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Oxidation-induced failure in semi-crystalline organic thin films
Accepted Manuscript
Oxidation-induced Failure in Semi-crystalline Organic Thin Films Bingxiao Zhao , M.A. Zikry PII: DOI: Reference:
S0020-7683(17)30007-0 10.1016/j.ijsolstr.2017.01.008 SAS 9422
To appear in:
International Journal of Solids and Structures
Received date: Revised date: Accepted date:
23 June 2016 10 December 2016 3 January 2017
Please cite this article as: Bingxiao Zhao , M.A. Zikry , Oxidation-induced Failure in Semicrystalline Organic Thin Films, International Journal of Solids and Structures (2017), doi: 10.1016/j.ijsolstr.2017.01.008
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Oxidation-induced Failure in Semi-crystalline Organic Thin Films Bingxiao Zhao and M.A. Zikry* Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910, USA
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*Corresponding Author. Email: [email protected] Abstract
Polymer oxidation is a major degradation mechanism in organic solar cells. However, microstructural details of diffusion-reaction processes and oxidation-induced
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failure in structured semi-crystalline active layers are difficult to be predicted or measured, due to material heterogeneities, such as different material phases, crystallinities, nano-film thickness. Hence, a diffusion-reaction process has been coupled
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to a crystalline-amorphous material model and fracture algorithm within a nonlinear microstructurally-based finite element (FEM) framework to investigate and predict
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heterogeneous oxidative degradation and embrittlement failure in semi-crystalline organic thin films due to the interrelated effects of diffusion, reaction, stress
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accumulations, and crystalline packing order. The edge-on packing oriented film was
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more susceptible to oxidation than the face-on oriented packing film due to higher local stresses and reaction accumulations that resulted in higher decrease of local toughness
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and extensive film cracking in the amorphous phase. The coupled effects of mechanical stresses and oxygen diffusion-reaction accelerated degradation mechanisms and resulted in film cracking and delamination occurring at lower nominal strains in comparison with the case without oxidation embrittlement. Degradation was dominated by the reaction process and exposure time, as opposed to the diffusion process due to the nano-sized
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films. This predictive framework can be used to understand fundamental local oxidative degradation mechanisms and the morphological effects on long term durability of semicrystalline organic thin films. Keywords: Semi-crystalline organic thin films, Polymer oxidation, Microstructural failure
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mechanisms, Delamination, Multi-physics coupling, organic electronics 1. Introduction
A fundamental understanding of polymer degradation is esssential for organic electronics because organic materials are more intrinsically susceptible to oxidation than
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inorganic materials. As organic thin film devices are exposed to aggressive field environments, such as combinations of oxygen, moisture, heat and mechanical loadings, both device performance and mechancial properties degrade faster due to physical and
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chemical processes (Jørgensen et al., 2012)(Jørgensen et al., 2008). Oxygen and water molecules diffuse into the active layers and react with polymeric materials, resulting in
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chain scission and crack formation. Oxidative degradation can be localized both within polymer active layers and at interfaces, and the loss of structural integrity and interfacial
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stability generally lead to a reduction of charge transfer and extraction (Reese et al.,
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2008)(Novoa et al., 2014)(Voroshazi et al., 2011). The macroscopic decay curves of either electrical and mechanical properties can
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be measured experimentally, however, that rarely provides fundamental details of the evolution of the diffusion-reaction processes, such as how different heterogenous polymer material effects, such as different material phases, and local reactions lead to degradation in structured active layers. As noted by Celina, physically-based computational models are needed to provide more fundamental understanding of local
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oxidative degradation mechanisms and morphological effects on long term durability (Celina, 2013). The fracture toughness of organic thin films can be significantly affected by environmental factors (Dupont et al., 2014). Oxidation embrittlement is a degradation
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process by which polymeric materials become brittle due to introduction of oxygen or water molecules. Environmentally assisted cracking can occur in degraded polymers when the local stresses are below the critical fracture stress. This results from interrelated mechanisms pertaining to diffusion, reaction, microstructure, fracture and external
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loadings. The oxidation induced embrittlement of semicrystalline polymers and their origin have been associated with microstructural changes (El-Mazry et al., 2013)(Gauthier et al., 2013)(Hsu et al., 2012)(Fayolle et al., 2000)(Fayolle et al.,
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2007)(Fayolle et al., 2008). The tensile stress will be dilatational and expected to interact with the diffusion-reaction process and accelerate oxidative embrittlement (Shyichuk et
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al., 2001). However, the influence of chemical reactions on microstructral failure mechanisms under long-term remain relatively unexplored.
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Finite element (FE) models of diffusion-reaction processes have been used to
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investigate oxidation-induced failure under coupled mechanical and environmental conditions (Yan and Oskay, 2015)(Liang and Pochiraju, 2014), but these approaches do
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not explicitly account for internal microstructural mechanisms and nano-sized thin films. To address these issues, we developed a microstructurally-based computational framework and a nonlinear finite-element fracture methodology that couples essential microstructural characteristics, mechanical response, oxygen diffusion and reaction, to predict and fundamentally understand heterogeneous oxidative degradation, interfacial
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delamination and film cracking in semi-crystalline organic thin films deposited on flexible PDMS substrates. In this framework, the interrelated effects of structural disorders, molecular packing orientations, crystallinity and domain sizes on local heterogeneous degradation and microstructural failure mechanisms of organic investigated for different coupled mechanical,
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semicrystalline thin films will be diffusion, and reaction conditions.
The paper is organized as follows: the multiphase material model and the stressassisted oxygen diffusion-reaction model are presented in Section 2. The microstructural-
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based failure criteria and numerical implementation approach are outlined in Section 3. The results and discussion are presented in Section 4, and a summary of results and conclusions are given in Section 5.
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2. Multiphase constitutive formulations and stress-assisted diffusion-reaction 2.1 Constitutive model for organic semi-crystalline thin films
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The crystalline-amorphous constitutive formulations of P3HT semi-crystalline thin films have been given in Zhao and Zikry (2016), only a brief outline is given here.
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A multiple-slip dislocation-density based crystalline plasticity formulation is used
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for the P3HT crystalline phase. Two possible types of disorders were taken into consideration for P3HT crystals: chain slip parallel to backbones and transverse slip
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perpendicular to backbones (Table 1), which is primarily with respect to the build-in lattice defects among ordered packing P3HT chains (Lee et al., 1993). It is assumed that the velocity gradient can be decomposed into a symmetric
deformation rate tensor
and an anti-symmetric spin tensor
. The tensors
are then additively decomposed into elastic and inelastic components as
and
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, and
.
(1a-b)
are the elastic part of total deformation tensor and lattice rotation.
and
are the inelastic parts of total deformation rate tensor and total spin rate tensor, which are defined in terms of the crystallographic slip rates as ̇
∑
,
( )
where () is summed over all slip systems, and
( ) ( )
̇
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( ) ( )
∑
( )
and
(2a-b)
are the symmetric and anti-
symmetric parts of the Schmid tensor in the current configuration respectively.
description on each slip system as
where ̇
̇
( )
[
( )
( )
][
( )
( )
]
,
(3)
is the reference shear strain rate which corresponds to a reference shear stress
, and m is the rate sensitivity parameter.
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( )
( )
)
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̇(
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A power law relation can be used to characterize the rate-dependent constitutive
( )
is the resolved shear stress on slip
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system . The reference shear stress is a modification of the classical forms (Franciosi et al., 1980) that relate reference shear stress to immobile dislocation-density ( )
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( )
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where G is the shear modulus, number of active slip systems, coefficients
∑ ( )
( )
√
( )
,
as (4)
is the static yield stress on slip system , nss is the
( )
is the magnitude of the Burgers vector, and the
are related to the strength of interactions between slip systems (Devincre
et al., 2008),(Kubin et al., 2008).
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Following the approach by Zikry and Kao (Zikry and Kao, 1996), it is assumed that, for a given deformed state of the crystalline domain, the total dislocation-density, ( )
, can be additively decomposed into a mobile dislocation density, ( )
, and an
. The evolution of mobile and immobile dislocation
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immobile dislocation-density,
( )
densities, including generation, interaction and annihilation, is determined as functions of the crystallography and deformation mode of P3HT crystalline phase. The interactions between slip systems are given in Zhao and Zikry (Zhao and Zikry, 2015).
Chain slip systems (100)[001]
Transverse slip systems (100)[010]
(010)[100]
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(010)[001]
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Table 1. Slip systems for P3HT crystalline phase
The P3HT amorphous phase is in a glassy state at room temperature, and it can be
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modeled as elasto-viscoplastic (Zhao and Zikry, 2015). We use Perzyna's viscoplastic
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model to account for the strain induced hardening behavior of the amorphous mixture (Schrauwen et al., 2004). Following the same decomposition approach as the finite strain
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crystalline plasticity approach, the symmetric deformation rate tensor Dij is decomposed into elastic and viscoplastic components as
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.
(5)
The yielding criterion of the amorphous phase is defined as
(
)
√. /
(
)
,
(6)
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where
√. /
is effective viscoplastic strain and
is the second
invariant of the deviatoric stress tensor of the amorphous phase. The function
(
where
)
is the initial yield stress, and
,
as
(7)
is the hardening modulus.
̇
and the effective
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A power law relation between the effective shear strain rate ̇ shear stress can then be defined as
)
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defines the current yield stress, and it is assumed to be linear in
(
̇ .
/ ,
(8)
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where N is the rate-sensitivity and ̇ is a reference shear strain rate. Hence, viscoplastic
is related to effective visco-plastic strain rate ̇
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as
. The viscoplatsic deformation by the normal direction
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rate tensor,
/
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strains are non-zero only if the flow function .
̇
,
(9)
. /
.
(10)
The accumulated effective viscoplastic strain in the amorphous phase is then given by ∫ ̇
.
(11)
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If the viscoplastic strain rates are zero, the deformation is finite elasticity.
The finite elasticity hypo-elastic formulation is used for PDMS substrates, which relates the deformation rate tensor to the objective stress rate is
(12)
The stress rate, ̇ , is given by ̇ is the objective stress rate and
deformation rate and
and
(13)
are the Lame´ parameters.
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where
.
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.
is the total
is the total spin rate.
2.2 Stress assisted oxygen diffusion and reaction
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For oxygen diffusion-reaction induced degradation and embrittlement failure, oxygen can diffuse into the material system and react with the polymer chain backbones,
( )
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which can cause chain scission and be accelerated by the stress field through the pressure (Serebrinsky et al., 2004). The stress-assisted diffusion-reaction equation is
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a modification of Fick’s second law, which can be given by (Dadfarnia et al., 2014;
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Olden et al., 2008; Serebrinsky et al., 2004) (Yan and Oskay, 2015)(Liang and Pochiraju, 2015) as
(
),
(14)
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( )
where C is the oxygen concentration, D is the oxygen diffusion coefficient of P3HT (Hintz et al., 2011), applied as 3 e-12 m2/s , k is the reaction constant (Hintz et al., 2010) given as 10-6 s-1, Vo is the partial molar volume of oxygen, and equal to 2.0 ×10-6 m3/mol (Sofronis and McMeeking, 1989), T is the absolute temperature. The reaction rate, R(C)
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= k C, is defined as a linear function of oxygen concentration, and it taken as part of diffusion for long time scales of hours, especially when the concentration is much lower than the saturation concentration. The pressure is positive for tensile stresses, and this stress coupling term (Eqn. 14) provides a link for coupling mechanical deformation to
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local oxidation degradation.
3. Microstructural failure criteria and numerical implementation approach
3.1 Microstructurally-based film cracking and interfacial delamination criteria
A brief outline of microstructurally-based fracture criteria of semi-crystalline
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polymers is presented here, for details see Zhao and Zikry (Zhao et al., 2016). The nonlinear fracture method is based on an overlap method and the use of phantom nodes to create multiple fracture surfaces (Wu and Zikry, 2014). For the P3HT crystalline phase, )(
)+ in the local coordinates.
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the fracture planes are associated with slip planes *(
The global orientations of these fracture planes is defined as a function of crystalline
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orientations and updated at each time step through lattice rotation matrix, , -*(
)(
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̇
as
)+.
(15)
.
(16)
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[T] is rotation matrix in terms of Euler angles to relate lattice local coordinates to global coordinates. For the amorphous phase, the fracture planes are assumed as )(
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*(
)+ in the global coordinate system, which would be perpendicular or parallel
to the tensile loading directions based on experimental observations (Awartani et al., 2013)(Lipomi et al., 2012). The normal component of the traction vector of all crack planes is monitored, and compared with a critical cohesive fracture stress determine fracture initiation and propagation as
to
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, where
*
+〈
(17) , -
〉
For the interfacial delamination, the effective interfacial stress based on normal . The
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and shear stresses is monitored to evaluate the interfacial strength maximum value was compared with a critical interfacial fracture stress
. The
adhesive strength is assumed to be smaller than the cohesive strength of the film so that the interfacial crack would propagate along the interface (Kim-Lee et al., 2014). The for both film cracking and interfacial
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crack planes and critical fracture stress delamination are listed in Table 2.
Table 2. Fracture criteria for each phase and interfacial delamination Crack planes
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Phase type
(i = a, c)
[T]{(100), (010)}
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P3HT Amorphous
(100), (010)
6
Interfacial delamination
(010)
1.5
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P3HT Crystalline
The failure criterion for oxidation embrittlement can be given by
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,
(18)
The presence of oxygen would decrease the critical fracture stress, and the
relationship between the critical fracture stress and oxygen concentration and reaction consumption, can, therefore, be assumed on the {100} fracture planes as, (
∫ ( )
)
(19)
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where σc0 is the initial critical fracture stress on {100} planes at a oxygen concentration of 1 ppm, C is oxygen concentration, R is reaction rate, the reaction consumption is calculated as an integral. To quantify the reduction of critical fracture stress, the decay factor is defined as (20)
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.
3.2 Computational implementation of multi-phase constitutive model The total deformation rate tensor,
of amorphous phase, are needed to update the material
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, of crystalline phase and
, and the plastic deformation rate tensor,
stress state. The method used here is the one developed by Zikry (Zikry, 1994) for ratedependent crystalline plasticity formulations, and only a brief outline will be presented here. For quasi-static formulation, an implicit finite element (FE) method is used to
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obtain the total deformation rate tensor
. To overcome numerical instabilities
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associated with stiffness, a hybrid explicit-implicit method is used to obtain the plastic deformation rate tensor,
and
. This hybrid numerical scheme is also used to , and immobile densities
. An
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update the evolutionary equations for the mobile,
incremental iterative approach with BFGS was used for the quasi-static update of the
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displacements with four-node plane strain quadrilaterals, and the B-bar method was used
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for the control of spurious modes. 4. Results and Discussion The diffusion-reaction process was coupled to the crystalline-amorphous material
models and fracture algorithms within the nonlinear FEM framework to investigate the heterogeneous oxidative degradation and long-term embrittlement failure in semicrystalline organic thin films. An initial oxygen concentration of 1 ppm was chosen, and
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for the boundaries, a constant oxygen concentration of 10 ppm was applied on the right surface of the thin film system. Two P3HT crystallinities of 60% and 80% were investigated. The tilt angle, which represents the initial vertical in-plane orientation of P3HT crystals, was assumed as 45o. Two packing patterns of P3HT crystals, the face-on
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and the edge-on packing orientations, were also investigated. The initial material properties and orientations were estimated based on experimental investigations of P3HT and PDMS systems (Awartani et al., 2013) and are given in Table 3. A convergent plane strain FE mesh of 6500 elements was used with a specimen size of 200 nm by 60 nm, and
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a quasi-static tensile loading, normal to the cross section, was applied on the right surface.
Table 3. Material properties and orientations of each phase
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P3HT Crystalline Phase
Static yield stress, Poisson’s ratio,
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Young’s modulus, E
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Rate sensitivity parameter, m
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Burger vector, b
0.34 GPa 1 MPa 0.35 0.01 3.0 x 10-10 m 1.0 E+06 m-2
Initial immobile dislocation density,
1.0 E+11 m-2
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Initial mobile dislocation density,
Tilt angle,
45o
Face-on orientation
( 0o , , 0o )
Edge-on orientation
( 90 o , , 0 o )
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P3HT Amorphous Phase Young’s modulus, E
0.1 GPa
Static yield stress,
2 MPa
Poisson’s ratio,
0.4 4
Hardening modulus, G
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Rate sensitivity parameter, N
5 MPa
PDMS Substrate Young’s modulus, E
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0.04 GPa
Poisson’s ratio,
0.49
4.1 Oxygen Diffusion-Reaction Induced Degradation
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We investigated how various microstructural characteristics, such as packing orientations and crystallinity, affect diffusion-reaction processes and local oxidative
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degradation. The oxygen concentration at a nominal strain of 30%, corresponding to a
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time of 20000s, is shown in Figure 1 for both face-on and edge-on packing orientations. As seen in Figure 1, edge-on and face-on orientations correspond to the direction of
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packing order (schematic in Figure 1). For the edge-on case (Figure 1b), oxygen diffused and accumulated in the
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amorphous phase between crystals, as indicated by the maximum value of 10.03 ppm, which was only slightly higher than the specified boundary condition of 10 ppm, and the minimum value of 9.94 ppm, which was slightly lower than the boundary condition. This non-uniform oxygen concentration distribution was associated with the accumulation of high pressures (Figure 2b), where the normalized (by the static yield stress) pressure in
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the amorphous phase of the edge-on film ranged from -5 to 9. The amorphous phase had compressive stresses in its vertical ligaments and tensile stresses in the horizontal ligaments of the edge-on film. This indicates that the higher pressure results in higher local oxygen concentration. However, for the face-on case, the normalized pressure was
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generally tensile with a maximum value of 3.4 (Figure 2a), which was much lower than that of the edge-on and correspondingly results in lower oxygen concentration within the film and a maximum value of 10.006 located in the substrate (Figure 1a).
The reaction generally followed this similar non-uniform spatial distribution as
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the concentration, since the reaction rate is linearly related to oxygen concentration (Eqn. 14). The highest reaction value occurs in the amorphous phase, and this signifies that this is a localized degradation zone for both face-on and edge-on packing orientations (Figure
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3). The reaction consumption of oxygen in the face-on film had a maximum value of 0.15004 ppm, while the edge-on film had a higher value of 0.1502 ppm associated with
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the higher local oxygen concentration.
Local pressure gradients (Figure 2) can result from the interrelated effects of
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structural defects and heterogeneous microstructural characteristics, such as film
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morphologies and orientations, crystalline-amorphous interaction and dislocation density evolutions. As shown in Figure 2 and Figure 4, the packing orientations significantly
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affect the local stresses and the inelastic deformation (Zhao and Zikry, 2015). This is indicated by the accumulation of shear slip due to dislocation density interactions, which could therefore lead to heterogeneous oxidative degradation in the semi-crystalline organic thin film. These predictions of stress-assisted diffusion and reaction are
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consistent with experimental observations that deformed polymer chains are more susceptible to chemical reactions (Dupont et al., 2014). The face-on film with a higher crystallinity of 80% was investigated to further understand different physically representative microstructures (Figure 5). In this case, the
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oxygen concentration magnitude had a larger range from 9.99 to 10.01 ppm with some localized regions. These localized sites had higher concentration magnitudes in comparison with the 60% case (Figure 1), and this effect can also be seen in the reaction field (Figure 5b). This behavior can be attributed to the larger range of normalized
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pressures, which vary from 0.8 to 3.6. This variation in pressure was due to the presence of larger crystalline domain size of the 80% case. Crystalline plastic shear strains for larger domains accumulated around the boundary adjacent to the amorphous phase with a
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higher maximum value of 0.34, in comparison with the lower case where the crystalline plastic shear slip activity were more widely distributed and occurred at the interfaces of
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crystalline domains of the film. Thus, the higher crystallinity in the organic thin films can enhance the heterogeneous degradation behavior, and it would result in larger magnitudes
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of interfacial reactions.
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4.2 Diffusion-reaction assisted interfacial delamination In this section, diffusion-reaction assisted fracture in semi-crystalline organic thin
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films has been investigated. As discussed in Section 4.1, the dislocation density evolution in the crystals and the interaction between crystalline and amorphous phases can results in high local stresses accumulation in the amorphous interfacial area. These high local stresses not only lead to localized oxygen accumulation and reaction, which decreases critical fracture stress as oxidation-induced embrittlement mechanisms (Fayolle et al.,
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2000)(Fayolle et al., 2008), but large stress components normal to favorable fracture planes. These stresses would be the driving mechanism for crack nucleation and growth along favorable planes. In this approach, film cracking and interfacial delamination can be represented. Therefore, the stresses on all possible crack planes were monitored to
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determine the failure mode of organic thin films with oxidation embrittlement.
The oxidation embrittlement behavior of a face-on film at a nominal strain of 10% corresponding to a time of 2000,000 s is shown in Figure 6. Interfacial delamination occurred under the coupled reaction, diffusion and mechanical loadings. This was due to
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the oxygen accumulation and reaction at the interfacial area. The time history of interfacial stress and interfacial fracture toughness at the delamination nucleation site were monitored to provide a more detailed understanding on how diffusion-reaction
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processes interact with mechanical behavior, and can lead to embrittlement failure (Figure 7). Diffusion-reaction induced delamination nucleated at 580,000 s with a 31.3%
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reduction of critical fracture stress (Eqn. 20). To further understand the coupling effects between the diffusion-reaction process
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and the mechanical deformation, the delamination behavior was investigated at different
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strains for the same time period (Figure 8). At a nominal strain of 20%, a delamination crack nucleated at 400,000 s. At a larger nominal strain of 30%, interfacial delamination
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nucleated earlier at 300,000 s. Since the interfacial toughness decay is the same for different mechanical strains, it’s the increasing interfacial stresses that accelerated the interfacial delamination (Figure 8). Different oxygen concentration boundary conditions and diffusion coefficients were investigated to further understand the role of diffusion process on oxidation
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embrittlement. As seen in Figure 9, the higher concentration boundary condition and lower diffusion coefficients didn’t significantly influence the interfacial toughness decay. This is due to the small length scale of film thickness, which ranged from 20 nm to 200
a major role in interfacial delamination nucleation.
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nm. This indicates that the diffusion process did not control degradation, and did not play
To further investigate the effects of reaction process, a case with a higher reaction constant of ten times the first model was used to further understand the thermally activated reaction process (Figure 10). The interfacial pressure, oxygen concentration,
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reaction, interfacial toughness decay factor were monitored along the film-PDMS interface (Figure 11). The interfacial delamination initially nucleated at the same location (Figure 11c), but propagated faster with a larger delamination area (Figure 11d). There
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was a severe reaction spike at the crack front due to the coupling effects of larger pressures that can furthermore drive the delamination propagation (Figure 11b,d). The
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time history plot of interfacial stresses and toughness (Figure 12) also indicates that the crack nucleated much earlier at a time of 200,000 s as compared with the lower reaction
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case where cracks nucleated at 580,000 s (Figure 7). Furthermore, the large stresses
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resulted in a crack nucleating at a low nominal strain of 3%. Crack nucleation, at such a low nominal strain, is another indication of film embrittlement. The reaction process was
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activated by higher reaction constants, and this results in accelerated degradation and earlier delamination. 4.3 Diffusion-reaction assisted film cracking and interfacial delamination For the edge-on film, the diffusion-reaction induced interfacial delamination and film cracking occurred at a nominal strain of 10% (Figure 14). The interfacial stresses
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were higher than that of the face-on case, and it resulted in earlier delamination nucleation (Figure 13). A crack in the film nucleated in the amorphous phase, and it propagated through the entire film thickness (Figure 14), while there was only interfacial delamination for the face-on case (Figure 5). At a nominal strain of 7% before crack
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nucleation, the reduction of film fracture toughness and film stress on the [001] crack plane of the two packing orientations are shown in Figure 15. We can see that the film stress resolved on the [001] crack plane of the edge-on film had a peak value in the amorphous phase, which was much higher than that of the face-on (Figure 15a,b). In
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addition, the film cracking and delamination associated with the edge-on film, indicates that the higher decrease of local film toughness is due to higher local stresses (Figure 15 c, d). Hence, these predictions indicate that different film microstructures, such as
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packing orientations and crystallinity, resulted in different local stresses distributions that led to long-term localized degradation and film cracking nucleation. This is consistent
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with experimental investigations that the long-term durability of semi-crystalline polymers depends on microstructures and morphological changes, and oxidation-induced
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film cracks nucleate in the amorphous phase (El-Mazry et al., 2013)(Gauthier et al.,
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2013)(Hsu et al., 2012)(Fayolle et al., 2000)(Fayolle et al., 2007)(Fayolle et al., 2008). 5. Conclusion
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A diffusion-reaction process was coupled to the crystalline-amorphous material
models and fracture algorithms within the nonlinear FEM framework to investigate oxidative degradation and embrittlement failure in semi-crystalline organic thin films. Degradation was dominated by the reaction process and exposure time, instead of the diffusion process. This was due to the length scales of the thickness of the thin films that
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generally ranged from 20 to 200 nms, and this nanoscale thickness resulted in a fast diffusion process. Furthermore, packing orientations and crystallinity had a significant effect on degradation and crack nucleation sites through localized reaction accumulations. The
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edge-on film was more susceptible to oxidation than the face-on film due to higher local stresses that resulted in higher decrease of local toughness and extensive film cracking in the amorphous phase. The coupled effects of mechanical stresses on oxygen diffusion and reaction accelerated degradation mechanisms of the organic thin film systems,
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resulted in film cracking and delamination occurring at lower nominal strains in comparison with systems that had no diffusion-reaction mechanisms. These degradation mechanisms underscore how interfacial delamination and film cracking are affected by
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the interrelated effects of diffusion, reaction, stress accumulations, crystallinity, and
Acknowledgements
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packing order.
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CE
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Support from NSF Grant # CMMI-1200340 is gratefully acknowledged.
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Figure 1 Distributions of oxygen concentration in semi-crystalline polymer thin films at 30% nominal tensile strain with (a) face-on packing orientations, (b) edge-on packing
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orientations.
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Figure 2 Distributions of pressure in semi-crystalline polymer thin films at 30% nominal
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tensile strain with (a) face-on packing orientations, (b) edge-on packing orientations.
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Figure 3 Distrubutions of oxygen reaction consumption in semi-crystalline polymer thin
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films at 30% nominal tensile strain with (a) face-on packing orientations, (b) edge-on
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packing orientations.
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Figure 4 Inelastic deformations in semi-crystalline polymer thin films at 30% nominal
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tensile strain with (a) face-on packing orientations, (b) edge-on packing orientations.
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Figure 5 Distributions of (a) oxygen concentration (b) reaction consumption (c)
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normalized pressure (d) inelastic deformation in the face-on film with a high crystallinity
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of 80% at 30% nominal strain.
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Figure 6 Diffusion-reaction assisted oxidation embrittlement failure behavior of a face-
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on film (a) oxygen concentration (b) reaction consumption (c) normalized pressure (d) failure mode of delamination at nominal strain of 10%.
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Figure 7 The time history plots of resolved interfacial stress and critical fracture stress
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decayed by oxygen diffusion-reaction at the delamination nucleation site.
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Figure 8 The time history plots of resolved interfacial stress and critical fracture stress
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decayed by oxygen diffusion-reaction at the interfacial delamination nucleation site for
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face-on films under the same environmental conditions but different mechanical strains.
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Figure 9 Time history plots of critical fracture stress at the interfacial delamination
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nucleation site with various diffusion coefficients and concentration boundary conditions.
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Figure 10 Diffusion-reaction assisted oxidation embrittlement failure behavior of a faceon film with a high K (reaction rate) of 10 times (a) oxygen concentration (b) reaction consumption (c) normalized pressure (d) failure mode of delamination at nominal strain of 10%.
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(a)
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Figure 11 Diffusion-reaction assisted interfacial behavior of a high K of 10 times (a) oxygen concentration (b) oxygen reaction consumption (c) decay factor as a function of oxygen concentration and reaction (d) pressure along the film-PDMS interface.
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Figure 12 The time history plots of resolved interfacial stress and critical fracture stress
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decayed by oxygen diffusion-reaction at the interfacial delamination nucleation site.
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Figure 13 The time history plots of resolved interfacial stress and critical fracture stress
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decayed by oxygen diffusion-reaction at the delamination nucleation site.
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Figure 14 Diffusion-reaction assisted oxidation embrittlement failure behavior of a edge-
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on film (a) oxygen concentration (b) reaction consumption (c) pressure (d) inelastic deformation at nominal strain of 10%.
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Figure 15 (a) Film stress on [100] crack plane in a face-on film (b) Film stress on [100] crack plane in an edge-on films (c) Reduction of film fracture toughness in a face-on film (d) Reduction of film fracture toughness in an edge-on film.
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Oxidation-induced Failure in Semi-crystalline Organic Thin Films Bingxiao Zhao , M.A. Zikry PII: DOI: Reference:
S0020-7683(17)30007-0 10.1016/j.ijsolstr.2017.01.008 SAS 9422
To appear in:
International Journal of Solids and Structures
Received date: Revised date: Accepted date:
23 June 2016 10 December 2016 3 January 2017
Please cite this article as: Bingxiao Zhao , M.A. Zikry , Oxidation-induced Failure in Semicrystalline Organic Thin Films, International Journal of Solids and Structures (2017), doi: 10.1016/j.ijsolstr.2017.01.008
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Oxidation-induced Failure in Semi-crystalline Organic Thin Films Bingxiao Zhao and M.A. Zikry* Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910, USA
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*Corresponding Author. Email: [email protected] Abstract
Polymer oxidation is a major degradation mechanism in organic solar cells. However, microstructural details of diffusion-reaction processes and oxidation-induced
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failure in structured semi-crystalline active layers are difficult to be predicted or measured, due to material heterogeneities, such as different material phases, crystallinities, nano-film thickness. Hence, a diffusion-reaction process has been coupled
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to a crystalline-amorphous material model and fracture algorithm within a nonlinear microstructurally-based finite element (FEM) framework to investigate and predict
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heterogeneous oxidative degradation and embrittlement failure in semi-crystalline organic thin films due to the interrelated effects of diffusion, reaction, stress
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accumulations, and crystalline packing order. The edge-on packing oriented film was
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more susceptible to oxidation than the face-on oriented packing film due to higher local stresses and reaction accumulations that resulted in higher decrease of local toughness
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and extensive film cracking in the amorphous phase. The coupled effects of mechanical stresses and oxygen diffusion-reaction accelerated degradation mechanisms and resulted in film cracking and delamination occurring at lower nominal strains in comparison with the case without oxidation embrittlement. Degradation was dominated by the reaction process and exposure time, as opposed to the diffusion process due to the nano-sized
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films. This predictive framework can be used to understand fundamental local oxidative degradation mechanisms and the morphological effects on long term durability of semicrystalline organic thin films. Keywords: Semi-crystalline organic thin films, Polymer oxidation, Microstructural failure
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mechanisms, Delamination, Multi-physics coupling, organic electronics 1. Introduction
A fundamental understanding of polymer degradation is esssential for organic electronics because organic materials are more intrinsically susceptible to oxidation than
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inorganic materials. As organic thin film devices are exposed to aggressive field environments, such as combinations of oxygen, moisture, heat and mechanical loadings, both device performance and mechancial properties degrade faster due to physical and
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chemical processes (Jørgensen et al., 2012)(Jørgensen et al., 2008). Oxygen and water molecules diffuse into the active layers and react with polymeric materials, resulting in
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chain scission and crack formation. Oxidative degradation can be localized both within polymer active layers and at interfaces, and the loss of structural integrity and interfacial
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stability generally lead to a reduction of charge transfer and extraction (Reese et al.,
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2008)(Novoa et al., 2014)(Voroshazi et al., 2011). The macroscopic decay curves of either electrical and mechanical properties can
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be measured experimentally, however, that rarely provides fundamental details of the evolution of the diffusion-reaction processes, such as how different heterogenous polymer material effects, such as different material phases, and local reactions lead to degradation in structured active layers. As noted by Celina, physically-based computational models are needed to provide more fundamental understanding of local
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oxidative degradation mechanisms and morphological effects on long term durability (Celina, 2013). The fracture toughness of organic thin films can be significantly affected by environmental factors (Dupont et al., 2014). Oxidation embrittlement is a degradation
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process by which polymeric materials become brittle due to introduction of oxygen or water molecules. Environmentally assisted cracking can occur in degraded polymers when the local stresses are below the critical fracture stress. This results from interrelated mechanisms pertaining to diffusion, reaction, microstructure, fracture and external
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loadings. The oxidation induced embrittlement of semicrystalline polymers and their origin have been associated with microstructural changes (El-Mazry et al., 2013)(Gauthier et al., 2013)(Hsu et al., 2012)(Fayolle et al., 2000)(Fayolle et al.,
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2007)(Fayolle et al., 2008). The tensile stress will be dilatational and expected to interact with the diffusion-reaction process and accelerate oxidative embrittlement (Shyichuk et
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al., 2001). However, the influence of chemical reactions on microstructral failure mechanisms under long-term remain relatively unexplored.
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Finite element (FE) models of diffusion-reaction processes have been used to
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investigate oxidation-induced failure under coupled mechanical and environmental conditions (Yan and Oskay, 2015)(Liang and Pochiraju, 2014), but these approaches do
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not explicitly account for internal microstructural mechanisms and nano-sized thin films. To address these issues, we developed a microstructurally-based computational framework and a nonlinear finite-element fracture methodology that couples essential microstructural characteristics, mechanical response, oxygen diffusion and reaction, to predict and fundamentally understand heterogeneous oxidative degradation, interfacial
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delamination and film cracking in semi-crystalline organic thin films deposited on flexible PDMS substrates. In this framework, the interrelated effects of structural disorders, molecular packing orientations, crystallinity and domain sizes on local heterogeneous degradation and microstructural failure mechanisms of organic investigated for different coupled mechanical,
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semicrystalline thin films will be diffusion, and reaction conditions.
The paper is organized as follows: the multiphase material model and the stressassisted oxygen diffusion-reaction model are presented in Section 2. The microstructural-
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based failure criteria and numerical implementation approach are outlined in Section 3. The results and discussion are presented in Section 4, and a summary of results and conclusions are given in Section 5.
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2. Multiphase constitutive formulations and stress-assisted diffusion-reaction 2.1 Constitutive model for organic semi-crystalline thin films
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The crystalline-amorphous constitutive formulations of P3HT semi-crystalline thin films have been given in Zhao and Zikry (2016), only a brief outline is given here.
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A multiple-slip dislocation-density based crystalline plasticity formulation is used
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for the P3HT crystalline phase. Two possible types of disorders were taken into consideration for P3HT crystals: chain slip parallel to backbones and transverse slip
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perpendicular to backbones (Table 1), which is primarily with respect to the build-in lattice defects among ordered packing P3HT chains (Lee et al., 1993). It is assumed that the velocity gradient can be decomposed into a symmetric
deformation rate tensor
and an anti-symmetric spin tensor
. The tensors
are then additively decomposed into elastic and inelastic components as
and
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, and
.
(1a-b)
are the elastic part of total deformation tensor and lattice rotation.
and
are the inelastic parts of total deformation rate tensor and total spin rate tensor, which are defined in terms of the crystallographic slip rates as ̇
∑
,
( )
where () is summed over all slip systems, and
( ) ( )
̇
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( ) ( )
∑
( )
and
(2a-b)
are the symmetric and anti-
symmetric parts of the Schmid tensor in the current configuration respectively.
description on each slip system as
where ̇
̇
( )
[
( )
( )
][
( )
( )
]
,
(3)
is the reference shear strain rate which corresponds to a reference shear stress
, and m is the rate sensitivity parameter.
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( )
( )
)
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̇(
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A power law relation can be used to characterize the rate-dependent constitutive
( )
is the resolved shear stress on slip
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system . The reference shear stress is a modification of the classical forms (Franciosi et al., 1980) that relate reference shear stress to immobile dislocation-density ( )
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( )
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where G is the shear modulus, number of active slip systems, coefficients
∑ ( )
( )
√
( )
,
as (4)
is the static yield stress on slip system , nss is the
( )
is the magnitude of the Burgers vector, and the
are related to the strength of interactions between slip systems (Devincre
et al., 2008),(Kubin et al., 2008).
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Following the approach by Zikry and Kao (Zikry and Kao, 1996), it is assumed that, for a given deformed state of the crystalline domain, the total dislocation-density, ( )
, can be additively decomposed into a mobile dislocation density, ( )
, and an
. The evolution of mobile and immobile dislocation
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immobile dislocation-density,
( )
densities, including generation, interaction and annihilation, is determined as functions of the crystallography and deformation mode of P3HT crystalline phase. The interactions between slip systems are given in Zhao and Zikry (Zhao and Zikry, 2015).
Chain slip systems (100)[001]
Transverse slip systems (100)[010]
(010)[100]
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(010)[001]
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Table 1. Slip systems for P3HT crystalline phase
The P3HT amorphous phase is in a glassy state at room temperature, and it can be
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modeled as elasto-viscoplastic (Zhao and Zikry, 2015). We use Perzyna's viscoplastic
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model to account for the strain induced hardening behavior of the amorphous mixture (Schrauwen et al., 2004). Following the same decomposition approach as the finite strain
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crystalline plasticity approach, the symmetric deformation rate tensor Dij is decomposed into elastic and viscoplastic components as
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.
(5)
The yielding criterion of the amorphous phase is defined as
(
)
√. /
(
)
,
(6)
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where
√. /
is effective viscoplastic strain and
is the second
invariant of the deviatoric stress tensor of the amorphous phase. The function
(
where
)
is the initial yield stress, and
,
as
(7)
is the hardening modulus.
̇
and the effective
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A power law relation between the effective shear strain rate ̇ shear stress can then be defined as
)
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defines the current yield stress, and it is assumed to be linear in
(
̇ .
/ ,
(8)
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where N is the rate-sensitivity and ̇ is a reference shear strain rate. Hence, viscoplastic
is related to effective visco-plastic strain rate ̇
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as
. The viscoplatsic deformation by the normal direction
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rate tensor,
/
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strains are non-zero only if the flow function .
̇
,
(9)
. /
.
(10)
The accumulated effective viscoplastic strain in the amorphous phase is then given by ∫ ̇
.
(11)
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If the viscoplastic strain rates are zero, the deformation is finite elasticity.
The finite elasticity hypo-elastic formulation is used for PDMS substrates, which relates the deformation rate tensor to the objective stress rate is
(12)
The stress rate, ̇ , is given by ̇ is the objective stress rate and
deformation rate and
and
(13)
are the Lame´ parameters.
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where
.
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.
is the total
is the total spin rate.
2.2 Stress assisted oxygen diffusion and reaction
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For oxygen diffusion-reaction induced degradation and embrittlement failure, oxygen can diffuse into the material system and react with the polymer chain backbones,
( )
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which can cause chain scission and be accelerated by the stress field through the pressure (Serebrinsky et al., 2004). The stress-assisted diffusion-reaction equation is
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a modification of Fick’s second law, which can be given by (Dadfarnia et al., 2014;
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Olden et al., 2008; Serebrinsky et al., 2004) (Yan and Oskay, 2015)(Liang and Pochiraju, 2015) as
(
),
(14)
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( )
where C is the oxygen concentration, D is the oxygen diffusion coefficient of P3HT (Hintz et al., 2011), applied as 3 e-12 m2/s , k is the reaction constant (Hintz et al., 2010) given as 10-6 s-1, Vo is the partial molar volume of oxygen, and equal to 2.0 ×10-6 m3/mol (Sofronis and McMeeking, 1989), T is the absolute temperature. The reaction rate, R(C)
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= k C, is defined as a linear function of oxygen concentration, and it taken as part of diffusion for long time scales of hours, especially when the concentration is much lower than the saturation concentration. The pressure is positive for tensile stresses, and this stress coupling term (Eqn. 14) provides a link for coupling mechanical deformation to
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local oxidation degradation.
3. Microstructural failure criteria and numerical implementation approach
3.1 Microstructurally-based film cracking and interfacial delamination criteria
A brief outline of microstructurally-based fracture criteria of semi-crystalline
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polymers is presented here, for details see Zhao and Zikry (Zhao et al., 2016). The nonlinear fracture method is based on an overlap method and the use of phantom nodes to create multiple fracture surfaces (Wu and Zikry, 2014). For the P3HT crystalline phase, )(
)+ in the local coordinates.
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the fracture planes are associated with slip planes *(
The global orientations of these fracture planes is defined as a function of crystalline
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orientations and updated at each time step through lattice rotation matrix, , -*(
)(
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̇
as
)+.
(15)
.
(16)
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[T] is rotation matrix in terms of Euler angles to relate lattice local coordinates to global coordinates. For the amorphous phase, the fracture planes are assumed as )(
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*(
)+ in the global coordinate system, which would be perpendicular or parallel
to the tensile loading directions based on experimental observations (Awartani et al., 2013)(Lipomi et al., 2012). The normal component of the traction vector of all crack planes is monitored, and compared with a critical cohesive fracture stress determine fracture initiation and propagation as
to
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, where
*
+〈
(17) , -
〉
For the interfacial delamination, the effective interfacial stress based on normal . The
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and shear stresses is monitored to evaluate the interfacial strength maximum value was compared with a critical interfacial fracture stress
. The
adhesive strength is assumed to be smaller than the cohesive strength of the film so that the interfacial crack would propagate along the interface (Kim-Lee et al., 2014). The for both film cracking and interfacial
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crack planes and critical fracture stress delamination are listed in Table 2.
Table 2. Fracture criteria for each phase and interfacial delamination Crack planes
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Phase type
(i = a, c)
[T]{(100), (010)}
6
P3HT Amorphous
(100), (010)
6
Interfacial delamination
(010)
1.5
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P3HT Crystalline
The failure criterion for oxidation embrittlement can be given by
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,
(18)
The presence of oxygen would decrease the critical fracture stress, and the
relationship between the critical fracture stress and oxygen concentration and reaction consumption, can, therefore, be assumed on the {100} fracture planes as, (
∫ ( )
)
(19)
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where σc0 is the initial critical fracture stress on {100} planes at a oxygen concentration of 1 ppm, C is oxygen concentration, R is reaction rate, the reaction consumption is calculated as an integral. To quantify the reduction of critical fracture stress, the decay factor is defined as (20)
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.
3.2 Computational implementation of multi-phase constitutive model The total deformation rate tensor,
of amorphous phase, are needed to update the material
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, of crystalline phase and
, and the plastic deformation rate tensor,
stress state. The method used here is the one developed by Zikry (Zikry, 1994) for ratedependent crystalline plasticity formulations, and only a brief outline will be presented here. For quasi-static formulation, an implicit finite element (FE) method is used to
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obtain the total deformation rate tensor
. To overcome numerical instabilities
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associated with stiffness, a hybrid explicit-implicit method is used to obtain the plastic deformation rate tensor,
and
. This hybrid numerical scheme is also used to , and immobile densities
. An
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update the evolutionary equations for the mobile,
incremental iterative approach with BFGS was used for the quasi-static update of the
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displacements with four-node plane strain quadrilaterals, and the B-bar method was used
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for the control of spurious modes. 4. Results and Discussion The diffusion-reaction process was coupled to the crystalline-amorphous material
models and fracture algorithms within the nonlinear FEM framework to investigate the heterogeneous oxidative degradation and long-term embrittlement failure in semicrystalline organic thin films. An initial oxygen concentration of 1 ppm was chosen, and
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for the boundaries, a constant oxygen concentration of 10 ppm was applied on the right surface of the thin film system. Two P3HT crystallinities of 60% and 80% were investigated. The tilt angle, which represents the initial vertical in-plane orientation of P3HT crystals, was assumed as 45o. Two packing patterns of P3HT crystals, the face-on
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and the edge-on packing orientations, were also investigated. The initial material properties and orientations were estimated based on experimental investigations of P3HT and PDMS systems (Awartani et al., 2013) and are given in Table 3. A convergent plane strain FE mesh of 6500 elements was used with a specimen size of 200 nm by 60 nm, and
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a quasi-static tensile loading, normal to the cross section, was applied on the right surface.
Table 3. Material properties and orientations of each phase
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P3HT Crystalline Phase
Static yield stress, Poisson’s ratio,
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Young’s modulus, E
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Rate sensitivity parameter, m
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Burger vector, b
0.34 GPa 1 MPa 0.35 0.01 3.0 x 10-10 m 1.0 E+06 m-2
Initial immobile dislocation density,
1.0 E+11 m-2
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Initial mobile dislocation density,
Tilt angle,
45o
Face-on orientation
( 0o , , 0o )
Edge-on orientation
( 90 o , , 0 o )
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P3HT Amorphous Phase Young’s modulus, E
0.1 GPa
Static yield stress,
2 MPa
Poisson’s ratio,
0.4 4
Hardening modulus, G
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Rate sensitivity parameter, N
5 MPa
PDMS Substrate Young’s modulus, E
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4.1 Oxygen Diffusion-Reaction Induced Degradation
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We investigated how various microstructural characteristics, such as packing orientations and crystallinity, affect diffusion-reaction processes and local oxidative
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degradation. The oxygen concentration at a nominal strain of 30%, corresponding to a
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time of 20000s, is shown in Figure 1 for both face-on and edge-on packing orientations. As seen in Figure 1, edge-on and face-on orientations correspond to the direction of
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packing order (schematic in Figure 1). For the edge-on case (Figure 1b), oxygen diffused and accumulated in the
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amorphous phase between crystals, as indicated by the maximum value of 10.03 ppm, which was only slightly higher than the specified boundary condition of 10 ppm, and the minimum value of 9.94 ppm, which was slightly lower than the boundary condition. This non-uniform oxygen concentration distribution was associated with the accumulation of high pressures (Figure 2b), where the normalized (by the static yield stress) pressure in
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the amorphous phase of the edge-on film ranged from -5 to 9. The amorphous phase had compressive stresses in its vertical ligaments and tensile stresses in the horizontal ligaments of the edge-on film. This indicates that the higher pressure results in higher local oxygen concentration. However, for the face-on case, the normalized pressure was
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generally tensile with a maximum value of 3.4 (Figure 2a), which was much lower than that of the edge-on and correspondingly results in lower oxygen concentration within the film and a maximum value of 10.006 located in the substrate (Figure 1a).
The reaction generally followed this similar non-uniform spatial distribution as
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the concentration, since the reaction rate is linearly related to oxygen concentration (Eqn. 14). The highest reaction value occurs in the amorphous phase, and this signifies that this is a localized degradation zone for both face-on and edge-on packing orientations (Figure
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3). The reaction consumption of oxygen in the face-on film had a maximum value of 0.15004 ppm, while the edge-on film had a higher value of 0.1502 ppm associated with
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the higher local oxygen concentration.
Local pressure gradients (Figure 2) can result from the interrelated effects of
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structural defects and heterogeneous microstructural characteristics, such as film
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morphologies and orientations, crystalline-amorphous interaction and dislocation density evolutions. As shown in Figure 2 and Figure 4, the packing orientations significantly
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affect the local stresses and the inelastic deformation (Zhao and Zikry, 2015). This is indicated by the accumulation of shear slip due to dislocation density interactions, which could therefore lead to heterogeneous oxidative degradation in the semi-crystalline organic thin film. These predictions of stress-assisted diffusion and reaction are
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consistent with experimental observations that deformed polymer chains are more susceptible to chemical reactions (Dupont et al., 2014). The face-on film with a higher crystallinity of 80% was investigated to further understand different physically representative microstructures (Figure 5). In this case, the
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oxygen concentration magnitude had a larger range from 9.99 to 10.01 ppm with some localized regions. These localized sites had higher concentration magnitudes in comparison with the 60% case (Figure 1), and this effect can also be seen in the reaction field (Figure 5b). This behavior can be attributed to the larger range of normalized
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pressures, which vary from 0.8 to 3.6. This variation in pressure was due to the presence of larger crystalline domain size of the 80% case. Crystalline plastic shear strains for larger domains accumulated around the boundary adjacent to the amorphous phase with a
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higher maximum value of 0.34, in comparison with the lower case where the crystalline plastic shear slip activity were more widely distributed and occurred at the interfaces of
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crystalline domains of the film. Thus, the higher crystallinity in the organic thin films can enhance the heterogeneous degradation behavior, and it would result in larger magnitudes
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of interfacial reactions.
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4.2 Diffusion-reaction assisted interfacial delamination In this section, diffusion-reaction assisted fracture in semi-crystalline organic thin
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films has been investigated. As discussed in Section 4.1, the dislocation density evolution in the crystals and the interaction between crystalline and amorphous phases can results in high local stresses accumulation in the amorphous interfacial area. These high local stresses not only lead to localized oxygen accumulation and reaction, which decreases critical fracture stress as oxidation-induced embrittlement mechanisms (Fayolle et al.,
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2000)(Fayolle et al., 2008), but large stress components normal to favorable fracture planes. These stresses would be the driving mechanism for crack nucleation and growth along favorable planes. In this approach, film cracking and interfacial delamination can be represented. Therefore, the stresses on all possible crack planes were monitored to
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determine the failure mode of organic thin films with oxidation embrittlement.
The oxidation embrittlement behavior of a face-on film at a nominal strain of 10% corresponding to a time of 2000,000 s is shown in Figure 6. Interfacial delamination occurred under the coupled reaction, diffusion and mechanical loadings. This was due to
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the oxygen accumulation and reaction at the interfacial area. The time history of interfacial stress and interfacial fracture toughness at the delamination nucleation site were monitored to provide a more detailed understanding on how diffusion-reaction
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processes interact with mechanical behavior, and can lead to embrittlement failure (Figure 7). Diffusion-reaction induced delamination nucleated at 580,000 s with a 31.3%
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reduction of critical fracture stress (Eqn. 20). To further understand the coupling effects between the diffusion-reaction process
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and the mechanical deformation, the delamination behavior was investigated at different
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strains for the same time period (Figure 8). At a nominal strain of 20%, a delamination crack nucleated at 400,000 s. At a larger nominal strain of 30%, interfacial delamination
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nucleated earlier at 300,000 s. Since the interfacial toughness decay is the same for different mechanical strains, it’s the increasing interfacial stresses that accelerated the interfacial delamination (Figure 8). Different oxygen concentration boundary conditions and diffusion coefficients were investigated to further understand the role of diffusion process on oxidation
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embrittlement. As seen in Figure 9, the higher concentration boundary condition and lower diffusion coefficients didn’t significantly influence the interfacial toughness decay. This is due to the small length scale of film thickness, which ranged from 20 nm to 200
a major role in interfacial delamination nucleation.
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nm. This indicates that the diffusion process did not control degradation, and did not play
To further investigate the effects of reaction process, a case with a higher reaction constant of ten times the first model was used to further understand the thermally activated reaction process (Figure 10). The interfacial pressure, oxygen concentration,
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reaction, interfacial toughness decay factor were monitored along the film-PDMS interface (Figure 11). The interfacial delamination initially nucleated at the same location (Figure 11c), but propagated faster with a larger delamination area (Figure 11d). There
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was a severe reaction spike at the crack front due to the coupling effects of larger pressures that can furthermore drive the delamination propagation (Figure 11b,d). The
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time history plot of interfacial stresses and toughness (Figure 12) also indicates that the crack nucleated much earlier at a time of 200,000 s as compared with the lower reaction
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case where cracks nucleated at 580,000 s (Figure 7). Furthermore, the large stresses
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resulted in a crack nucleating at a low nominal strain of 3%. Crack nucleation, at such a low nominal strain, is another indication of film embrittlement. The reaction process was
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activated by higher reaction constants, and this results in accelerated degradation and earlier delamination. 4.3 Diffusion-reaction assisted film cracking and interfacial delamination For the edge-on film, the diffusion-reaction induced interfacial delamination and film cracking occurred at a nominal strain of 10% (Figure 14). The interfacial stresses
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were higher than that of the face-on case, and it resulted in earlier delamination nucleation (Figure 13). A crack in the film nucleated in the amorphous phase, and it propagated through the entire film thickness (Figure 14), while there was only interfacial delamination for the face-on case (Figure 5). At a nominal strain of 7% before crack
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nucleation, the reduction of film fracture toughness and film stress on the [001] crack plane of the two packing orientations are shown in Figure 15. We can see that the film stress resolved on the [001] crack plane of the edge-on film had a peak value in the amorphous phase, which was much higher than that of the face-on (Figure 15a,b). In
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addition, the film cracking and delamination associated with the edge-on film, indicates that the higher decrease of local film toughness is due to higher local stresses (Figure 15 c, d). Hence, these predictions indicate that different film microstructures, such as
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packing orientations and crystallinity, resulted in different local stresses distributions that led to long-term localized degradation and film cracking nucleation. This is consistent
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with experimental investigations that the long-term durability of semi-crystalline polymers depends on microstructures and morphological changes, and oxidation-induced
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film cracks nucleate in the amorphous phase (El-Mazry et al., 2013)(Gauthier et al.,
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2013)(Hsu et al., 2012)(Fayolle et al., 2000)(Fayolle et al., 2007)(Fayolle et al., 2008). 5. Conclusion
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A diffusion-reaction process was coupled to the crystalline-amorphous material
models and fracture algorithms within the nonlinear FEM framework to investigate oxidative degradation and embrittlement failure in semi-crystalline organic thin films. Degradation was dominated by the reaction process and exposure time, instead of the diffusion process. This was due to the length scales of the thickness of the thin films that
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generally ranged from 20 to 200 nms, and this nanoscale thickness resulted in a fast diffusion process. Furthermore, packing orientations and crystallinity had a significant effect on degradation and crack nucleation sites through localized reaction accumulations. The
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edge-on film was more susceptible to oxidation than the face-on film due to higher local stresses that resulted in higher decrease of local toughness and extensive film cracking in the amorphous phase. The coupled effects of mechanical stresses on oxygen diffusion and reaction accelerated degradation mechanisms of the organic thin film systems,
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resulted in film cracking and delamination occurring at lower nominal strains in comparison with systems that had no diffusion-reaction mechanisms. These degradation mechanisms underscore how interfacial delamination and film cracking are affected by
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the interrelated effects of diffusion, reaction, stress accumulations, crystallinity, and
Acknowledgements
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packing order.
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Support from NSF Grant # CMMI-1200340 is gratefully acknowledged.
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Figure 1 Distributions of oxygen concentration in semi-crystalline polymer thin films at 30% nominal tensile strain with (a) face-on packing orientations, (b) edge-on packing
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orientations.
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Figure 2 Distributions of pressure in semi-crystalline polymer thin films at 30% nominal
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tensile strain with (a) face-on packing orientations, (b) edge-on packing orientations.
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Figure 3 Distrubutions of oxygen reaction consumption in semi-crystalline polymer thin
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films at 30% nominal tensile strain with (a) face-on packing orientations, (b) edge-on
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packing orientations.
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Figure 4 Inelastic deformations in semi-crystalline polymer thin films at 30% nominal
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tensile strain with (a) face-on packing orientations, (b) edge-on packing orientations.
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Figure 5 Distributions of (a) oxygen concentration (b) reaction consumption (c)
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normalized pressure (d) inelastic deformation in the face-on film with a high crystallinity
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of 80% at 30% nominal strain.
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Figure 6 Diffusion-reaction assisted oxidation embrittlement failure behavior of a face-
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on film (a) oxygen concentration (b) reaction consumption (c) normalized pressure (d) failure mode of delamination at nominal strain of 10%.
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Figure 7 The time history plots of resolved interfacial stress and critical fracture stress
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decayed by oxygen diffusion-reaction at the delamination nucleation site.
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Figure 8 The time history plots of resolved interfacial stress and critical fracture stress
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decayed by oxygen diffusion-reaction at the interfacial delamination nucleation site for
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face-on films under the same environmental conditions but different mechanical strains.
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Figure 9 Time history plots of critical fracture stress at the interfacial delamination
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nucleation site with various diffusion coefficients and concentration boundary conditions.
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Figure 10 Diffusion-reaction assisted oxidation embrittlement failure behavior of a faceon film with a high K (reaction rate) of 10 times (a) oxygen concentration (b) reaction consumption (c) normalized pressure (d) failure mode of delamination at nominal strain of 10%.
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(a)
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Figure 11 Diffusion-reaction assisted interfacial behavior of a high K of 10 times (a) oxygen concentration (b) oxygen reaction consumption (c) decay factor as a function of oxygen concentration and reaction (d) pressure along the film-PDMS interface.
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Figure 12 The time history plots of resolved interfacial stress and critical fracture stress
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Figure 13 The time history plots of resolved interfacial stress and critical fracture stress
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Figure 14 Diffusion-reaction assisted oxidation embrittlement failure behavior of a edge-
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Figure 15 (a) Film stress on [100] crack plane in a face-on film (b) Film stress on [100] crack plane in an edge-on films (c) Reduction of film fracture toughness in a face-on film (d) Reduction of film fracture toughness in an edge-on film.
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