comparison between of Gc and COS for all films considered is provided in Figure 6a. The HMw-P3HT is not included in the plot due

morphology associated with the different casting conditions used to obtain the desired film thickness leading to changes in the modulus. A possible morphological contribution to the variation in elastic modulus requires further investigation. In addition, the HMw-P3HT was found to have a larger elastic modulus than the LMw-P3HT. The elastic modulus of P3HT has been reported to be invariant over the Mw considered based upon molecular dynamic simulations and nanomechanical dynamic analysis.40,14 Thus, we attribute the difference in elastic modulus primarily to differences in film crystallinity. The HMw-P3HT has greater regioregularity (>98%) than the LMwP3HT (91−93%). A decrease in regioregularity has been shown to also result in films with lower crystallinity.41 With P3HT having a glass transition temperature below the measurement temperature,41 a change in crystallinity will be reflected in the measured elastic modulus. Crack Onset Strain. The COS of the films with varying thickness are given in Figure 5b, and the characteristic crack features as observed by optical microscopy are given in Figure S3. The COS varied from 2% to over 120%. The HMw-P3HT COS is not plotted, as the PDMS ruptured (∼120% strain) prior to observing cracks in these films. pBTTT and PCDTPT exhibited a low COS with an average of 2% and 16%, respectively. Both polymers had COS values that were invariant with thickness. These values are consistent with previous reports of COS for pBTTT and PCDTPT.15,42 This brittle behavior may be attributed to high crystallinity typically found in these materials and their rigid backbones.15,42 DPP-DTT and P(NDI2OD-T2) both had a COS of approximately 40% and with little thickness dependence. Finally, LMw-P3HT and PTB7-Th had COS that varied from approximately 50% to 80% as the film thickness is decreased from 200 to 50 nm. Fracture in both pBTTT and PCDTPT films had unstable growth forming channel cracks.24 The remainder of the films had characteristically stable crack growth. P(NDI2OD-T2) and DPP-DTT films formed cracks that arrested quickly after formation. PTB7-Th and LMw-P3HT films had similar diamond shape cracks that had very little propagation once initiated. COS is driven by the stress in the film produced during the applied strain. The ability for the polymer to reorient under an applied load and transfer load between entangled chains enables a large COS. Entanglement density of polymer chains is dependent upon combination of parameters including Mw, chain persistence length, and casting conditions.40,43 It is difficult to delineate the effect of these parameters individually. In the polymers considered, P3HT is the only polymer tested known to be above its Tg providing significant chain mobility leading to the large COS. The other ductile polymers strained below their Tg undergo cold drawing (Figure S4). The entanglement density is not expected to change over the thickness range considered18 and is thus not expected to be the origin of the variation in COS with thickness that is observed in Figure 5b. Instead, thicker films may result in increased nonuniformity in the film that would act as points of stress concentration resulting in lower COS. The change in COS between the LMw-P3HT and HMw-P3HT is consistent with previous reports on P3HT, where it was reported that the COS varied from 13% to approximately 145% with an increase in Mw from 22 to 102 kDa.14 This can be attributed to an increase in polymer chain length which would allow for a larger maximum extension.40

Figure 6. (a) Comparison of the fracture energy (Gc) and crack onset strain (COS) for all the polymer specimens considered. The shaded area indicates zone within which the values lie. (b) Relationship between Gc /t and COS for all polymers considered. A linear fit of the data is also provided.

to the indeterminate COS. It is observed that among different polymers there is a general correlation between these two mechanical properties where an increase in COS also shows an increase in Gc. A shaded region that encompasses the data in Figure 6a is included to highlight this relationship. This general trend can broadly be attributed to common molecular and morphological features that dictate the mechanical behavior in the two measurements. For example, the low Tg of P3HT leads to ductile films and a large COS. The ductility also results in a large plastic zone around the crack tip in the FPB tests resulting in a large Gc. Similarly, the pBTTT was found to have a low COS and Gc compared to the other polymers associated with its brittle nature. For channel cracks that form in brittle materials confined to an elastic substrate, a direct relationship between Gc and COS can be found analytically. In this case, the fracture energy is given by21,24 Gc = E

tσc 2(1 − ν 2) g Ef

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Macromolecules where t is the thickness of the film, σc is the critical stress, and g is a dimensionless parameter that takes different values depending upon the configuration of the crack, the Dundurs’ parameters, and the stress−strain behavior of the film and substrate. This relationship was derived using LEFM and relies on the critical strain energy release rate leading to unstable crack propagation.22 The critical stress can then be directly related to COS when the stress−strain behavior of the film is known. Equation 3 has been extended to the case of an elastic film on an elastic−plastic substrate by applying a shear lag analysis.23 Furthermore, it has been successfully extended to inelastic films on elastic and elastic−plastic substrates.25 In this case, the films continued to form channel cracks at relatively low applied strains of less that 10%. In systems with an inelastic thin film, the general form of eq 3 is still applied with modification to the dimensionless g term.25 Here, we consider the applicability of the general form of eq 3 to the polymer semiconductor films. Equation 3 provides a relationship between Gc and COS given an appropriate constitutive relationship between σc and COS is known. From this perspective, we plot Gc /t vs COS in Figure 6b. A linear fit is applied to this data with a coefficient of determination (r2) of 0.95, demonstrating a clear linear correlation between these parameters. The polymer that deviates the most from this trend is P(NDI2OD-T2), and removing this from the data set results in an r2 of 0.97. Equation 3 along with the correlation observed in Figure 6b suggests a proportional trend between σc and COS. This is likely to be due to a common stress−strain relationship in the COS tests. Assuming good adhesion of the film to the elastomer substrate, plastic deformation of the ductile polymer films will occur uniformly without necking. Without neck formation strain hardening is likely, and in this regime a largely linear relationship between stress and strain is expected. Taking this to be the case, the correlation suggests that the films have a similar yield strain and strain hardening behavior. This is supported in part by a recent study by Rodriquez et al. where stress−strain curves of pseudo-free-standing films of P3HT of different molecular weights were measured.17 A largely linear relationship between stress and strain was found for the films after the yield point and the fracture stress were along a similar load−elongation curve. If the Poisson’s ratio and g term of all films are considered to be the same, the critical stress given in eq 3 is proportional to GcEf /t . However, GcEf /t does not follow the clear trend

been observed in metals, where the localized necking lead to crack onset.45,46 Furthermore, it has also been shown that higher COS can be observed for polymer films when improving the adhesion between the film and PDMS.47 Here, the adhesion of the polymers to the PDMS is expected to be similar, and delamination prior to crack formation is not considered to be a major factor dictating COS, suggesting mode I failure is dominant. Thus, applying the in-plane modulus found through buckling may not be applicable in eq 3. However, it is noteworthy that most polymers had a similar measured in-plane elastic modulus between 0.1 and 0.3 GPa, suggesting that treating the modulus as a constant between samples is a reasonable approximation. In addition, with all polymers falling along the same trend line in Figure 6b suggests that g is similar for the polymers considered. The correlation between Gc /t and COS provided in Figure 6b is found to fit the moderately ductile polymers best, where LMw-P3HT and PTB7-Th follow a well-defined thickness dependence. The correlation also generally holds well for the brittle polymers considered, although the thickness dependence is not captured. The correlation may not hold as well for highly ductile polymer semiconductors, such as HMw-P3HT. In this case, the 87 nm thick HMw-P3HT had a fracture energy of 3.6 J/m2 and a COS over 120%. The large COS would put this film outside the highlighted zone in Figure 6a and significantly off the correlations established in Figure 6b. This may be attributed to changes in the strain hardening behavior of the film that would significantly change the dimensionless g parameter. Importantly, this correlation is not expected to be universal for all polymer films. Diverse materials with similar crack onset can have widely varying fracture energy. For example, brittle materials such as glass and porous silica can have a similar fracture strain but very different fracture energy.48 Yet, the polymer semiconductors with conjugated backbones and aliphatic side chains appear to provide a commonality in molecular features that allow for this broad correlation to be observed. Generally, all of the polymers considered have conjugated backbones with some level of cofacial molecular packing with π-orbital coupling. All the polymers have backbones with locations of single carbon bonds that may be locations of chain scission. There will also be packing between the aliphatic side chains that are expected to be mechanically weak. These similarities likely contribute to the films following a common trend line between Gc and COS. Differences in the polymers including Mw, chain rigidity, and crystallinity then likely drive the differences observed in ductility and toughness. The polymer that deviates the most from the correlation given in Figure 6b is P(NDI2OD-T2). This could be associated with the greater face-on packing nature.39 It is expected that the cofacial packing of the conjugated backbone would have stronger intermolecular forces than the interactions between the aliphatic side chains. Given the FPB Mode I loading is acting out of the plane of the film, this packing behavior may lead to the larger fracture energy compared to the other polymers. However, further research is necessary to understand the deviation of P(NDI2OD-T2) from the observed trend.

that Gc /t follows when using the elastic modulus measured by the buckling metrology approach. One reason for this is the complex dependence of g on the elastic modulus mismatch between the film and substrate and the stress−strain behavior of the film and substrate.22,25 Determining the specific form of g is beyond the scope of this work. Additionally, an anisotropic elastic modulus is known to be present in these conjugated polymer films,15,44 and there are differences in loading conditions between the FPB and buckling measurements. In the FPB tests, the film will be under mixed mode loading with a phase angle, ψ ∼ 43°.4 Comparatively, the fracture mode for COS measurement depends upon whether the film cracks prior to or after delamination from the PDMS substrate. In the case of film fracture after delamination, failure is mixed mode with the phase angle ψ ∼ 40°, while it is mode I (ψ ∼ 0°) if there is no delamination. Under tensile strain, film delamination will result in localized necking in the ductile films.45,46 This has

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CONCLUSION

A linear correlation between Gc /t and COS was found for a range of polymer semiconductor thin films. This relationship accurately represents the fracture behavior of polymers that have a large range in ductility with COS that spanned from 2% F

DOI: 10.1021/acs.macromol.7b01282 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

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to 80%. This correlation is believed to occur due to the strain hardening behavior of supported thin films and the critical stress required for cohesive fracture. The ability to establish this relationship is associated in part to the common physical characteristics that drive fracture in these films. For example, polymers with greater ductility that lead to large COS will also have large plastic zones surrounding the crack tip in FPB tests contributing to larger Gc. While the correlation between COS and Gc may not be universal for all polymer films, it appears that structural commonality of polymer semiconductors is enough to establish this broad relationship. Extended this correlation to ductile films and across a variety of polymer semiconductors enables COS to be an indirect measure of mechanical toughness. Finally, COS and Gc are shown to provide complementary information that assists in capturing a broad perspective of the fracture behavior of polymer thin films. Gc and the related fracture surface profiles provide information on fracture features such as crazing and yielding at the crack tip, while the COS captures the film ductility more directly and the deformation of the polymer film prior to fracture. The COS measurements can also be paired with morphological characterization tools to capture how the polymer chains rearrange prior to crack formation.3

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01282. Polymer film casting conditions, example four-point bending data, AFM measurements of thick PCDTPT and P(NDI2OD-T2) polymer films, and polymer T g information (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (B.T.O.). ORCID

Brendan T. O’Connor: 0000-0002-8999-5184 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The authors gratefully acknowledge support for this research through NSF CAREER Award 1554322. The authors thank Dr. J. Muth for assistance with dicing the four-point probe specimens. The DTS and ellipsometry measurements were also made possible through support from the UNC Board of Governors’ Research Opportunity Initiative.

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DOI: 10.1021/acs.macromol.7b01282 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.7b01282 Macromolecules XXXX, XXX, XXX−XXX