Mechanical Properties of Polymer–Fullerene Bulk Heterojunction

Apr 11, 2017 - This paper reports the tensile properties and fracture mechanism of PTB7:PC71BM bulk heterojunction (BHJ) films as a function of compos...
0 downloads 12 Views 1MB Size
Subscriber access provided by HACETTEPE UNIVERSITESI KUTUPHANESI

Article

Mechanical Properties of Polymer-Fullerene Bulk Heterojunction Films: Role of Nanomorphology of Composite Films Jae-Han Kim, Jonghyeon Noh, Hyesun Choi, Jung-Yong Lee, and Taek-Soo Kim Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b00184 • Publication Date (Web): 11 Apr 2017 Downloaded from http://pubs.acs.org on April 14, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Chemistry of Materials is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Mechanical Properties of Polymer-Fullerene Bulk Heterojunction Films: Role of Nanomorphology of Composite Films Jae-Han Kim,§,†,∥ Jonghyeon Noh,§,‡ Hyesun Choi,† Jung-Yong Lee,*,‡ and Taek-Soo Kim*,† †

Department of Mechanical Engineering, KAIST, Daejeon, 34141, Korea

∥Korea Atomic ‡

Energy Research Institute, Daejeon, 34057, Korea

Graduate School of Energy Environment, Water, and Sustainability (EEWS), KAIST, Daejeon,

34141, Korea

ABSTRACT: : This paper reports the tensile properties and fracture mechanism of PTB7:PC71BM bulk heterojunction (BHJ) films as a function of composition mixing ratio. An increased concentration of fullerene makes the BHJ films stiffer and more brittle, and fracture occurs along aggregated fullerene domain boundaries. The tensile strength is maximized at a polymer-fullerene content ratio of 1:1. Furthermore, an additive, 1,8-diiodoctane (DIO), in the films induces fine nanomorphology, which increases the stiffness and strength and reduces the ductility of the films further. This is especially true under a high PC71BM load due to the expanded interfacial surface areas between the PC71BM and PTB7 polymer domains. The photovoltaic performance of the BHJ films on polydimethylsiloxane (PDMS) substrates after tensile stretching cycles is also examined in detail.

ACS Paragon Plus Environment

1

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 25

1. INTRODUCTION Organic photovoltaic cells (OPVs) based on polymer-fullerene bulk heterojunction (BHJ) structure have been highlighted as a lightweight power source for next generation wearable electronic devices because of advantages such as roll-to-roll processability, low cost, and a high power density per weight of 10 Wg−1. Through rapid developments in the synthesis of new polymer materials, nanomorphology engineering, and charge transport layers for efficient charge collection at both electrodes, the power conversion efficiency (PCE) of BHJ OPVs recently reached over 11%.1-3 Despite extensive research on enhancing the efficiency of organic photovoltaic cells, however, study on the mechanical reliability of OPVs for wearable and stretchable devices have been relatively overlooked. In the early research, metal electrodes and oxide layers such as silver, aluminum, indium tin oxide (ITO), and MoO3 have been regarded as primary limitations on the mechanical reliability of OPVs due to their brittle characteristics.4,5 Undeniably, the long-term mechanical reliability of the wearable organic devices should be guaranteed because they are constantly exposed to external loading and deformation that could lead to cracking and delamination of the BHJ films. Some approaches have been suggested to enhance the mechanical reliability of OPVs by controlling adhesion and cohesion force of interlayer and BHJ films.6-8 Contrary to much effort for flexible electrodes and interfacial engineering to overcome such barriers, the mechanical behavior of BHJ films is less understood. Usually, the mechanical properties of BHJ films have been quantified on an elastomer polydimethylsiloxane (PDMS) substrate using a buckling technique9,10 under a compressive stress. However, the buckling technique would be limited to use in low fullerene content films because of the brittleness and poor adhesion to the PDMS substrate at a high fullerene content,

ACS Paragon Plus Environment

2

Page 3 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

which leads to the fracture and delamination of the BHJ films.11 Furthermore, characterization of the film under compressive stress might not estimate the mechanical properties under tensile stress properly,12 which are directly related to the actual operating conditions of stretchable and wearable organic photovoltaics. Nevertheless, the direct characterization of the tensile properties and fracture mechanism of pristine BHJ films has been scarce. This is mainly due to the difficulty in preparing and handling very thin (~100 nm) and fragile BHJ films in a freestanding form, especially at a high concentration of fullerene in the films. In this study, for the first time, we successfully characterize the intrinsic tensile properties of pristine polymer-fullerene bulk heterojunction films over a wide range of the content mixing ratio and an organic additive using a direct tensile testing technique shown in Figure 1. Typically, 1,8diiodoctane (DIO) is used as an additive to optimize the morphology of the low bandgap polymer and a fullerene derivative such as [6,6]-phenyl-C71-butyric acid methyl ester (PC71BM). As the DIO additive is a selective solvent for PCBM, it hinders early solidification of polymers and enables the BHJ films to develop a fine morphology without PCBM aggregations during the drying process, thus improving the electrical properties of the photovoltaic devices.13,14 Among the

low

bandgap

polymers

that

show

high

PCEs,

we

chose

poly[[4,8-bis[(2-

ethylhexyl)oxy]benzo[1,2-b:4,5-b']dithiophene-2,6-diyl][3-fluoro-2-[(2-ethylhexyl)

carbonyl]

thieno[3,4-b]thiophenediyl]] (PTB7), for which the nanomorphology and effect of additives on its electrical properties are well understood15-17 (Figure 1a). Nanoscale BHJ films are delaminated from a glass substrate and transferred to water, where, subsequently, the mechanical properties of BHJ films are measured.18 The effect of nanomorphology on the mechanical properties and fracture mechanism of the films are investigated in detail. Lastly, we demonstrate the effect of tensile strain on the photovoltaic properties of the BHJ films on a PDMS substrate.

ACS Paragon Plus Environment

3

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 25

Figure 1. Specimen fabrication and tensile testing processes. (a) Molecular structures of polymer donor (PTB7), fullerene accepter (PC71BM) and DIO additive. (b) Spin-coated PTB7:PC71BM 1:1 blend film on a PEDOT:PSS/glass substrate. Two insets present the cross-sectional SEM image of PTB7:PC71BM/PEDOT:PSS/glass and diced sample, respectively. (c-d) Femtosecond laser patterning of dog-bone-shaped tensile specimen and optical images of patterned specimen. (e) Water-assisted transfer of the BHJ film on water surface. Left inset depicts the dog-boneshaped specimen with separated fragments (scale bar 100 m). (f) The PTB7:PC71BM blend film transferred on water surface. (g-h) The tensile specimen is gripped by PDMS-coated Al grips using van der Waals adhesion between the PDMS and the specimen surface. The tensile test is performed by applying tensile strain until the fracture occurred at the specimen.

ACS Paragon Plus Environment

4

Page 5 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

2. EXPERIMENTAL SECTION Tensile Testing of Polymer-Fullerene BHJ Film. It has been considered challenging to perform a direct tensile characterization of polymer-fullerene BHJ films because of the following critical difficulties: first, the manipulation of very thin (~100 nm) and fragile BHJ films in a freestanding form after separating the films from a substrate without damages or wrinkles; second, non-contact strain measurement of polymeric thin films during the tensile tests without using a strain gauge. Here, a water-assisted exfoliation technique was used to separate the films from the substrate using a water-soluble sacrificial layer. Furthermore, the water surface was utilized as a platform for the direct tensile test because the high surface tension and low viscosity of water enables the easy manipulation and frictionless sliding of BHJ films. Previously, the tensile tests of ultra-thin films on water were performed to measure the mechanical properties of Au thin films19 and polymeric thin films.18,20,21 Non-contact strain measurement of thin films was performed using a digital image correlating (DIC) system.19 The preparation of the PTB7:PC71BM BHJ films for the tensile tests is depicted in Figure 1b-h. Figure 1b presents a spin-coated BHJ film on a poly(3,4-ethylenedioxythiophene)poly(styrenesulfonate)(PEDOT:PSS)/glass substrate, the cross-sectional scanning electron microscope (SEM) image of PTB7:PC71BM/PEDOT:PSS/glass layer (upper inset), and a diced sample (lower inset). A dog-bone-shaped tensile testing specimen was fabricated using a femtosecond laser patterning technique (Figure 1c). Figure 1d shows the optical images of a laser-patterned BHJ blend film. We adopted two different pointed wings as displacement marks (Figure 1d) in the DIC system; otherwise, the wrinkles appearing on the film surface under tensile strain can disturb the tracking of initial displacement marks. The PEDOT:PSS layer was used as a water-soluble sacrificial layer. By instilling water into the PEDOT:PSS layer, the BHJ

ACS Paragon Plus Environment

5

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 25

film was delaminated from the glass substrate (Figure 1e) and, subsequently, set afloat on the water surface. After eliminating surrounding fragments (Figure 1e inset), the dog-bone-shaped BHJ film specimen on the water surface remained (Figure 1f). The BHJ film specimen was gripped via van der Waals adhesion between the PDMS-coated grip and the film surface, enabling easy manipulation of the film on the water. The tensile testing system mainly consists of a DIC camera, a load cell, and a linear actuator on an anti-vibration table (Supporting Information, Figure S1). The tensile strain was applied at a rate of ~3.0 × 10−4 per s using a linear stage until failure occurred at the specimen (Figure 1g,h). From stress-strain curves, the mechanical properties of the films including, elastic modulus (stiffness), crack onset strain (ductility), and tensile strength, can be obtained. Sample Preparation. The PTB7 was obtained from 1-Material with a Mw of 123,000 kg mol−1 and polydispersity (PDI) of ~2.5. PC71BM was supplied from Nano-C. PEDOT:PSS (Clevios PH1000) was purchased from Heraeus. Zonyl FS-300 (Zonyl), DMSO, chlorobenzene(CB) and 1,8-diiodoctane (DIO) were purchased from Sigma-Aldrich. PTB7:PC71BM at a weight ratio of 1:0, 1:0.5, 1:1, 1:1.5 and 1:2 were dissolved in CB at 50 °C. This solution was stirred for 12 h in a N2 environment. For the formation of DIO-added BHJ films, 3 wt% of DIO was added to the solution. PEDOT:PSS was first spun on to the glass substrate at 3000 rpm for 30 s, and PTB7:PC71BM-dissolved CB solution was spun on the PEDOT:PSS/glass substrate. The average thicknesses of the BHJ films were within 100−120 nm. The dog-bone-shaped BHJ tensile specimen was prepared using a femtosecond laser patterning technique with the power of 0.2 mW at a patterning speed of 1 mm s−1.

ACS Paragon Plus Environment

6

Page 7 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Fabrication and Characterization of Organic Photovoltaic Cells. 1) PDMS membrane was coated on the glass substrate; 2) high conductive PEDOT:PSS (PH1000) with surfactant (Zonyl FS-300) film was spin-coated on the PDMS as a transparent electrode and a hole transport layer (HTL); 3) The PTB7:PC71BM active layer was transferred on the PEDOT:PSS/PDMS/glass substrate by a stamping process; 4) PTB7:PC71BM /PEDOT:PSS/PDMS structure was simply detached from the glass substrate; 5) the 10 tensile stretching cycles from 0 to 10% tensile strain were applied to the active layer using a custom stretching jig; 6) The photovoltaic properties were measured after MoO3 and Ag electrode deposition. The current density-voltage (J-V) characteristics of the cells were measured using a solar simulator (PEC-L12, Peccell Technologies) under irradiance of 100 mW cm−2 from a 150 W Xe short-arc lamp filtered by an air mass 1.5 G filter. A 6.25 mm2 aperture mask was attached to the device to define the illuminated area clearly.

3. RESULTS AND DISCUSSION Morphology Characterization. PTB7:PC71BM BHJ films with and without DIO additive were prepared with the blend ratios of 1:0, 1:0.5, 1:1, 1:1.5 and 1:2. The surface morphologies of the PTB7:PC71BM blend films were characterized by atomic force microscopy (AFM) as shown in Figure 2. The surface morphology of the 1:0.5 blend film changed slightly compared to the neat polymer film (1:0 blend ratio) (Figure 2a,b and k). For the higher PC71BM content (over 50%) the surface morphology of the films became rougher and the sphere-shaped domains were created as a result of PC71BM aggregation (Figure 2c-e, k, and Figure S2a,b). The PC71BM-rich domains were 100–200 nm in diameter at 1:1 blend films, and they became larger with increased PC71BM. While the BHJ films without additive exhibited critical phase separation of PTB7 and PC71BM

ACS Paragon Plus Environment

7

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 25

with significant roughness increment, the DIO-added films showed uniform surface morphology with much reduced surface roughness (Figure 2h-k, and Figure S2c,d). These significant morphological changes result from the solubility balance of PTB7 and PC71BM during a drying process of chlorobenzene(CB) solution. As shown in Figure 2c-e, the aggregated PC71BM is firstly formed because of the solubility limit of PC71BM.13 However, this phase separation did not appear at the low PC71BM content films (e.g., 1:0.5 blend ratio) because the amount of PC71BM is too small to reach the solubility limit (Figure 2b). On the other hand, the use of DIO helps to create the uniform and fine morphology of PTB7:PC71BM mixture by interfering with the PC71BM aggregation owing to its selective solubility only for PC71BM.13,15,16 AFM images verify such fine morphology of BHJ films without the aggregated PC71BM domains (Figure 2f-j).

Figure 2. Atomic force microscopy images and surface roughness of PTB7:PC71BM blend films. Surface morphologies of PTB7:PC71BM blend films (a-e) without DIO additive, and (f-j) with DIO additive. A square area of 5 m × 5 m was scanned (scale bar 1 m). (k) Root mean squared surface roughness of the PTB7:PC71BM blend films as a function of PC71BM content and DIO additive.

ACS Paragon Plus Environment

8

Page 9 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Tensile Properties of BHJ Films. The mechanical properties of PTB7:PC71BM BHJ films have been investigated. The representative stress–strain curves of PTB7:PC71BM BHJ films are shown in Figure S3. The obtained mechanical properties of the films including elastic modulus, crack onset strain and tensile strength are presented in Figure 3a-c and Table S1 in the Supporting Information. The elastic modulus, crack onset strain, and tensile strength of neat PTB7 films were determined to be 0.44±0.04 GPa, 27.4±2.5%, and 14.5±0.3 MPa, respectively. Our results are slight different from the previous results for PTB7; the modulus of 1.58 GP and the crack onset strain of 2.2% measured on PDMS substrate,22 and the modulus of 0.5–1.4GPa from molecular dynamic (MD) simulation.23 The difference in the experimental results is primarily attributed to the different molecular weight (140 kDa vs. 14kDa), testing method (tension vs. compression), and the type of platform (PDMS vs. water).24 Also, the tensile strain rate affects the elastic modulus of polymeric films; a higher strain rate leads to a higher modulus.24 Overall, stiffer and more brittle BHJ films were obtained as the PC71BM content increased. On the other hand, the tensile strength showed a maximum value of 17.9±0.5 MPa with the 1:1 blend films. In fact, similar tendencies for stiffness and ductility with a low fullerene load (≤ 50%) have been reported previously using various conjugated polymers measured on PDMS substrates including P3ATs:PCBM at 1:0.5 ratio,11 P3HT:PCBM at 1:0.8 ratio25 and P3HT:PCBM at 1:1 ratio.26-29 The tensile behavior of PTB7:PCBM at 1:1.5 ratio acquired from MD simulations also showed increased elastic modulus.23 The increase in elastic modulus of polymer-fullerenes composite is due to the filler effect of fullerenes, which have a higher stiffness than polymers. Indeed, adding nanoparticles such as silicate30 and graphite31 generally results in the increased stiffness and decreased ductility of polymeric nanocomposites.31-34 Contrary to the progressive

ACS Paragon Plus Environment

9

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 25

changes in stiffness and ductility, the tensile strength is usually maximized at a certain particle content.32-34 The PTB7:PC71BM films with a 1:0.5 ratio still exhibited excellent ductile behavior against the tensile strain, and the surface roughness of the films was also similar to that of neat PTB7 films (Figure 2a,b and k), suggesting that such a small amount of PC71BM (33.3 wt%) does not significantly influence the surface morphology or the ductility of the films (Figure 3d left). On the other hand, the 1:1.5 blend BHJ films became stiffer and more brittle with increased PC71BM content (Figure 3e left). The fractured surfaces of 1:0.5 and 1:1.5 blend films were observed by SEM as shown in Figure 3d and e right. The fracture occurred along the aggregated PC71BM domains, which are clearly observed in the 1:1.5 blend films (detailed SEM images are shown in Figure S4). This result indicates that the main fracture mechanism in the BHJ films is debonding crack extension at polymer-fullerene interfaces because of their weak adhesion.35 The ductility reduction is mainly attributed to the larger volume of PC71BM, which behaves as debonding sites in the BHJ films. The ductility of BHJ films (thickness: ~100 nm) can also be affected by the surface roughness of the aggregated PC71BM domains, which could cause local defects or stressconcentrated regions (Figure 2c-e, k, and Figure S2a,b).

ACS Paragon Plus Environment

10

Page 11 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Figure 3. Tensile properties and fracture mechanism of PTB7:PC71BM blend films as a function of the PC71BM content and DIO additive. (a) Elastic modulus, (b) crack onset strain, and (c) tensile strength of PTB7:PC71BM blend films as a function of blend ratio and DIO additive. Fracture mechanism and SEM images of fractured surface of PTB7:PC71BM bulk heterojunction films with respect to PC71BM content and DIO additive: (d) 1:0.5 blend films, (e) 1:1.5 blend films without DIO additive, and (f) 1:1.5 blend films with DIO additive (scale bar 200 nm).

Effect of Additive on the Tensile Properties of BHJ Films. The effect of 1,8-diiodoctane (DIO) on the mechanical properties of BHJ films needs to be investigated in detail because the additive is often used to enhance the photovoltaic performance of OPVs. The mechanical properties of the 3% DIO-added PTB7 film were similar to those of neat PTB7 film, suggesting that such small amounts of DIO additive would not critically affect the mechanical properties of the neat PTB7 films. The addition of 3% DIO lowered the elastic modulus from 0.83±0.05 to 0.65±0.04 GPa at the low PC71BM content of 1:0.5 blend ratio, which can be attributed to the plasticizing effect of DIO

ACS Paragon Plus Environment

11

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 25

that increases free volume in the films.11 Interestingly, however, with PC71BM content above 50%, the DIO-added BHJ films showed 20–30% higher elastic moduli than the BHJ films without DIO additive (Figure 3a and Table S1). At the same time, the tensile strength also increased, and the maximum value of 24.5±1.2 MPa was observed with the 1:1 blend films (Figure 3c). Furthermore, the crack onset strain decreased by approximately 2.2–3.2 times compared to the BHJ films without the DIO additive (Figure 3b and Table S1). These transitions in stiffness, strength, and ductility are attributed to significant morphology changes within the BHJ films caused by the DIO additive. In the DIO-added BHJ films with high PC71BM content, PC71BM was uniformly dispersed in the film, resulting in a decrease in surface roughness, and finer PC71BM and PTB7 domains were created without PC71BM aggregation (Figure 2h-k, and Figure S2c,d). In polymeric nanocomposite films, embedded particle size plays a critical role in the mechanical properties of the films because it determines the interfacial surface areas between the nanoparticle and polymer matrix.30,32,36-38 With the same blend ratio of PTB7 and PC71BM, the interfacial surface area between the PC71BM domains and PTB7 polymer matrix is much increased in the DIO-added BHJ films because of the finer PC71BM domains, further increasing the elastic modulus and tensile strength of the films.36,38 Moreover, the finer PC71BM domains generate more debonding sites in the BHJ films than the aggregated PC71BM domains, hence degrading the ductility of the films. Therefore, much stiffer, stronger and more brittle PTB7:PC71BM blend films were obtained by adding DIO additive as depicted in Figure 3f. The fracture surface of DIO-added 1:1.5 blend films showed fine morphology without aggregated PC71BM domains.15,16 Increased stiffness and strength can improve the load bearing capacity of BHJ films. On the other hand, unfortunately, decreased ductility can be deleterious in flexibility

ACS Paragon Plus Environment

12

Page 13 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

and stretchability of BHJ films, which are key factors for wearable devices, although fiber-like PC71BM and fine PTB7 domains in BHJ films are often advantageous for photovoltaic performances.

Theoretical Prediction of the Elastic Modulus of BHJ Films. Despite extensive research on the elastic modulus of BHJ films, a systematic prediction of the elastic modulus of BHJ films considering fullerene content as well as nanomorphology has been rarely studied. Here, we exploited the rule of mixtures39-41 and Halpin–Tsai equations42,43 to predict the elastic modulus of PTB7:PC71BM blend films. For the theoretical models, we assumed linear-elastic behavior of materials, uniform distribution of filler, and perfect bonding between the matrix and the filler, which may not be possible in reality.

Figure 4. Theoretical prediction of elastic moduli of BHJ films. Elastic moduli of BHJ films are compared with the spherical and randomly oriented short fiber models from Halpin–Tsai equations and the rule of mixtures.

ACS Paragon Plus Environment

13

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 25

The predicted moduli of BHJ films from the rule of mixtures increase when increasing the volume fraction of PC71BM, and the measured moduli lie well between the Voigt and Reuss boundaries as shown in Figure 4 (more details in Supporting Information, Note 1). Occasionally, synergistically greater modulus than the upper-bound modulus (Voigt model) is observed in some polymer-polymer composites due to the formation of reactive products or the increased crystallinity of components.44,45 However, only van der Waals and electrostatic interactions exist between polymer and fullerene, without any chemical reorganization in our BHJ films.35 The crystallinity of PTB7 would not be increased because of the miscibility of PC71BM with PTB7.15 Thus, the elastic modulus within the Voigt and Reuss boundaries are reasonable. The semi-empirical Halpin–Tsai model considers the detailed geometries of fillers, and has been widely employed in predicting the mechanical properties of nanocomposites.34,38,46,47 The elastic modulus of composites for Halpin-Tsai model can be expressed as:

 =  

 



(3)

where

=

 /    / 

(4)

and  is a shape factor to describe the geometry effect of particles; various empirical equations for this factor are available in the literature. For the spherical particle or circular fiber, the value of  is given by  = 2(/) + 40 or 2(/$) + 40 , where L is the length of a fiber and T and D is the thickness and diameter of the filler, respectively.43 The 40 term is a modified shape factor to compensate the possible disagreement of Halpin-Tsai equation at a high volume fraction of particle since the particle fraction can affect the interaction between the particles.43,48 Among the various geometrical models, the spherical and randomly oriented short fiber models

ACS Paragon Plus Environment

14

Page 15 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

were adopted as the most applicable models for the BHJ films without DIO (sphere-like PC71BM domains) and with DIO additive (fiber-like PC71BM domains), respectively, based on our AFM, SEM, and TEM analyses (Figure 2, S4, and S5), and previous studies15,16. In the spherical model, the aspect ratio is unity regardless of the size of the PCBM domains, and hence the shape factor is 2. On the other hand, for the randomly oriented short fiber model, short fibers with an average aspect ratio of 6.66 (shape factor: 13.3) were assumed for the elongated PC71BM domains in the analysis based on the TEM analysis (Figure S5 and Note 2 in Supporting Information). The elastic modulus of the randomly oriented short fiber model (% ) is determined by the empirical equation46,49 expressed as % = (3/8)( + (5/8)* where EL and ET are the elastic moduli along longitudinal and transverse directions for aligned fiber composites. The elastic moduli of EL and ET of BHJ films were calculated using equation (3) and (4) with the aspect ratios of 6.66 and 1 (shape factors of 13.3, and 2), respectively. Figure 4 shows that the spherical and the short fiber models seem to represent well the BHJ films without DIO and with DIO, respectively. The theoretical values of DIO-added BHJ films calculated using the randomly oriented short fiber model showed the larger moduli than the spherical model due to the large shape factor. The disagreement in the DIO-added 1:0.5 blend films is due to the low PC71BM content, and it seems more reasonable to adopt the spherical model considering the similar morphologies to the 1:0.5 blend films without DIO (Figure 2). Measured moduli generally lie slightly below the predicted values, which can be attributed to particle aggregation38 or imperfect bonding.38,47 Moreover, the discrepancy between theoretical and experimental values gradually increased as the PC71BM content increased. This is mainly due to the significantly increased PC71BM domain size, which reduces the filler effects.38 The initially assumed aspect ratio of PC71BM domains may be varied with respect to the PC71BM content,

ACS Paragon Plus Environment

15

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 25

which could also be responsible for the disagreement. Using the theoretical analysis and the experimental data, for the first time, we applied the conventional prediction models for the nanocomposite to the BHJ films, and showed that reliable prediction of the elastic modulus of BHJ films with respect to the PC71BM content as well as DIO additive is viable.

Figure 5. Photovoltaic properties and mechanical reliability of OPVs. (a) Schematic illustration of fabrication process for PTB7:PC71BM-based OPVs on PDMS substrates after tensile stretching cycles. Optical microscopic images of (b-e) 1:0.5 and (f-i) 1:1.5 PTB7:PC71BM blend films under different tensile strain from 0% to 20% (scale bar 20 m). J-V characteristics of (j) 1:0.5 and (k) 1:1.5 PTB7:PC71BM-based OPVs on PDMS substrate under AM 1.5G 100 mW cm−2 illumination.

ACS Paragon Plus Environment

16

Page 17 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Stretchable Behavior and Photovoltaic Properties. To see the potential of the BHJ OPVs for wearable applications, we examined photovoltaic properties of the DIO-added PTB7:PC71BM blend films (1:0.5 and 1:1.5) on a PDMS substrate after tensile stretching cycles. Figure 5a depicts a fabrication process for OPVs for characterizing the photovoltaic properties of the BHJ films after tensile stretching cycles (Figure S4). Figure 5b-i show the optical microscopic images of the BHJ films transferred on the PDMS substrate with increasing tensile strain. The 1:0.5 blend films allowed for tensile strain up to 20% without significant damages (Figure 5b-e). In contrast, cracks were observed in the 1:1.5 blend films even at a low tensile strain of 5% (Figure 5f,g). Once cracks were formed, further crack propagation and the delamination of the films occurred with increasing tensile strain (Figure 5h,i). Figure 5j,k show the current density-voltage (J-V) characteristics of the OPVs with a flux of 100 mW cm−2 under AM 1.5G spectrum. The photovoltaic properties before and after tensile stretching cycles are presented in Table S2. As shown in Figure 5j, the OPVs with 1:0.5 blend films showed tolerance to tensile strain without critical degradation. The slight Voc drop from 0.14 V to 0.12 V could be induced by the delamination of PEDOT:PSS, resulting in a surface charge recombination. On the contrary, the photovoltaic properties of 1:1.5 blend film were severely damaged after tensile stretching cycles (Figure 5k). Although the DIO-added 1:1.5 BHJ film showed an optimum condition as compared to the 1:0.5 BHJ film in terms of PCE performance as shown in Figure S7, the 1:0.5 BHJ film had great advantages in mechanical resilience with much higher ductility (19.4 and 2.1% for 1:0.5 and 1:1.5, respectively).

ACS Paragon Plus Environment

17

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 25

4. CONCLUSION In summary, the intrinsic tensile properties of PTB7:PC71BM bulk heterojunction films as a function of the PC71BM content and DIO additive were characterized, and the fracture mechanism was investigated. We showed that the tensile properties of BHJ films are strongly dependent on the nanomorphology that is controlled by the composition, and this fact was rigorously confirmed by theoretical analyses. The effect of tensile strain on stretchability and photovoltaic properties of BHJ films indicates that co-optimization of both mechanical and photovoltaic properties is essential to obtain reliable performance of wearable optoelectronic devices.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publication website. Details of tensile testing method, 3-dimensional surface morphology, stress-strain curves, and stretching-releasing process of BHJ films; tables of mechanical and photovoltaic properties of BHJ films; and theoretical prediction of elastic moduli for BHJ films.

AUTHOR INFORMATION Corresponding Authors *Email: [email protected] *Email: [email protected] Author Contributions

ACS Paragon Plus Environment

18

Page 19 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

§

Chemistry of Materials

These authors contributed equally to this work.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This research was supported by the Basic Science Research Program (2015R1A1A1A05001115, 2015R1A2A2A01006689, 2015M1A2A2057509) and Wearable Platform Materials Technology Center (2016R1A5A1009926) funded by the National Research Foundation under the Ministry of Science, ICT and Future Planning.

REFERENCES (1)

Liao, S. H.; Jhuo, H. J.; Cheng, Y. S.; Chen, S. A. Fullerene Derivative‐Doped Zinc

Oxide Nanofilm as the Cathode of Inverted Polymer Solar Cells with Low‐Bandgap Polymer (PTB7‐Th) for High Performance. Adv. Mater. 2013, 25, 4766-4771. (2)

He, Z.; Zhong, C.; Su, S.; Xu, M.; Wu, H.; Cao, Y. Enhanced Power-Conversion

Efficiency in Polymer Solar Cells Using an Inverted Device Structure. Nat. Photonics 2012, 6, 591-595. (3)

Zhao, J.; Li, Y.; Yang, G.; Jiang, K.; Lin, H.; Ade, H.; Ma, W.; Yan, H. Efficient Organic

Solar Cells Processed from Hydrocarbon Solvents. Nat. Energy 2016, 1, 15027. (4) Lipomi, D. J.; Tee, B. C.-K.; Vosgueritchian, M.; Bao, Z. Stretchable Organic Solar Cells, Adv. Mater. 2011, 23, 1771-1775. (5) Savagatrup, S.; Chan, E.; Renteria-Garcia, S. M.; Printz, A. D.; Zaretski, A. V.; O'Connor T. F.; Rodriquez, D.; Valle, E.; Lipomi, D. J. Plasticization of PEDOT:PSS by Common Additives

ACS Paragon Plus Environment

19

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 25

for Mechanically Robust Organic Solar Cells and Wearable Sensors, Adv. Funct. Mater. 2015, 25, 427-436. (6) Dupont, S. R.; Oliver, M.; Krebs, F. C.; Dauskardt, R. H. Interlayer Adhesion in Roll-to-Roll Processed Flexible Inverted Polymer Solar Cells. Sol. Energy Mater. Sol. Cells 2012, 97, 171-175. (7) Brand, V.; Bruner, C.; Dauskardt, R. H. Cohesion and Device Reliability in Organic Bulk Heterojunction Photovoltaics Cells. Sol. Energy Mater. Sol. Cells 2012, 99, 182-189. (8) Bruner, C.; Miller, N. C.; McGehee, M. D.; Dauskardt, R. H. Molecular Intercalation and Cohesion of Bulk Heterojunction Photovoltaic Devices. Adv. Funct. Mater. 2013, 23, 2863-2871. (9)

Savagatrup, S.; Printz, A. D.; O'Connor, T. F.; Zaretski, A. V.; Rodriquez, D.; Sawyer, E.

J.; Rajan, K. M.; Acosta, R. I.; Root, S. E.; Lipomi, D. J. Mechanical Degradation and Stability of Organic Solar Cells: Molecular and Microstructural Determinants. Energy Environ. Sci. 2015, 8, 55-80. (10)

Stafford, C. M.; Harrison, C.; Beers, K. L.; Karim, A.; Amis, E. J.; VanLandingham, M.

R.; Kim, H.-C.; Volksen, W.; Miller, R. D.; Simonyi, E. E. A Buckling-Based Metrology for Measuring the Elastic Moduli of Polymeric Thin Films. Nat. Mater. 2004, 3, 545-550. (11)

Savagatrup, S.; Makaram, A. S.; Burke, D. J.; Lipomi, D. J. Mechanical Properties of

Conjugated Polymers and Polymer‐Fullerene Composites as a Function of Molecular Structure. Adv. Funct. Mater. 2014, 24, 1169-1181. (12)

Landel, R. F.; Nielsen, L. E., Mechanical properties of polymers and composites. CRC

Press: 1993. (13)

Shin, N.; Richter, L. J.; Herzing, A. A.; Kline, R. J.; DeLongchamp, D. M. Effect of

Processing Additives on the Solidification of Blade‐Coated Polymer/Fullerene Blend Films via In‐Situ Structure Measurements. Adv. Energy Mater. 2013, 3, 938-948.

ACS Paragon Plus Environment

20

Page 21 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

(14)

Liu, Y.; Zhao, J.; Li, Z.; Mu, C.; Ma, W.; Hu, H.; Jiang, K.; Lin, H.; Ade, H.; Yan, H.

Aggregation and Morphology Control enables Multiple Cases of High-Efficiency Polymer Solar Cells. Nature Commun. 2014, 5, 5293. (15) Liu, F.; Zhao, W.; Tumbleston, J. R.; Wang, C.; Gu, Y.; Wang, D.; Briseno, A. L.; Ade, H.; Russell, T. P. Understanding the Morphology of PTB7:PCBM Blends in Organic Photovoltaics. Adv. Energy Mater. 2014, 4, 1301377. (16)

Hedley, G. J.; Ward, A. J.; Alekseev, A.; Howells, C. T.; Martins, E. R.; Serrano, L. A.;

Cooke, G.; Ruseckas, A.; Samuel, I. D. Determining the Optimum Morphology in HighPerformance Polymer-Fullerene Organic Photovoltaic Cells. Nature Commun. 2013, 4, 2867. (17)

Kim, W.; Kim, J. K.; Kim, E.; Ahn, T. K.; Wang, D. H.; Park, J. H. Conflicted Effects of

a Solvent Additive on PTB7:PC71BM Bulk Heterojunction Solar Cells. J. Phys. Chem. C 2015, 119, 5954-5961. (18)

Kim, T.; Kim, J.-H.; Kang, T. E.; Lee, C.; Kang, H.; Shin, M.; Wang, C.; Ma, B.; Jeong,

U.; Kim, T.-S. Flexible, Highly Efficient All-Polymer Solar Cells. Nature Commun. 2015, 6, 8547. (19)

Kim, J.-H.; Nizami, A.; Hwangbo, Y.; Jang, B.; Lee, H.-J.; Woo, C.-S.; Hyun, S.; Kim,

T.-S. Tensile Testing of Ultra-Thin Films on Water Surface. Nature Commun 2013, 4, 2520. (20)

Kim, J.-S.; Kim, J.-H.; Lee, W.; Yu, H.; Kim, H. J.; Song, I.; Shin, M.; Oh, J. H.; Jeong,

U.; Kim, T.-S.; Kim, B. J. Tuning Mechanical and Optoelectrical Properties of Poly (3hexylthiophene) through Systematic Regioregularity Control. Macromolecules 2015, 48, 43394346. (21)

Liu, Y.; Chen, Y.-C.; Hutchens, S.; Lawrence, J.; Emrick, T.; Crosby, A. J. Directly

Measuring the Complete Stress–Strain Response of Ultrathin Polymer Films. Macromolecules 2015, 48, 6534-6540.

ACS Paragon Plus Environment

21

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 25

(22) Roth, B.; Savagatrup, S.; Santos, V. de los N.; Hagemann, O.; Carlé, J. E.; Helgesen, M.; Livi, F.; Bundgaard, E.; Søndergaard, R. R.; Krebs, F. C.; Lipomi, D. J. Mechanical Properties of a Library of Low-Band-Gap Polymers. Chem. Mater. 2016, 28, 2363-2373. (23) Root, S. E.; Jackson, N. E.; Savagatrup, S.; Arya, G.; Lipomi, D. J. Modelling the Morphology and Thermomechanical Behaviour of Low-Bandgap Conjugated Polymers and Bulk Heterojunction Films. Energy Environ. Sci. 2017, 10, 558-569. (24) Rodriquez, D.; Kim, J.; Root, S.; Fei, Z.; Boufflet, P.; Heeney, M.; Kim, T.; Lipomi, D. J. Comparison of Methods for Determining the Mechanical Properties of Semiconducting Polymer Films for Stretchable Electronics. ACS Appl. Mater. Interfaces 2017, 9, 8855-5562. (25)

Tahk, D.; Lee, H. H.; Khang, D.-Y. Elastic Moduli of Organic Electronic Materials by the

Buckling Method. Macromolecules 2009, 42, 7079-7083. (26)

Lipomi, D. J.; Chong, H.; Vosgueritchian, M.; Mei, J.; Bao, Z. Toward Mechanically

Robust and Intrinsically Stretchable Organic Solar Cells: Evolution of Photovoltaic Properties with Tensile Strain. Sol. Energy Mater. Sol. Cells 2012, 107, 355-365. (27) Awartani, O.; Lemanski, B. I.; Ro, H. W.; Richter, L. J.; DeLongchamp, D. M.; O'Connor, B. T. Correlating Stiffness, Ductility, and Morphology of Polymer:Fullerene Films for Solar Cell Applications. Adv. Energy Mater. 2013, 3, 399-406. (28)

Printz, A. D.; Savagatrup, S.; Rodriquez, D.; Lipomi, D. J. Role of Molecular Mixing on

the Stiffness of Polymer:Fullerene Bulk Heterojunction Films. Sol. Energy Mater. Sol. Cells 2015, 134, 64-72. (29)

Savagatrup, S.; Rodriquez, D.; Printz, A. D.; Sieval, A. B.; Hummelen, J. C.; Lipomi, D.

J. [70]PCBM and Incompletely Separated Grades of Methanofullerenes Produce Bulk Heterojunctions with Increased Robustness for Ultra-Flexible and Stretchable Electronics. Chem.

ACS Paragon Plus Environment

22

Page 23 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Mater. 2015, 27, 3902-3911. (30)

Douce, J.; Boilot, J.-P.; Biteau, J.; Scodellaro, L.; Jimenez, A. Effect of Filler Size and

Surface Condition of Nano-Sized Silica Particles in Polysiloxane Coatings. Thin Solid Films 2004, 466, 114-122. (31)

Fouad, H.; Elleithy, R. High Density Polyethylene/Graphite Nano-Composites for Total

Hip Joint Replacements: Processing and in Vitro Characterization. J. Mech. Behav. Biomed. Mater. 2011, 4, 1376-1383. (32)

Fu, S.-Y.; Feng, X.-Q.; Lauke, B.; Mai, Y.-W. Effects of Particle Size, Particle/Matrix

Interface Adhesion and Particle Loading on Mechanical Properties of Particulate–Polymer Composites. Composites, Part B 2008, 39, 933-961. (33)

Cheang, P.; Khor, K. Effect of Particulate Morphology on the Tensile Behaviour of

Polymer–Hydroxyapatite Composites. Mater. Sci. Eng., A 2003, 345, 47-54. (34)

Ku, H.; Wang, H.; Pattarachaiyakoop, N.; Trada, M. A Review on the Tensile Properties

of Natural Fiber Reinforced Polymer Composites. Composites, Part B 2011, 42, 856-873. (35)

Tummala, N. R.; Bruner, C.; Risko, C.; Brédas, J.-L.; Dauskardt, R. H. Molecular-Scale

Understanding of Cohesion and Fracture in P3HT:Fullerene Blends. ACS Appl. Mater. Interfaces 2015, 7, 9957-9964. (36) Ji, X. L.; Jing, J. K.; Jiang, W.; Jiang, B. Z. Tensile Modulus of Polymer Nanocomposites. Polym. Eng. Sci. 2002, 42, 983-993. (37)

Al-Turaif, H. A. Effect of Nano TiO2 Particle Size on Mechanical Properties of Cured

Epoxy Resin. Prog. Org. Coat. 2010, 69, 241-246. (38)

Xia, L.; Xu, Z.; Sun, L.; Caveney, P. M.; Zhang, M. Nano-Fillers to Tune Young’s

Modulus of Silicone Matrix. J. Nanopart. Res. 2013, 15, 1-11.

ACS Paragon Plus Environment

23

Chemistry of Materials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(39)

Page 24 of 25

Voigt, W. Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper

Körper. Ann. Phys 1889, 274, 573-587. (40)

Reuss, A. Calculation of the flow limit of mixed crystals due to the plasticity condition

for single crystals. J. of Appl. Math. Mech. 1929, 9, 49-58. (41)

Facca, A. G.; Kortschot, M. T.; Yan, N. Predicting the Elastic Modulus of Natural Fibre

Reinforced Thermoplastics. Composites, Part A 2006, 37, 1660-1671. (42) Halpin, J. C. Effects of Environmental Factors on Composite Materials; DTIC Document: 1969. (43)

Affdl, J.; Kardos, J. The Halpin‐Tsai Equations: a Review. Polym. Eng. Sci. 1976, 16,

344-352. (44)

Granado, A.; Eguiazábal, J. I.; Nazábal, J. Solid‐State Structure and Mechanical

Properties of Blends of an Amorphous Polyamide and a Poly (amino‐ether) Resin. Macromol. Mater. Eng. 2004, 289, 281-287. (45)

Ramiro, J.; Eguiazabal, J.; Nazabal, J. Synergistic Mechanical Behaviour and Improved

Processability of Poly(ether imide) by Blending with Poly(trimethylene terephthalate). Polym. Adv. Technol. 2003, 14, 129-136. (46)

Mortazavian, S.; Fatemi, A. Effects of Fiber Orientation and Anisotropy on Tensile

Strength and Elastic Modulus of Short Fiber Reinforced Polymer Composites. Composites, Part B 2015, 72, 116-129. (47)

Johnsen, B.; Kinloch, A.; Mohammed, R.; Taylor, A.; Sprenger, S. Toughening

Mechanisms of Nanoparticle-Modified Epoxy Polymers. Polymer 2007, 48, 530-541. (48) Bouafia, F.; Serier, B.; Bouiadjra, B. A. B. Finite Element Analysis of the Thermal Residual Stresses of SiC Particle Reinforced Aluminum Composite, Comput. Mater. Sci. 2012, 54,

ACS Paragon Plus Environment

24

Page 25 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

195-203. (49)

Tsai, S. W.; Pagano, N. J. Invariant properties of composite materials; DTIC Document:

1968.

Table of Contents

ACS Paragon Plus Environment

25