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Simulating Phase Separation during Spin Coating of a PolymerFullerene Blend: A Joint Computational and Experimental Investigation VIKAS NEGI, Olga Wodo, Jacobus J. van Franeker, René A. J. Janssen, and Peter A. Bobbert ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.7b00189 • Publication Date (Web): 02 Feb 2018 Downloaded from http://pubs.acs.org on February 4, 2018

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ACS Applied Energy Materials

Simulating Phase Separation during Spin Coating of a Polymer-Fullerene Blend: A Joint Computational and Experimental Investigation *†

Vikas Negi ,

‡

Olga Wodo,

†,¶

Jacobus J. van Franeker,

René A. J. Janssen,

†,¶

* †,§

and Peter A. Bobbert

†Molecular Materials and Nanosystems, Eindhoven University of Technology P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands ‡Department of Materials Design and Innovation and Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260, USA ¶Institute of Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands §Center for Computational Energy Research, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

Abstract

During spin coating of the photoactive layer of a bulk heterojunction organic solar cell, phase separation between the donor (D) and acceptor (A) components is triggered by solvent evaporation. The morphology of the resulting layer is one of the main determinants of the device efficiency and critically depends on processing conditions such as the spinning speed, D-A mixing ratio and choice of solvents. It is crucial to understand how these conditions influence the nanostructure of the photoactive layer. Optical experiments have a limited spatial resolution and cannot probe the short length 1

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scales of phase separation. In this work, we present three-dimensional simulations of evaporation-induced phase separation in a diketopyrrolopyrrole-fullerene D-A blend, where we derive the simulation parameters from in-situ laser interference and contact angle experiments. Depending on the drying rate, phase separation initiates in different regions of the thinning film. We estimate from a linear stability analysis the early-stage length scale of phase separation and compare it with simulations. The normalized drying rate is shown to be the key parameter. The experimentally found power law dependence of the characteristic length scale of phase separation on this parameter is reproduced with a matching exponent.

Keywords organic photovoltaic devices, bulk heterojunction, process-structure relationships, spin-coating, phase separation, Cahn-Hilliard-Cook equations

1

Introduction

Solution-processed organic photovoltaics (OPV) aims to be a cost-effective alternative to the traditional silicon-based technology that currently dominates the solar energy market. 1 Other advantages include roll-to-roll processing on flexible substrates, which is appealing with regard to its potential for large-scale production. 2,3 The power conversion efficiency (PCE) of both singlejunction 4 and multi-junction 5,6 OPV cells has steadily improved over the years and recently reached the 13% mark. 7,8 In order to compete with silicon-based photovoltaics, which can have a PCE close to 26%, 9 a lot of progress still needs to be made. One of the key reasons for the rise in the PCE of solution-processed OPV has been the development of low-band gap semiconducting polymers. 10–12 These polymers contain alternating electron-rich and electron-deficient units in a so-called “push-pull” configuration 13 . Since the first published report in 2008, 14 diketopyrrolopy2


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rrole (DPP) has become a popular electron-deficient unit for use in low-bandgap polymers. Such polymers allow fine-tuning of their optical and electronic properties by selectively changing the aromatic substituents, π-conjugated segments and the alkyl side chains. 15–17 An important factor known to limit the PCE of DPP-based solar cells is the nanostructure of the photoactive layer. 18–20 It is well established that characteristics of the photoactive layer morphology such as the degree of phase separation, the presence of percolating pathways towards the electrodes for electrons and holes, the donor (or acceptor)-rich domain sizes, the degree of crystallization of the donor polymer, etc., play a crucial role in determining the final device efficiency. 21–23 The morphology of the photoactive layer, in turn, is critically dependent on the device processing or post-processing conditions. 24–26 Solution-processing provides an elegant way to fabricate a bulk heterojunction (BHJ) type of morphology for the photoactive layer. 27 The donor (D) and acceptor (A) components are dissolved in a volatile solvent and spin coated on a rapidly spinning substrate. As the solvent evaporates, the two components phase separate into donor-rich and acceptor-rich domains. The degree to which phase separation occurs depends on a variety of factors, such as the rate of evaporation, the solubility of the D and A components, the D-A mixing ratio and the type of solvents used. 28 Thus, for a given D-A combination, the number of ways in which a device can be fabricated is extremely large, resulting in an enormous optimization space. 29 Trial-and-error based experimental approaches cost a lot of time and effort, hindering technological progress. Therefore, it is necessary that a rational design strategy to fabricate BHJ devices with well-balanced morphologies is developed. To achieve that goal, we first need a clear understanding of how phase separation leads to the formation of the photoactive layer nanostructure. 28,30 Visualizing morphology evolution of bulk-heterojunctions for OPV cells in real time is challenging because of the required temporal and spatial resolution. 31 Experimental techniques based on light scattering are usually limited by their spatial resolution. 28,32–34 In addition to optical studies, in-situ X-ray scattering and diffraction measurements have also been used to investigate the kinetics of morphology formation during drying, covering smaller to longer length scales. 35–42 However, the X-ray signal is averaged over a large area and needs further analysis when convert-

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ing from reciprocal to real space. Some studies have used direct imaging techniques to track the onset of phase separation as the blend film thins over time during spin coating. 43–45 In order to obtain clear images, the phase separating components need to have sufficient contrast, which limits the applicability of such techniques. Moreover, the early length scales associated with phase separation are too small to be tracked with optical imaging methods. Computer simulations can aid experiments to overcome these limitations and help elucidate the role of processing conditions in determining the photoactive layer morphology and, ultimately, the device efficiency. They further enable us to visualize morphology evolution in three dimensions, which is currently beyond experimental capabilities. The ability to perform automated highthroughput computational analysis is also expected to make OPV device manufacturing cheaper and much more efficient. Due to the high spatial resolution required to study phase separation, continuum-based simulation approaches are the most practical to use. Phase field methods based on solving the Cahn-Hilliard-Cook equations are quite versatile in their applicability and can easily be used to represent complex morphologies. 46–48 Some progress has already been made using this approach. 49–51 However, the reported simulations have either made use of model parameters 49,50 or have been restricted to a 2D domain. 51 Such morphologies therefore cannot be directly compared with realistic OPV films. We present a computational framework based on 3D phase field simulations that allows us to access the experimental length and time scales associated with phase separation. The simulated morphologies are further validated by comparing their dominant features with corresponding imaging experiments. 30 We focus our attention on modeling phase separation triggered by solvent evaporation in a ternary blend consisting of PDPP5T (diketopyrrolopyrrole-quinquethiophene) and PC71 BM ([6,6]Phenyl-C71 butyric acid methyl ester) dissolved in chloroform. Due to solvent removal during spin-coating of the photoactive layer, the blend enters the unstable region of the ternary phase diagram. In this region, thermal fluctuations in the composition get amplified and result in the formation of PC71 BM-rich droplets in a PDPP5T-rich phase. These isolated droplets stay until the film dries and are clearly visible in dry film TEM images. 30 In-situ experiments have revealed that

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for a ternary system with chloroform as the solvent, liquid-liquid (L-L) phase separation initiates around a solvent content of 80 vol. %. 28,30 Polymer aggregation for such blends happens later, close to a solvent content of 50 vol. %. 28 In such a scenario, the dominant length scale in the dry film is mainly determined by the PC71 BM-rich droplets that form at the onset of L-L phase separation. 28 Polymer aggregation has been shown to influence phase separation in blends with co-solvents such as ortho-dichlorobenzene. 28 However, simulations with co-solvents is outside the scope of this work where we present a model for a ternary system. We therefore exclusively probe the origin and evolution of the dominant length scale due to formation of PC71 BM-rich domains. Earlier work based on the ternary phase diagram for a system of a donor, acceptor, and a solvent are a starting point for our work. 51–53 Kouijzer et al. 51 have made important observations regarding the phase separation process using two-dimensional (2D) phase field simulations on the PDPP5T:PC71 BM system. However, their strategy to simulate an effective 2D top-view by removing solvent uniformly from the entire simulation domain differs substantially from the actual film thinning process. It is also difficult, if not impossible, to implement substrate or airsurface interactions in the followed approach. Also, vertical stratification, if present, would not be revealed. 32,44,45 In this work, we present results obtained using a realistic description of the solvent evaporation process where we make use of a finite-element based approach to model the governing Cahn-Hilliard-Cook equations in three dimensions (3D). 49,50 The homogeneous free energy of the ternary mixture is described using the Flory-Huggins formulation, while the interfacial energy is obtained using a square-gradient approximation. 49 As shown in Figure 1, the kinetic input parameters for our simulations are obtained from in-situ laser interference experiments, 30 whereas the thermodynamic parameters are based on surface energy data. 51 Solvent is removed from the top surface at a rate that is consistent with experimental spinning speeds. 30 Our simulations show that depending on the rate of evaporation, phase separation initiates either in the top layers or uniformly across the thickness of the drying film. Using Fast Fourier Transform (FFT)-based autocorrelation function (ACF) methods, we are able to determine the average size of PC71 BM domains in our

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Figure 1: Summary of experimental and computational techniques used in this work. (a) Schematic illustration of an in-situ laser interference setup used to determine the rate of change of film height as the film thins over time. This rate determines the Biot number, which is a crucial input parameter for our phase field model. (b) Contact angle measurements provide surface energy data used to estimate the Flory-Huggins interaction parameters. This image (used as an example here) has been reproduced with permission from reference 54. Copyright 2018 The Royal Society of Chemistry. (c) Simulation snapshot showing solvent removal from the top of the film as implemented in the phase field model, resulting in a reduction of the height of the film. Evaporation-induced phase separation leads to formation of PC71 BM-rich droplets suspended in the PDPP5T matrix. The color scale depicts the PC71 BM volume fraction, with deep red representing the highest concentration. The other components are rendered transparent for clarity. simulated morphologies. We accurately reproduce the scaling law between the dominant length scale and the normalized evaporation, or drying rate, reported previously from experiments. 30 Using linear stability analysis, 50 we establish that thermal fluctuations are responsible for setting the early-stage length scales of phase separation as the system crosses the spinodal boundary.

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2 Discussion and Results 2.1

Ternary phase field model

Our simulations focus on a ternary system consisting of an electron donor (the conjugated polymer PDPP5T), an electron acceptor (the fullerene derivative PC71 BM), and a solvent (chloroform). We assume that the system is incompressible. The volume fractions of each of the components at every position~r = (x, y, z) in the system are the order parameters φ p , φ f , and φs , respectively, and satisfy φ p + φ f + φs = 1. Hence, we only need to keep track of two independent order parameters, e.g., φ p and φ f , and put φs = 1 − φ p − φ f . We now have to specify the free energy functional F for the ternary system. In its basic form, F consists of an integral over the free energy density of mixing, f , and the interfacial free energy density, I:

F=

Z h V

i ~ ~ f (φ p , φ f ) + I(∇φ p , ∇φ f ) dV.

(1)

The free energy density of mixing f , also known as the homogeneous free energy density, is constructed using a lattice-based approach pioneered by Flory and Huggins, 55 widely used for polymer mixtures: φf φs RT φ p f (φ p , φ f , φs ) = ln(φ p ) + ln(φ f ) + ln(φs ) + χ p f φ p φ f + χ ps φ p φs + χ f s φ f φs , Vs N p Nf Ns

(2)

where R is the gas constant, T is the temperature, Ni = Vi /Vs is the effective degree of polymerization, with Vi being the molar volume of component i (i = p, f , s), and χi j is the Flory-Huggins binary interaction parameter between component i and j. The first three terms in Equation (2) describe the entropic and the last three terms the enthalpic contribution to the free energy density of mixing. The Flory-Huggins interaction parameters χi j have been estimated by an approach previously used by Moons et al. 56 We make use of the values (see Table 1) as given in literature. 51 The degrees of polymer-

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Table 1: Flory-Huggins interaction parameters and degrees of polymerization calculated for the PDPP5T:PC71 BM:CHCl3 system 51 . We note that Kouijzer et al. 51 estimate χ ps to be around 0.4 but report results using χ ps = 0.1, in which case the entropic contribution χs is not considered (see Equation 7 in reference 51). For a fair comparison, we also use χ ps = 0.1 in this work. We tested χ ps = 0.4 and found that this does not affect the conclusions from our simulations. Np 87

Nf 5

Ns 1

χp f 1.0

χ ps 0.1

χfs 0.9

ization Ni are estimated based on the molar volume of the polymer and fullerene with respect to the solvent. The interfacial energy density I is described using a square-gradient expression: I(~∇φ p , ~∇φ f ) = ∑i=p, f

εi2 2

| ~∇φi |2 . 46,57 In this work, we set the interfacial parameters ε p = ε f =

ε. 46,49,50 There is little experimental information about interfaces between PDPP5T and PC71 BM. We therefore take the value ε 2 = 10−10 Jm−1 , which is commonly used for organic systems. 46,50 Having defined the order parameters and the free energy of the system, we can now set up the governing equations for the two independent volume fractions φ p and φ f , while the solvent volume fraction φs is known through the incompressibility assumption. Mass transport is driven by gradients in chemical potentials of the polymer and fullerene components. The chemical potentials for the polymer and fullerene are defined as µ p = δ F/δ φ p and µ f = δ F/δ φ f . Using Fick’s law for diffusion J~i = −Mi~∇µi and the continuity equation ∂ φi /∂t + ~∇ · J~i = 0 for i = p, f , we get the following Cahn-Hilliard-Cook (CHC) equations: 49 ∂ f (φ p , φ f ) ∂ φp z ∂ φp ~ 2 2 ~ +u = ∇ · Mp ∇ − ε ∇ φ p + ξ p, ∂t h(t) ∂ z ∂ φp

(3)

∂φf ∂ f (φ , φ ) z ∂φf ~ p f 2 2 +u = ∇ · M f ~∇ −ε ∇ φf +ξf . (4) ∂t h(t) ∂ z ∂φf In these equations, Mi = Di / ∂ 2 fideal /∂ φi2 links the mobility of a component to its (self-)diffusivity Di , with fideal being the free energy density of an ideal solution where the χi j have been put equal to zero. 46,55 The second term (advection term) at the left-hand-sides in Equation (3) and (4) accounts for the change in height (thickness) of the film as solvent evaporates from the top surface. The fraction z/h(t) equals zero at the bottom surface (z = 0) and one at the top surface (z = h(t)),

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with h(t) being the height of the film at time t. The rate of change of height is u = ∂ h/∂t. The last terms ξi on the right-hand-sides of Equation (3) and (4) are the Langevin force terms, which are related to the mobilities Mi of the components by the fluctuation-dissipation theorem. We follow the implementation of the random Langevin forces by Shen et al. 58 in the case of space and time discretization. These random forces are known to play an important role in the early stages of spinodal decomposition. 59

2.2

Modeling solvent evaporation using in-situ laser interference data

In the experiments, a slightly defocused laser beam is incident on a spinning substrate during spin coating. 30 The reflected signal is collected by a photodiode positioned at a specular angle (see Figure 1a). The oscillating specular signal is due to the interference between the reflections from the top and bottom surface of the film. As the film height decreases due to solvent evaporation, its thickness satisfies conditions for constructive and destructive interference repeatedly. The final thickness (hdry ) of the dry layer is measured independently using a profilometer. The thickness of the film can then be back-calculated, thus providing the rate of decrease of height dh/dt over time as shown in Figure 2a. We assume that solvent is the only component lost from the film. In our model, it is removed from the top surface of the film at a uniform rate as shown in Figure 1c. This leads to a decrease of the film height over time. In-situ laser interference experiments measure an initial rapid decrease in film height that is attributed to radially outward fluid flow on the spinning substrate. 30 Thereafter, film thinning occurs due to evaporation with a linear rate of change of height. Our assumption of a constant solvent evaporation rate is therefore valid. As solvent is removed from the top layer, the layer becomes enriched in polymer and fullerene components. Solvent from the bulk of the film will therefore move to the top layer to replenish the solvent lost due to evaporation. The effectiveness of this process depends on the rate of diffusion of the solvent towards the top layer compared to the rate of solvent removal. To quantify this competition, we introduce the mass Biot 9



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Figure 2: (a) Top - Drying curve of a PDPP5T:PC71 BM:CHCl3 film for a spinning speed of 6000 rpm. The initial decrease in height is due to radial outflow of the fluid on the spinning substrate. Thereafter, film thinning occurs primarily due to evaporation. The rate of change of height dh/dt is obtained from a linear fit. The starting height h(t = 0) in our simulation box is 1000 nm. Bottom - Laser interference signals measured as the film thins over time. Knowing the final film thickness, the height of the film at any instant is back-calculated, resulting in the drying curve for a given evaporation rate. (b) Transmission Electron Microscopy (TEM) images of dry films obtained using a spinning speed of 6000 rpm (top) and 500 rpm (bottom). PC71 BM regions appear darker and form droplet-like structures embedded in the PDPP5T matrix. (c) Chemical structure of the polymer and fullerene derivative used. number, 49,50 defined as: Bi =

dh/dt , Ds /L

(5)

where dh/dt is the rate of change of film height, Ds the diffusivity of the solvent, and L a characteristic length, which we take to be the initial height of the film: L = h(t = 0). As shown in Figure 2a, we estimate dh/dt by determining the slope of the experimental drying curve in the linear regime. 30 We start our simulations when the solvent content is 90 vol. % which lies outside the spinodal region of the ternary phase diagram as shown in Figure 3. The drying curves indicate that the film thickness is close to 1000 nm at this point. Using the characteristic length

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L = 1000 nm and Ds = 2.95 × 10−5 cm2 s−1 for chloroform, 60 we calculate the Biot numbers for different drying speeds; see Table 2. The relative diffusivities of PDPP5T and PC71 BM are set e p = D p /Ds = 0.001 and D e f = D f /Ds = 0.005 respectively. Further details can be found in to D Section 1 of the Supporting Information (SI). Table 2: Biot number (Equation 5) for different spinning speeds. The rate of change of film height dh/dt is obtained from the slope of a linear fit to the linear regime of the experimental drying curves. 30 Spinning speed (rpm) 6000 3000 1500 500

dh/dt (nm s−1 ) 21591 15249 9689 5755

Initial film height (nm) 1000 1000 1000 1000

Biot number 0.0073 0.0051 0.0033 0.0019

The governing CHC equations are solved using a finite-element approach. 49,61 Technical details regarding the numerical methods can be found in Section 2 of the SI. We have performed 3D and, for comparison, also 2D simulations; see Section 3 of the SI. As mentioned above, the starting solvent fraction is φs = 0.90, which fixes the sum of polymer and fullerene fractions due to the incompressibility assumption. Experiments indicate that a polymer-fullerene weight ratio of 1:2 (w/w) leads to devices with the highest power conversion efficiency. 30 We use the same in our simulations to enable a direct comparison with experiments. Hence, using a polymer-fullerene weight ratio of 1:2 and a polymer density ρ p = 1.0 g cm−3 along with a fullerene density ρ f = 1.5 g cm−3 , we get φ p = 0.043 and φ f = 0.057. For the 3D simulations, we use a simulation box of size Lx = Ly = 500 nm and Lz = 1000 nm (the initial film height), with a mesh of 125 × 125 × 250 elements. The mesh density is chosen such that convergence is achieved for all time steps and the polymer-fullerene interface is adequately resolved. Periodic boundary conditions are imposed in the x- and y-directions. The rate u = ∂ h/∂t with which the film height decreases is proportional to the flux of the solvent from the top layer into air above the film: ∂h = −Vs Jsair , ∂t 11


(6)


where Jsair is the normal component of solvent molar flux into the air. The mass balance for the moving air-film interface at z = h is set according to u(φsair − φs (z = h)) = Vs (Jsa − Js (z = h)) under the assumption that only the solvent evaporates from the top surface and the solvent content in the air is very low (φsair 1). 49 To account for the enrichment of polymer and fullerene components in the top of the film, we use von Neumann boundary conditions: J p = −Jsair φ p and J f = −Jsair φ f . 49

Figure 3: Ternary phase diagram of PDPP5T:PC71 BM:CHCl3 . The colors indicate the wavelength λm of the fastest growing instability, which is obtained from a linear stability analysis (LSA). 50 The isocontour of λm = ∞ corresponds to the boundary of the spinodal region. Outside this boundary, there exists no real, positive λm , which indicates that the composition is stable. The smallest values of λm lie deep within the spinodal region, indicating that the composition fluctuations with those wavelengths are the most unstable. Left: The black data points represent the composition of the simulation domain corresponding to the starting configuration with 90 vol. % of solvent and a PDPP5T:PC71 BM weight ratio of 1:2. Right: Solvent evaporation leads to a quench into the spinodal region, after which the system evolves to a composition as represented in the diagram.

2.3

Analysis of the simulated film morphology

We track the PDPP5T and PC71 BM volume fractions both in the spatial and temporal domain. The 3D simulations are carried out at four different evaporation rates corresponding to experimental spinning speeds of 6000, 3000, 1500, and 500 rpm. All presented results are for room temperature. We use linear stability analysis (LSA) to determine the fastest growing instability, as illustrated in Figure 3. 50 The ternary phase diagram is obtained using the Flory-Huggins theory. As input for 12


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this calculation, the three interaction parameters (χ p f ,χ ps ,χ f s ) as well as the effective degrees of polymerization (N p ,N f ,Ns ) from Table 1 were used following the model described in reference 50. Further details can be found in Section 5 of the supporting information. In Figure 4, we show simulation results corresponding to a spinning speed of 6000 rpm. Initially, the film appears homogeneous. As evaporation proceeds, the film thins and the average solvent content decreases. The composition is now pushed into the unstable spinodal region. For the fast evaporation rate that corresponds to this high spinning speed, we observe that phase separation initiates in the top region of the film. As seen in the top panels of Figure 4, PC71 BM-rich droplets start to form when the height of the film is reduced to about 700 nm. The droplets are seen to grow over time. In Figure 5, we show the results for a drying rate corresponding to a spinning speed of 500 rpm. The evaporation is now much slower than in the previous case. More time is therefore available for domain coarsening. Hence, the average size of the PC71 BM domains is larger, which is also confirmed by experimental TEM images; see Figure 2b. During evaporation of the solvent, the phase field composition traverses a path within the spinodal region of the phase diagram represented by the collection of black data points as shown in the bottom panels of Figure 4 and 5. The noise term in the CHC equations introduces random fluctuations in the composition field that get amplified over time. The wavelength λm of the fastest growing fluctuation (see Figure 3) sets the characteristic length scale for the initial phase separation. For the fast evaporation occurring at 6000 rpm, the top layer of the film gets depleted of solvent before it can be replenished from the bulk of the film. Hence, phase separation initiates close to the top surface. This can also be seen from the composition of the system (black dots) in the bottom panel of Figure 4. At h = 700 nm, a large part of the film is still outside the spinodal region. The top layers of the film correspond to data points that form the branches within the spinodal region, whereas the bulk and bottom layers correspond to the points outside the spinodal. Such a mechanism for phase separation has previously been reported for a polystyrene-polyisoprene blend using in-situ stroboscopic illumination techniques. 43 The time scale of 20-50 ms during which the main features of the phase-separated morphology arise matches well with the in-situ laser scatter-

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ing data. 30 For a slow drying rate at 500 rpm, see Figure 5, the solvent has enough time to diffuse from the bulk and replenish the depleted solvent content in the top layers of the film. Hence, phase separation occurs uniformly in a bulk-like fashion. Due to the slower rate of solvent evaporation, the time scales (> 100 ms) for morphology evolution are considerably larger.

6000 rpm, Bi = 0.0073

Time Bulk droplets

Solvent evaporation Surface droplets

h= 700 nm, t = 0.017s Ternary phase diagram

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Bulk

h= 600 nm, t = 0.023s

h= 400 nm, t = 0.037s

ΦPC

70

BM

h= 250 nm, t = 0.049s

PC71BM-rich top layers

Figure 4: Top panels: 3D snapshots captured at different instances during evaporation-induced phase separation in a ternary blend of PDPP5T:PC71 BM:CHCl3 . The PC71 BM volume fraction is highlighted using a logarithmic color scale, with deep red indicating the highest concentration. PDPP5T and CHCl3 are rendered transparent for clarity. The evaporation speed corresponds to a spinning speed of 6000 rpm. The starting film height is 1000 nm, with a solvent content of 90 vol.%. The lateral dimensions of the simulated film are 500 × 500 nm2 . Bottom panels: Composition of the film represented by black data points in the ternary phase diagram of Figure 3 is shown for the respective film heights. Change of the composition during the entire evaporation process is shown as a movie which can be found in the SI. We see in Figure 4 and 5 that PC71 BM-rich droplets grow at the top surface. In the current setup of our model, we make use of a flat surface approximation and these droplets therefore do not protrude from the top surface. The PC71 BM-rich droplets have been the subject of experimental studies with in-situ grazing-incidence small-angle x-ray scattering (GISAXS). 62 Protrusion of the droplets from the top surface in the experiments is found from atomic force microscopy (AFM). 62

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From our simulations, we can determine the time at which these surface droplets appear as compared to bulk droplets. When the composition enters the unstable region in the top layers of the film, PC71 BM-rich bulk droplets start to appear. These result in the off-specular scattering signal. 30 The surface droplets appear later and result in the GISAXS scattering signal. 62 A time delay ∆t between the occurrence of the two signals has been experimentally established for polystyrene(PS)based films of PS:PC71 BM:o-xylene during spin coating. 62 PS:PC71 BM:o-xylene has a similar ternary phase diagram as PDPP5T:PC71 BM:CHCl3 62 and thus also shows phase separation via liquid-liquid demixing. For the PS-based films, the average inter-droplet distance does not change after the appearance of the GISAXS signal. Hence, it is argued that morphology development primarily occurs within the time interval ∆t. 62 Our simulations indicate that a similar process occurs for PDPP5T-based films. We estimate ∆t to be about 20-30 ms for a drying rate corresponding to 6000 rpm and about 40-50 ms for a drying rate corresponding to 500 rpm. We note that these time intervals are smaller compared to what is experimentally found for PS:PC71 BM:o-xylene. 62 This can be readily explained based on the fact that o-xylene is less volatile than CHCl3 and therefore solvent evaporation in PS:PC71 BM:o-xylene film occurs over a longer period of time.

2.4 Effect of evaporation rate on the fullerene domain size As explained in Figure 6, the 3D dry layer morphologies are used to extract the average domain size dav of the PC71 BM-rich phase for four different evaporation rates. In Figure 7a, we show the normalized autocorrelation function (ACF) of the PC71 BM-rich phase for the four different spinning speeds. The first minimum of the ACF is used as an estimate for dav . The domain size is seen to become larger for slower spinning speeds. This is again consistent with experiments where TEM images reveal a similar trend; see Figure 2b. We note that the calculated average domain size dav of PC71 BM is smaller than what is observed in TEM images of films obtained at a given spinning speed. This is because we only see the vertical projection (widest cross section) of a PC71 BM droplet in a TEM image. Our ACF analysis involves averaging over 2D slices across the film height, including all the PC71 BM droplet cross sections. Instead of absolute length scales, we 15



500 rpm, Bi = 0.0019

Time Bulk droplets

Solvent evaporation Surface droplets

h= 700 nm, t =0.062 s Ternary phase diagram

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

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h= 500 nm, t =0.106 s

h= 400 nm, t =0.130 s

ΦPC

70

BM

h= 250 nm, t = 0.174s

PC71BM-rich phase

Figure 5: Same as Figure 4, but for a spinning speed of 500 rpm, leading to a much slower evaporation. therefore focus on a comparison of trends between simulation and experiment for various drying rates. In our earlier work, we have shown that the dominant length scale d in the dry film, which can be defined in a number of ways, is related to the normalized evaporation or drying rate α = dh dt /hdry as d ∝ α b , where hdry is the dry layer thickness. 30 In Figure 7b, we plot the average PC71 BM domain size dav as a function of the normalized drying rate α. We recover the power law found in the experiments and obtain an exponent b = −0.31 ± 0.02. This is in excellent agreement with experiments, 30 where the value of b was found to be −0.33 ± 0.01. We conclude that dav is another proper measure of the dominant length scale: dav ∝ d. The ACFs for the four different spinning speeds almost fall on top of each other when plotted as a function of distance normalized by dav (see the inset of Figure 7a), which suggests a scaling property of the ACF.

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Figure 6: Estimating PC71 BM domain size from a simulated 3D morphology. (a) 3D rendering of a phase field morphology obtained at a drying rate corresponding to a spinning speed of 3000 rpm, with PC71 BM-rich regions highlighted in red. (b) The image in (a) is converted to a stack of slices with a spacing of 1 nm. (c) The images in the stack are converted to a binary format by choosing an adequate threshold for each image. (d) The binarized stack is used as an input to an ImageJ 63 “Radially Averaged Autocorrelation” macro that calculates the radial average of the pixel autocorrelation as a function of distance for every image in the stack. The final autocorrelation function (ACF) is obtained as an average over all the slices in the stack. The position of the first minimum of the ACF is used to estimate the average PC71 BM domain size.

2.5

Origin of the dominant length scale

It has been suggested that the rate of quenching dφs /dt plays an important role in determining the dominant length scale in dry layer morphologies. 44 In our case, dφs /dt is proportional to the normalized drying rate: dφs /dt ∝ α. 30 The time tcoarse available for coarsening of PC71 BM droplets after their generation depends on the normalized drying rate as tcoarse ∝ α −1 . 30 The dominant length-scale d in the dry films is therefore expected to depend either on the rate of quenching dφs /dt or on the coarsening time tcoarse , or on both. 30 As shown in Figure 4, for fast spinning speed, phase separation initiates in the top region of

17



(b)

(a) 1.0

0.8

6000 rpm 3000 rpm

0.6

av

0.8

(nm)

1.0

BM domain size d

1500 rpm 0.4

500 rpm

0.6 0.2

0.0

0.4

-0.2 0.0

0.2

0.5

1.0

1.5

2.0

d

500 rpm

b av

with b = - 0.31 R

2

0.02

= 0.99

90

1500 rpm

80

3000 rpm 70

71

Distance/Average domain size

100

0.0

PC

Normalized autocorrelation (ACF)

6000 rpm

-0.2 60 0

20

40

60

80

100

120

20

140

Distance (nm)

Normalized drying rate

240

d

(s

-1

80

)

180

2

3000 rpm 1.59

6000 rpm 120 1.26

slower

1

evaporation

60

71

BM domain size

60

500 rpm 1500 rpm

av

(nm)

(c)

40

PC

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

Page 18 of 31

0.01

0.05

0.10

0.20

Time (s)

Figure 7: (a) Autocorrelation function (ACF) for four different evaporation rates, calculated using the procedure described in Figure 6. The first minimum in the ACF is used to estimate the average PC71 BM domain size dav . The inset shows the same plot, with the distance normalized to dav . (b) Dependence of the average PC71 BM domain size dav on the normalized drying rate α for the final film height of 200 nm. The value of the exponent b in the power law is calculated as b = −0.31 ± 0.02, using a linear fit (shown as a dashed line) with R2 = 0.99 reflecting the fit quality (closer to 1 is better). (c) Evolution of the average PC71 BM domain size dav as a function of time for evaporation rates corresponding to spinning speeds 6000, 3000, 1500 and 500 rpm. At time t = 0, the film composition for a given evaporation rate enters the spinodal region of the ternary phase diagram. The final film thickness is 200 nm for all evaporation rates. Dotted lines indicate a power law dependence dav ∝ t 1/3 as expected from Lifshitz-Slyozov-Wagner (LSW) kinetics. For clarity, the data points for 3000, 1500 and 500 rpm have been multiplied by the indicated factors.

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the film. Using our ACF analysis, we estimate the emerging length scale during early stages of phase separation to be about 35 nm for the fastest drying rate corresponding to 6000 rpm, close to a film height of 700 nm as seen in the top row of Figure 4. This length scale is consistent with the fastest growing wavelength λm determined using LSA as seen in the bottom panel of Figure 4. In Figure 7c, we plot the average PC71 BM domain size dav for spinning speeds of 6000, 3000, 1500 and 500 rpm, as the film thins over time. The coarsening kinetics at longer times for the case of 6000 rpm (high Biot number Bi) is seen to differ significantly from the Lifshitz-Slyozov-Wagner (LSW) theory, where the domain size is predicted to increase like t 1/3 (dotted lines). 64,65 We observe a faster power-law like dependence with slope greater then 0.33, which indicates that there is insufficient time available for the LSW kinetics to take over from the initial spinodal decomposition. We can therefore conclude that the dominant length scale d for fast evaporation speeds such as 6000 rpm is primarily determined by the early-stage processes of spinodal decomposition, which can be linked to the rate of quenching dφs /dt. For a slower evaporation rate, we expect the time tcoarse available for coarsening to play a more important role in determining the dominant length scale d. We hypothesize that coarsening during later stages of drying for such a case should more closely follow LSW kinetics. To test this hypothesis, we study dav as a function of time for spinning speeds of 3000 rpm, 1500 rpm and 500 rpm. As shown in Figure 7c, at longer times the growth of dominant length scale d approaches the t 1/3 behavior for a drying rate corresponding to the slowest spinning speed of 500 rpm. This indicates that for slower evaporation rates, coarsening proceeds more in agreement with LSW kinetics and therefore lies in the regime of Ostwald ripening. 66 Due to the slower evaporation rate, the system has more time available for coarsening. The larger tcoarse leads to a larger dominant length scale d in the dry layer morphologies, differing significantly from the early-stage length scales. Our simulations therefore indicate that, depending on the rate of evaporation, the key determinant of the dominant length scale d is either the early-stage spinodal decomposition processes depending on the rate of quenching dφs /dt (fast evaporation) or late-stage coarsening processes

19



depending on the time tcoarse available for coarsening (slow evaporation). In the latter scenario, the occurrence of an exponent b = −1/3 in the relation d ∝ α b is readily understood, 30 but we are not aware of any theory that explains the occurrence of this exponent in the first scenario.

3 Summary, conclusions, and outlook Using large-scale three-dimensional phase field simulations, we were able to simulate phase separation triggered by solvent evaporation in a PDPP5T:PC71 BM:CHCl3 blend. Our simulations make use of realistic kinetic parameters obtained from in-situ laser interference experiments 30 and thermodynamic parameters estimated using contact angle measurements. We successfully capture the phase separation dynamics leading to liquid-liquid spinodal decomposition in the blends. A linear stability analysis (LSA) shows that the early-stage length scales in the decomposition are set by the instability with the fastest growing wavelength λm . We observed that phase separation for fast drying rates proceeds in an inhomogeneous manner, with PC71 BM-rich droplets appearing first in the top of the film. We also observed that PC71 BM droplets first appear within the film (below the top surface) and later on the surface of the film. This is similar to what has been observed for polystyrene:PC71 BM using grazing-incidence x-ray scattering (GISAXS). 62 Our simulations suggest that the time window ∆t between the appearance of bulk and surface PC71 BM droplets is larger for slower drying rates. We extracted an average size dav of the PC71 BM domains from an analysis of a compositional autocorrelation function (ACF). The dependence of dav in the dry film on the normalized evaporation rate α is in excellent agreement with the power-law dependence d ∝ α b of the dominant length scale d on α found in experiments. 30 The precise origin of this power law remains elusive. For slow evaporation rates, a late-stage coarsening process following the Lifshitz-Slyozov-Wagner (LSW) theory appears to govern dav , from which the observed power law could indeed be explained. However, for fast evaporation rates, dav appears to be predominantly determined by the

20


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early-stage spinodal decomposition processes. Understanding liquid-liquid phase separation is crucial for optimizing the film morphology in OPV cells. The PC71 BM droplet-like morphologies do not perform well in OPV cells because the size of the droplets exceeds the exciton diffusion length (about 10 nm) and because the droplets dispersed in the polymer-rich phase do not form optimal pathways to the electron-collecting electrode. 30 A solution to this problem has emerged in the form of high boiling-point co-solvents (such as ortho-dichlorobenzene). 28 When these are added, aggregation of the polymer occurs before liquid-liquid demixing sets in. Also changing other process variables, like substrate interactions, can potentially prevent liquid-liquid demixing and lead to better performing morphologies. We aim to explore these possibilities in future work.

4 Associated Content 4.1

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website. Additional information on the numerical methods, software packages and 2D simulation results (PDF), movies showing system composition traversing the phase diagram (AVI).

5 Author Information 5.1

Corresponding Authors

*E-mail: [email protected] *E-mail: [email protected]

21



5.2

Notes

The authors declare no competing financial interest.

6 Acknowledgement The authors would like to acknowledge the support given by the Center for Computational Research at the University at Buffalo. The 3D simulations were carried out on the Dutch national supercomputer Cartesius with the support of SURF Cooperative. The authors thank Dr. Charley Schaefer and Dr. Jasper Michels for fruitful discussions. This work is part of the Industrial Partnership Programme (IPP) “Computational sciences for energy research” of the Netherlands Organisation for Scientific Research Institutes (NWO-I). This research programme is co-financed by Shell Global Solutions International B.V.

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Simulating Phase Separation during Spin Coating ... - ACS Publications

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