Large charge mobilities of semi-crystalline organic semiconducting films could be obtained by mechanically aligning the material phases of the film with the loading axis. A key element is to utilize the inherent stiffness of the material for optimal or desired alignment. However, experimentally determining the moduli of semi-crystalline organic thin films for different loading directions is difficult, if not impossible, due to film thickness and material anisotropy. In this paper, we address these challenges by presenting an approach based on combining a composite mechanics stiffness orientation formulation with a Gaussian statistical distribution to directly estimate the in-plane stiffness (transverse isotropy) of aligned semi-crystalline polymer films based on crystalline orientation distributions obtained by X-ray diffraction experimentally at different applied strains. Our predicted results indicate that the in-plane stiffness of an annealing film was initially isotropic, and then it evolved to transverse isotropy with increasing mechanical strains. This study underscores the significance of accounting for the crystalline orientation distributions of the film to obtain an accurate understanding and prediction of the elastic anisotropy of semi-crystalline polymer films.

Semi-crystalline organic semiconducting thin films, such as poly(3-hexylthiophene) (P3HT) films on flexible polymer substrates, have the potential for novel optical and electronic applications, such as flexible electronics and solar cells. Accurate predictions or measurements of structure-property correlations in these organic semiconducting thin films need to be obtained for desired mechanical behavior and desired charge mobility.1 Large charge mobilities could be obtained through mechanical aligning processes, such as crystalline orientation alignment,2 so that crystalline domains of semi-crystalline P3HT are aligned with the loading directions. The crystalline orientation distributions of strained films can be measured by X-ray diffraction (XRD) as a function of applied strains,2–4 and these aligned films can result in significantly improved charge mobility.5 A key element, however, is to utilize the inherent stiffness of the material for optimal or desired alignment. However, experimentally determining the moduli of P3HT semi-crystalline thin films is difficult, due to film thickness,6 material anisotropy, and loading instabilities.

The stiffness of organic thin films has been indirectly measured by buckling metrology techniques and estimates7 that relate the wrinkles and film thicknesses to an isotropic stiffness. However, this method is not sufficient to characterize the orientation effects on the in-plane stiffness (transverse isotropy) of semi-crystalline polymer thin films, and it is generally not sufficient for different loading conditions and modes, such as tensile loading conditions and for buckling loading along different orientations. The wrinkled wavelengths are generally non-uniform8 and the film is not elastically isotropic, and this does not meet the key assumption of isotropy for buckling techniques and estimates. Furthermore, the non-uniform wrinkle patterns are associated with complex local stress distributions of the different amorphous and crystalline phases of semi-crystalline organic thin films.8,9 In this paper, we address these challenges by presenting an approach based on combining a composite mechanics stiffness orientation formulation with a Gaussian statistical distribution to directly estimate the in-plane stiffness of aligned semi-crystalline polymer films based on crystalline orientation distributions obtained by XRD experimentally at different applied strains. The methodology for determining the in-plane stiffness (or the transverse isotropy moduli) is introduced, which allows investigating the effects of orientation alignment on the transverse isotropic evolution of P3HT thin films.

In Fig. 1, φi is the in-plane crystalline orientation distribution for the face-on crystals [(100) in-plane diffraction peak]. It is observed that the crystals can rotate toward the axial loading direction during the stretching of the P3HT-PDMS thin film system. The crystalline orientation distributions {φi} of P3HT semi-crystalline films were experimentally obtained by XRD techniques (see, for example, Ref. 4) at different strains for thermally annealed films (180 °C for 5 min), and these orientations are shown in Fig. 2. As seen from Fig. 2, these orientation curves, {φi}, approximately correspond to a Gaussian distribution N(0,σ2), with a standard deviation, σ, and a density function of orientations, fφ(x), as

{φi}N(0,σ2),
(1a)
fφ(x)=12πσe(x22σ2)dx.
(1b)
FIG. 1.

Top view of semi-crystalline polymer thin films and orientation alignment induced by mechanical loadings.

FIG. 1.

Top view of semi-crystalline polymer thin films and orientation alignment induced by mechanical loadings.

Close modal
FIG. 2.

High-resolution point detector XRD scan of the scanned P3HT crystalline orientation distributions at different strains for annealed films.

FIG. 2.

High-resolution point detector XRD scan of the scanned P3HT crystalline orientation distributions at different strains for annealed films.

Close modal

As seen from Fig. 2, one standard deviation σ of the 50% strained film is at approximately 15°, and that of the 100% strained film is at approximately 7.5°. The smaller deviation of the orientation distributions indicates that a higher percentage of crystals rotated towards the axial loading direction. Therefore, the standard deviation represents the degree of alignment, and it decreases with increasing mechanical strains. While the X-ray diffraction only measured face-on crystallites, this is considered the in-plane orientation distribution for all crystals.2 

A representative cell is used to represent an arbitrary two-phase local area consisting of the ith crystalline phase and the amorphous phase. The orientation of each local representative cell is given by φι, characterized as the XRD-scanned Gaussian distributed curves. For transverse isotropy, the local in-plane axial stiffness, Qxxi, along the loading direction and the stiffness, Qyyi, perpendicular to the loading direction can be defined as a function of the crystalline orientation of each local representative cell8 as

Qxxi(φi)=cos4(φi)Q11+sin4(φi)Q22+2(Q12+2Q66)sin2(φi)cos2(φi),
(2a)
Qyyi(φi)=sin4(φi)Q11+cos4(φi)Q22+2(Q12+2Q66)sin2(φi)cos2(φi),
(2b)

where the in-plane stiffnesses Q11, Q22, Q12, and Q66 of the representative cell were estimated experimentally from the in-plane stiffness of the highly aligned film (e.g., 100%-AN film in Fig. 2) with an offset orientation φi near 0° with respect to the loading axis, which would indicate an alignment of the loading axis with the crystalline orientations. By buckling this 100%-AN highly oriented film along different loading orientations from 0° to 90° to the previously strain-aligned direction, the experimental data of in-plane stiffness varied continuously between the high value of Q11 loading parallel to the strain-aligned direction (φi=0°) and the low value of Q22 loading perpendicular to the strain-aligned direction of the film (φi=90°) based on Eq. 2(a).10 In other words, the local crystal orientations evolve to the loading axis at φi=0° in highly aligned films. From experiments10 pertaining to loading the film in different orientations and based on a buckling method, the in-plane stiffnesses of Q11 = 0.40 GPa, Q22 = 0.22 GPa, Q12 = 0.20 GPa, and Q66 = 0.05 GPa were obtained.

The global in-plane stiffness can then be calculated as a function of the local axial stiffness based on the distributed orientations of films. The influence of orientation alignment on the in-plane stiffness is

Q¯xx{φi}=E[Qxxi(φi)]=+Qxxi(x)fφ(x)dx,
(3a)
Q¯yy{φi}=E[Qyyi(φi)]=+Qyyi(x)fφ(x)dx.
(3b)

The in-plane transversely isotropic stiffness evolution as a function of increasing orientation alignment is shown in Figure 3, and this was based on Eqs. (3a) and (3b). At a large deviation of 90°, Q¯xx and Q¯yy had the same value of 0.31 GPa. This indicates that the global in-plane stiffness was initially isotropic due to randomly distributed crystalline orientations. By decreasing the standard deviation, the stiffness Q¯xx parallel to the loading direction increased to 0.405 GPa, while the stiffness Q¯yy perpendicular to the loading direction decreased to 0.225 GPa. This indicates that strain-induced transverse isotropy resulted from the crystals rotating towards the loading direction. This is consistent with anisotropic stiffness evolution observed in other nanostructured polymer films.11–13 

FIG. 3.

The anisotropic evolution of expected in-plane axial stiffness.

FIG. 3.

The anisotropic evolution of expected in-plane axial stiffness.

Close modal

A comparison of experimental and computational data at 0% strain, 50% strain, and 100% strain for an annealing film is given in Table I. The elastic anisotropy degree is defined as Q¯xx/Q¯yy. This predicted ratio increased from 1.0 to 1.8, which was close to the experimental values obtained by buckling techniques and estimates (Table I). The difference between the experimental and predicted results is because the tensile modulus from computational approach is not equal to the compressive modulus obtained from experimentally buckling the specimen. Furthermore, it is difficult to obtain uniform stiffness data for each buckling measurement. It should also be noted that for the experimental results, the loading axis is varied to obtain the moduli in each direction, but the assumption is that for each loading case, the modulus is isotropic.

TABLE I.

Experimental and computational axial stiffness and anisotropy degree at different strains for annealing films (AN).

Axial stiffness at strainsQ¯xx 0% strain (GPa)Q¯yy 0% strain (GPa)Q¯xxQ¯yy 0% strainQ¯xx 50% strain (GPa)Q¯yy 50% strain (GPa)Q¯xxQ¯yy 50% strainQ¯xx 100% strain (GPa)Q¯yy 100% strain (GPa)Q¯xxQ¯yy 100% strain
Exp. Buckling 0.3254 0.3479 0.94 0.3816 0.2357 1.62 0.4601 0.2244 2.05 
Comp. 0.3146 0.3146 1.0 0.3930 0.2362 1.66 0.4045 0.2247 1.80 
Axial stiffness at strainsQ¯xx 0% strain (GPa)Q¯yy 0% strain (GPa)Q¯xxQ¯yy 0% strainQ¯xx 50% strain (GPa)Q¯yy 50% strain (GPa)Q¯xxQ¯yy 50% strainQ¯xx 100% strain (GPa)Q¯yy 100% strain (GPa)Q¯xxQ¯yy 100% strain
Exp. Buckling 0.3254 0.3479 0.94 0.3816 0.2357 1.62 0.4601 0.2244 2.05 
Comp. 0.3146 0.3146 1.0 0.3930 0.2362 1.66 0.4045 0.2247 1.80 

In this study, a statistical composite mechanics model, in combination with XRD scanned crystalline orientation distributions, has been developed to predict the transversely isotropic behavior of semi-crystalline organic thin films. Based on the predictions, the global in-plane stiffness was initially isotropic due to random orientation distributions, and then it evolved to transverse isotropy with increasing mechanical straining of the aligned films. Furthermore, the anisotropy degree increased significantly as the orientations were almost aligned with the loading axis. This study highlights the significance of accounting for the crystalline orientation distributions of the film to obtain an accurate understanding and prediction of the elastic anisotropy of semi-crystalline polymer films that are consistent with experimental measurements.

Support from NSF Grant No. # CMMI-1200340 is gratefully acknowledged. Portions of this research were carried out at the Stanford Synchrotron Radiation Lightsource, a Directorate of SLAC National Accelerator Laboratory, and an Office of Science User Facility operated for the U.S. Department of Energy Office of Science by Stanford University. We gratefully thank Dr. Michael F. Toney and Dr. R. Joseph Kline for their assistance with the X-ray diffractions measurements.

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