Revealing the Importance of Energetic and Entropic Contributions to

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Revealing the Importance of Energetic and Entropic Contributions to the Driving Force for Charge Photogeneration Melissa P. Aplan, Jason Munro, Youngmin Lee, Alyssa N. Brigeman, Christopher Grieco, Qing Wang, Noel C. Giebink, Ismaila Dabo, John B. Asbury, and Enrique D Gomez ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b12077 • Publication Date (Web): 15 Oct 2018 Downloaded from http://pubs.acs.org on October 18, 2018

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ACS Applied Materials & Interfaces

Revealing the Importance of Energetic and Entropic Contributions to the Driving Force for Charge Photogeneration Melissa P. Aplan1, Jason M. Munro2, Youngmin Lee1, Alyssa N. Brigeman3, Christopher Grieco4, Qing Wang2, Noel C. Giebink3, Ismaila Dabo2, John B. Asbury4, and Enrique D. Gomez1,2,5* 1Department

of Chemical Engineering, 2Department of Materials Science and Engineering, and of Electrical Engineering, 4Department of Chemistry, and 5Materials Research Institute, The Pennsylvania State University, University Park, PA 16802 USA 3Department

Email: [email protected]

Keywords: organic photovoltaics; dielectric constant; block copolymers; exciton dissociation; charge transfer state; all-polymer solar cells; non-fullerene acceptors; quantum efficiency

Abstract Despite significant recent progress, much about the mechanism for charge photogeneration in organic photovoltaics remains unknown. Here, we use conjugated block copolymers as model systems to examine the effects of energetic and entropic driving forces in organic donor-acceptor materials. The block copolymers are designed such that an electron donor block and an electron acceptor block are covalently linked, embedding a donor-acceptor interface within the molecular structure. This enables model studies in solution where processes occurring between one donor and one acceptor are examined. First, energy levels that make up the driving force for charge transfer are systematically tuned and charge transfer within individual block copolymer chains is quantified. Results indicate that in isolated chains a significant driving force of ~ 0.3 eV is necessary to facilitate significant exciton dissociation to charge transfer states. Next, block copolymers are cast into films, allowing for intermolecular interactions and charge delocalization over multiple chains. In the solid state, charge transfer is significantly enhanced relative to isolated block copolymer chains. Results indicate changes in the energetic driving force alone cannot explain the increased efficiency of exciton dissociation to charge transfer states in the solid state. This implies that increasing the number of accessible states for charge transfer introduces an entropic driving force that can play an important role in the charge generation mechanism of organic materials, particularly in systems where the excited state energy level is close to that of the charge transfer state. 1 ACS Paragon Plus Environment

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Introduction Over the past two decades, significant efforts have attempted to elucidate the mechanism of photocurrent generation in organic photovoltaics.1-14 Several studies have suggested an energetic offset is required to dissociate excited states and should be ≥ 0.3 eV for high photovoltaic efficiency.15-20 This energetic offset is defined as the energy difference between the singlet exciton and charge transfer (CT) state, ES1 – ECT. It is important to minimize ES1 – ECT without decreasing the quantum yield of CT states, as this gap introduces an energy loss that reduces photovoltage. Nevertheless, multiple studies have reported high quantum efficiencies with driving forces significantly below the empirical value of 0.3 eV, suggesting a pathway to push device efficiencies beyond 15%.21-29 Considerable external quantum efficiency (EQE) values (max ~ 60%) have been demonstrated for OPV

devices

incorporating

a

poly(2,6-[(4-(7-bromo-[1,2,5]thiadiazolo[3,4-c]pyridine)]-[4,4-bis(2-

ethylhexyl)cyclopenta-[2,1-b:3,4-b’]-dithiophene]-alt-[4,4,9,9-tetrakis(4-hexylphenyl)-4,9-dihydro-sindaceno[1,2-b:5,6-b']dithiophene-2,7-diyl]) (PIPCP) electron donor blended with a [6,6]-phenyl-C61 butyric acid methyl ester (PC61BM) electron acceptor; the energetic offset is reported to be ≤ 0.05 eV.27, 30 Very low energy losses (Eloss) between the singlet exciton and open circuit voltage (VOC), Eloss = ES1 – qVOC, of 0.52 eV support a small energetic offset. While ES1 is easily measured from absorbance spectra, ECT is not observed using spectroscopic methods commonly used to characterize CT states, including photothermal deflection spectroscopy and sensitive EQE measurements. A shoulder present in both the photoluminescence and electroluminescence spectra is assigned to CT state emission; this value is used to quantify the energetic offset as ≤ 0.05 eV. In addition to rigorous characterization of the CT state in low Eloss systems, the crucial material properties needed to achieve high performance with a low driving force remain unclear. Although often neglected, the role of entropic gains during the charge generation process has been examined in a few recent studies.31-37 For example, the role of entropy was investigated using temperature dependent VOC measurements of devices incorporating a poly(3-hexylthiophene-2,5-diyl) (P3HT) electron donor blended with PC60BM.32 It is predicted that VOC should increase linearly with decreasing 2 ACS Paragon Plus Environment

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temperature.38 Unexpectedly, when the devices were examined at temperatures below 100 K, it was found that VOC decreases as temperature decreases. The authors rule out nonselective contacts, disorder in the film, and a decrease in the effective bandgap as plausible explanations for this trend. They conclude that the decrease in VOC must be due to decreased charge carrier density. This is interpreted as a decrease in charge separation efficiency. With no evidence for a temperature dependence on the energetic (enthalpic) driving force, the authors assume the temperature dependence of VOC must be due to the temperature dependence of the entropic contribution to free energy (i.e., ΔG = ΔH-TΔS); specifically, an entropic contribution for the dissociation of CT states to free charges. The influence of entropy has also been examined by adjusting the active layer morphology of different polymer/fullerene blend systems.35 Mixing two different electron donor polymers with various fullerene acceptors led to enthalpic driving forces (defined by the authors as the difference between LUMO energies of donor and acceptor) ranging from 0.7-1.3 eV. First, samples were made using a 1:1 polymer:fullerene blend ratio. Despite different material systems, a consistent trend is observed; as driving energy increases, the rate of free charge generation increases roughly linearly. The size of fullerene aggregates in the polymer/fullerene blend films was increased by incorporating high fullerene volume fractions (1:4 polymer:fullerene blend ratio). This in turn increases the density of delocalized states on fullerene, and potential entropic gain during the exciton dissociation process. Any changes to the enthalpic driving force as fullerene aggregate size increases are neglected, and thus, differences in charge generation are attributed to increased density of delocalized states, which is consistent with an entropic driving force for CT state dissociation to free charges. Nevertheless, only the rate of free charge generation is measured and thus, the influence of entropy on the initial charge transfer step remains unclear. Furthermore, in all of the 1:4 polymer:fullerene blend samples, charge generation is enhanced, but the degree to which charge generation increases with enthalpic driving force is dependent on the donor polymer. Thus, although both energetic and entropic driving forces are likely important for charge photogeneration, the relative contributions are not obvious.

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The energetic landscape in an organic film is complex, particularly near interfaces. As a consequence, it is challenging to decouple the roles of energetic and entropic driving forces. Furthermore, it may not be possible to accurately characterize the driving force for charge transfer in a film. It has been demonstrated that molecular orientation at the donor-acceptor interface can have a profound effect on ECT, leading to energy distributions of up to 0.6 eV.39-40 Given the complex, non-equilibrium morphologies present in a bulk heterojunction film, there is likely to be a broad distribution of molecular orientations at the donor-acceptor interface. Furthermore, to provide insight on the mechanism for photocurrent generation in systems with a small energetic offset, it is desirable to examine entropic effects in systems that do not already have a significant energetic driving force (ES1 – ECT < 0.7 eV). Studies on simple model systems could provide additional insight into the roles of the energetic offset and entropy. In this work, we present a systematic study using conjugated donor-acceptor block copolymers as model systems to investigate both energetic and entropic driving forces for exciton dissociation to CT states. The block copolymers consist of a P3HT electron donor block covalently linked to a push-pull polymer electron acceptor. When the block copolymers are dissolved as isolated chains in solution, entropic effects are reduced compared to a polymer film and molecular orientation at the donor-acceptor interface is established by the covalent linkage between the blocks. Exciton dissociation is quantified at the donoracceptor interface between a single donor and a single acceptor. The constituent energy levels of the energetic driving force, ES1 and ECT, are adjusted through small modifications to the chemical structure and dielectric constant of the solvent. Charge transfer is examined in systems with a wide range of energetic driving forces including values similar to those observed in “low-loss” systems, ES1 – ECT ≈ 0 eV, as well as values previously suggested to be necessary for efficient charge generation, ES1 – ECT ≈ 0.3 eV. The entropic driving force is increased by casting the block copolymers into thin films. This introduces intermolecular interactions which increase the number of accessible states and enhance delocalization. We find that although both energetic and entropic driving forces are important for exciton dissociation to a charge transfer state, harnessing entropy is crucial when energetic driving forces are less than 0.3 eV.


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Experimental Section Polymer

Synthesis.

Poly(3-hexylthiophene)-block-2,6-(4,4-bis-(2-ethylhexyl)-4H-

cyclopentadithiophene)-alt-[4,7-bis(3-dodecylylthiophen-5-yl)-2,1,3-benzothiadiazole]-2’,2"-diyl) (P3HT-b-PCPDT12BT),

poly(3-hexylthiophene)-block-poly-((9-(9-heptadecanyl)-9H-carbazole)-1,4-

diyl-alt-[4,7-bis(3-hexylthiophen-5-yl)-2,1,3-benzothiadiazole]-2’,2"-diyl) (P3HT-b-PCT6BT), poly(3hexylthiophene)-block-poly-((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-bis(3-hexylthiophen-5-yl)-2,1,3benzothiadiazole]-2’,2"-diyl)

(P3HT-b-PFT6BT),

poly(3-hexylthiophene)-block-poly-((2,5-

dihexylphenylene)-1,4-diyl-alt-[4,7-bis(3-hexylthiophen-5-yl)-2,1,3-benzothiadiazole]-2’,2"-diyl) (P3HTb-PPT6BT),

poly(3-hexylthiophene)-block-2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopentadithiophene)-alt-

[4,7-bis(thiophen-5-yl)-2,1,3-benzothiadiazole]-2’,2"-diyl) (P3HT-b-PCPDTBT), poly(3-hexylthiophene)block-poly-((9-(9-heptadecanyl)-9H-carbazole)-1,4-diyl-alt-[4,7-bis(thiophen-5-yl)-2,1,3benzothiadiazole]-2’,2"-diyl)

(P3HT-b-PCDTBT),

poly(3-hexylthiophene)-block-poly-((9,9-

dioctylfluorene)-2,7-diyl-alt-[4,7-bis(thiophen-5-yl)-2,1,3-benzothiadiazole]-2’,2"-diyl)

(P3HT-b-

PFTBT), poly(3-hexylthiophene)-block-poly-((2,5-dihexylphenylene)-1,4-diyl-alt-[4,7-bis(thiophen-5-yl)2,1,3-benzothiadiazole]-2’,2"-diyl) (P3HT-b-PPDTBT), and the corresponding homopolymers were synthesized using previously reported methods.41 Nuclear Magnetic Resonance (NMR) Spectroscopy. Solutions were prepared at ~ 10 mg mL in deuterated chloroform. 1H NMR analysis was carried out on Bruker Avance-III-850 MHz), Bruker AVIIIHD-500 MHz, or Bruker AV-360 instruments. The number average molecular weight (Mn) of P3HT was determined by end-group analysis. The weight composition of the block copolymers was determined by comparing the relative intensities of signals known to correspond to P3HT and the acceptor block. Together, these values were used to determine Mn of the block copolymers. NMR spectra are presented in the Supporting Information Figure S1. Gel Permeation Chromatography (GPC). Chain extension in the block copolymers and molecular weight distributions were characterized using GPC (Supporting Information, Figure S2). Samples were prepared in HPLC-grade chlorobenzene at 1 mg mL-1, dissolved overnight, and filtered through 0.2 µm filters before 5 ACS Paragon Plus Environment


injection. Data was obtained on an Agilent Technologies gel permeation chromatograph (ResiPore 300 x 7.5 mm column, Agilent 1260) equipped with refractive index, multiwavelength, light scattering, and viscometer detectors. Chlorobenzene was used as the mobile phase at 40°C with a flow rate of 0.5 mL min-1. Molar mass distributions were determined relative to polystyrene standards. Constrained Density-Functional Theory (CDFT). ECT values were calculated in 1,2,4-trichlorobenzene (ε0 = 2.24), chloroform (ε0 = 4.81), and 1,2-dichlorobenzene (ε0 = 9.93) using CDFT as described elsewhere.42 Dynamic Light Scattering (DLS). Isolated chain solutions were prepared at ~ 0.1-0.5 mg mL-1, stirred overnight, filtered through a 0.1 µm filter at least three times, and loaded into a 10 mL test tube for measurements. DLS measurements were performed on a Brookhaven Instruments BI-200 SM static/dynamic light scattering system equipped with a 35 mW diode laser (λ = 637 nm) and 90 mW near infrared laser (λ = 781 nm). The mean decay rate (Γ ) of the autocorrelation function was calculated using the CONTIN algorithm.43 Diffusion coefficients of the particles in the different solutions were estimated by plotting Γ versus the scattering vector (q) squared. The apparent hydrodynamic radius (Rh) was calculated from the diffusion coefficient according to the Stokes-Einstein relationship. To achieve sufficient scattering signal, block copolymer isolated chain DLS solutions were approximately 100-500 times more concentrated than those used for absorbance and fluorescence measurements. Absorbance and Fluorescence Spectroscopy. Solutions of isolated polymer chains were prepared by dissolving samples at ~ 1 mg mL-1 in solution and stirring overnight in a nitrogen-filled glovebox. Solutions were then diluted to ~ 1 mg L-1, loaded into 1 cm quartz cuvettes, sealed, and removed from the glovebox for testing. Polymer films were prepared by dissolving polymers at 10 mg mL-1 in chloroform, stirring overnight at 80°C, filtering through a 0.2 µm PVDF filter, and spincoating onto 1 cm2 quartz substrates. Films were thermally annealed at 165°C for 10 minutes. Absorbance spectra were measured on an Agilent Technologies Cary 60 UV-vis. Fluorescence emission spectra of polymer solutions were measured at several different excitation wavelengths (410, 430, 450, and 470 nm) on a Photon Technology International QuantaMaster 300 fluorometer equipped with a 6 ACS Paragon Plus Environment

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Xe Arc lamp and 914 photomultiplier detection system. Quantum yields (Φ) of homopolymers and block copolymers in solution were measured by comparing absorbance and fluorescence spectra to a dye of known quantum efficiency, 4-(Dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (Φ = 0.44 in ethanol). 44-45 Fluorescence spectra of polymer films were excited at 550 nm using the same setup. For low-temperature photoluminescence measurements, samples were mounted in an optically accessible Janis ST-100 liquid-nitrogen cryostat. Temperature was monitored with a LakeShore 335 Cryogenic Temperature Controller. Films were excited with a 10 mW continuous wave laser (λ = 532 nm), and emission was collected with a Horiba fibre-coupled spectrometer and cooled Si CCD array. Spectra were calibrated with an Ocean Optics tungsten-halogen calibration lamp.

Results and Discussion Materials Design, Synthesis, and Energy Level Characterization. We have previously shown that small differences in molecular structure can have a profound impact on the efficiency of exciton dissociation within individual block copolymer chains.42 Here, we make further perturbations to the molecular structure in order to adjust the energetic offset and examine exciton dissociation in isolated block copolymer chains. The block copolymers consist of a P3HT electron donor covalently linked to various push-pull polymer electron acceptors. Materials were synthesized using previously established procedures.41 Briefly, the P3HT donor block was synthesized using a Kumada catalyst transfer polymerization, yielding P3HT that is functionalized on one end with a bromine group. Using P3HT as a macroreagent, the acceptor block was added on in a chain-extension reaction using Suzuki or Stille polycondensation, yielding the series of block copolymers that are denoted in Figure 1. The corresponding acceptor homopolymers were also synthesized using standard Suzuki or Stille reaction conditions. Molecular weight characterization is presented in the Supporting information, Table S1. Most block copolymers and acceptor homopolymers were synthesized using Suzuki coupling. To prevent protodeboronation of boronic ester functional groups on cyclopentadithiophene monomers, Stille polycondensation was used for the chain extension reaction of P3HT-b-PCPDT12BT and P3HT-b-PCPDTBT block copolymers and polymerization of PCPDT12BT and 7 ACS Paragon Plus Environment


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PCPDTBT homopolymers.46 The dithienyl benzothiadiazole moieties were designed with different R groups to enhance either solubility or solid-state packing. To enhance solubility, either hexyl or dodecyl alkyl chains were appended to the thienyl units flanking the benzothiadiazole (R = C6H13, T6BT or C12H25, T12BT). To enhance solid state packing, these additional alkyl side chains were removed (R = H, TBT). Thus, “T6BT” and “T12BT” derivatives were used for isolated chain solution experiments and “TBT” derivatives were used for solid-state film experiments. We assume that side chains do not significantly alter electronics of the conjugated backbone but will have a profound effect on solubility and solid state packing.47-48 C6H13 S S

S

m

n R

N

S

R

N

C8H17

= S

N

S C8H17

C 2H 5 C 4H 9

C8H17

P3HT-b-PFT6BT, R = C6H13 P3HT-b-PFTBT, R = H C6H13

C8H17

P3HT-b-PCT6BT, R = C6H13 P3HT-b-PCDTBT, R = H C 2H 5

C 4H 9

C6H13

P3HT-b-PPT6BT, R = C6H13 P3HT-b-PPDTBT, R = H

P3HT-b-PCPDT12BT, R = C12H25 P3HT-b-PCPDTBT, R = H

Figure 1. Chemical structures of block copolymers. All block copolymers consist of a P3HT electron donor covalently linked to a push-pull polymer electron acceptor. In the conjugated backbone, the electron-rich unit of the acceptor block (colored aromatic moieties) is adjusted to tune the bandgap. R groups are also adjusted to enhance solubility or solid-state packing without altering the electronics of the conjugated backbone. Block copolymers were designed such that in solution, there is only one dominant pathway available for efficient charge transfer. In principle, when both the electron donor and acceptor efficiently absorb light, there are two pathways for charge transfer: electron transfer from donor to acceptor and hole transfer from the acceptor to the donor. In push-pull alternating copolymers, the LUMO will often localize to the strongest electron withdrawing group. Linking the P3HT electron donor directly to the “push” unit of the push-pull polymer acceptor creates a barrier for excited-state electron transfer between P3HT and the highly electron withdrawing benzothiadiazole (“pull” moiety). This does not disrupt hole transfer from the acceptor to the donor (ground state electron transfer from the donor to the acceptor) as the HOMO of such push-pull polymer blocks can be delocalized over both moieties.49 Thus, we assume that in solution 8 ACS Paragon Plus Environment

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charge transfer predominantly occurs via hole transfer from acceptor to donor after excitation in the acceptor (see Supporting Information Figure S3 for details).42 The energetic driving force for exciton dissociation to a charge transfer state is then defined as the energy difference between the singlet excited state of the acceptor block and the charge transfer state (ES1A – ECT). Values of ES1A and ECT are selectively tuned by altering the electronics of the acceptor block and the dielectric polarization of the surrounding environment, enabling a systematic investigation on the role of the energetic driving force on exciton dissociation to a charge transfer state. ES1A is tuned by altering the chemical structure of the acceptor block. To precisely tune ES1A, all acceptor blocks incorporate the same electron-deficient unit, a dithienyl benzothiadiazole, but different electron-rich units. Throughout the series, the electron donating ability of the electron-rich unit in the acceptor is systematically decreased by incorporating cyclopentadithiophene (P3HT-b-PCPDT12BT), carbazole (P3HT-b-PCT6BT), fluorene (P3HT-b-PFT6BT), and phenyl (P3HT-b-PPT6BT) moieties. This systematically increases ES1A, as measured by the absorbance onset of the acceptor homopolymers in dilute solution. Polymers were dissolved in either 1,2,4-trichlorobenzene (static dielectric constant, ε0 = 2.24), chloroform (ε0 = 4.81), or 1,2-dichlorobenzene (ε0 = 9.93). ES1A values vary minimally with solvent, < 0.1 eV. As the molecular structure of the acceptor block is synthetically tuned, the ES1A values range from ~ 1.6 to 2.2 eV. ECT is tuned by altering the static dielectric constant of the surrounding environment, here, the solvent. ECT is calculated using constrained density-functional theory (CDFT), which is able to accurately characterize the CT state in these donor-acceptor systems.42 Theoretical calculations demonstrate that as the static dielectric constant of the surrounding environment increases from about 2 to 10, the intramolecular charge transfer state is stabilized by roughly 0.5 eV. Across P3HT-b-PCT6BT, P3HT-bPFT6BT, and P3HT-b-PPT6BT, ECT values are nearly constant, but vary significantly with ε0 of the solvent. ECT of P3HT-b-PCPDT12BT is consistently about 0.2 eV less than the other block copolymers due to the small ES1 of the PCPDT12BT acceptor block (~ 1.7 eV). In addition to using chemistry to tune ES1A, ECT is selectively tuned by altering the dielectric polarization of the surrounding environment. Thus, we 9 ACS Paragon Plus Environment


selectively tune both ES1A and ECT, the energy levels that make up the driving force for charge transfer (Figure 2).

Figure 2. Energy level characterization of the block copolymers in solution. Optical bandgaps of the acceptor blocks (ES1A) are measured from the absorption onset. Charge transfer state energies (ECT) are calculated using constrained density-functional theory (CDFT). The driving force for hole transfer is defined as the difference between these two energies, ES1A – ECT. All values are plotted in eV as a function of the static dielectic constant of the solvent (ε0). Photoluminescence Quenching of Isolated Block Copolymer Chains. We quantify intramolecular exciton dissociation to a charge transfer state within isolated block copolymer chains in solution. Multiangle dynamic light scattering confirms that block copolymer chains are indeed isolated chains in solution (Figure S4, Supporting Information). All measured Rh values are consistent with isolated semiflexible chains (Table S2, Supporting Information). Furthermore, at the relatively low molecular weights used in this study, the contour length of each block is approximately 2-3 times the persistence length. The chain stiffness prevents the backbone from folding back onto itself, and prevents the formation of additional donor-acceptor contacts other than the covalent linkage between the blocks. Thus, any exciton dissociation observed occurs at the donor-acceptor interface embedded in the conjugated backbone. Steady state absorbance and photoluminescence spectra of the block copolymers and constituent homopolymers are measured in the different solvents. Representative spectra of chloroform solutions are 10 ACS Paragon Plus Environment

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presented in Figure 3; additional spectra are presented in the Supporting Information Figure S5 and Figure S6. In solution, linear combinations of the homopolymer absorbance and emission spectra describe the block copolymer absorbance and emission spectra. The block copolymer spectra are deconvoluted to measure the individual contributions of each block to both absorbance and emission. Exciton dissociation to a CT state at the intramolecular donor-acceptor interface, the CT state yield, is quantified by examining photoluminescence quenching of the block copolymers, as described in a previous study.42

Figure 3. Steady state absorbance as molar absorptivity (circles) and photoluminescence (squares) spectra of dilute polymer solutions in chloroform. Filled-in colored markers are the block copolymers, unfilled black markers are P3HT homopolymer, and unfilled gray markers are the different acceptor homopolymers. A linear combination of the homopolymer spectra (solid black lines) fits the block copolymer spectra. The homopolymer spectra are scaled by their contribution to the block copolymer spectra. The CT state yield is measured for all 4 block copolymers in 3 different solvents (i.e., under 12 different driving forces). We plot the CT state yield as a function of the driving force in Figure 4. The data



is fit assuming charge transfer (kCT) and radiative decay to the ground state (kR) are the dominant decay mechanisms for excited states along the acceptor block. The rate of charge transfer is estimated using Marcus theory and the rate of radiative decay is estimated using standard models for fluorescence emission.44, 50-51 The fit parameters used include the center-to-center distance between donor and acceptor, R, a pre-exponential factor, A, which is predominately determined by electronic coupling between the donor and acceptor, and the internal reorganization energy, λi. We fit the data to an R value of 3.4 ± 0.6 nm, an A value of 4.2 ± 6 x 108 eV1/2 s-1, and a λi value of 0.5 ± 0.2 eV; upper and lower bounds were calculated from standard error of the fit (See Supporting Information for details). An R value of 3.4 nm corresponds physically to charge transfer occurring within ~ 2 nm of the donor-acceptor interface, which we believe is quite reasonable. This length scale is similar to the exciton diffusion length of P3HT in chloroform solution as well as the repeat unit size of the acceptor blocks.52 Furthermore, a λi value of about 0.5 eV is reasonable considering previous reports of λ for solid state OPV systems.14, 53 Results for block copolymers dissolved in 1,2,4-trichlorobenzene are not fit as significant charge transfer is not observed in this solvent. Based on our model, we predict a maximum CT state yield ranging from 48-62% based on uncertainty in the fitting parameters.


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Figure 4. CT state yield (YCT) as a function of driving force, ES1A – ECT. Each block copolymer (colored markers) has a driving force dependent on solvent, yielding 3 different driving forces for each block copolymer and a total of 12 different data points. Squares represent samples measured in 1,2,4trichlorobenzene, circles represent chloroform (CF), and triangles represent 1.2-dichlorobenzene (DCB). The CT state yield (YCT) is modeled assuming charge transfer (kCT) and radiative decay to the ground state (kR) are the dominant mechanisms for exciton decay. Due to differences in solvent reorganization energy, the CT state yield will have a slightly different function in each solvent. The model for chloroform is shown in grey and 1,2-dichlorobenzene is shown in black. Data for 1,2,4-trichlorobenzene is not modeled. In the isolated chains in dilute solutions, the entropic driving force is reduced relative to a film; there is likely a lower number of accessible states for dissociation to a CT state. Quantifying the CT state yield as a function of driving force reveals that within isolated chains, where exciton dissociation occurs between one donor and one acceptor, a driving energy of about 0.3 eV is necessary for significant exciton dissociation, and about 0.7 eV is needed to maximize the CT state yield. Furthermore, it demonstrates that the effect of modulating the dielectric constant is mainly to perturb ECT, but for any given ECT the CT state yield from exciton dissociation is invariant. Photoluminescence Quenching of Block Copolymer Films. In block copolymer thin films, intermolecular interactions increase the number of states available for exciton dissociation to a CT state. Furthermore, in the solid state polymer chains adopt longer effective conjugation lengths, as evidenced by a reduction in the optical bandgap of about 0.1 to 0.3 eV, which enhances delocalization (Table S4, Supporting Information). The block copolymers used in solid-state measurements were the “TBT” 13 ACS Paragon Plus Environment


derivatives (P3HT-b-PCPDTBT, P3HT-b-PCDTBT, P3HT-b-PFTBT, and P3HT-b-PPDTBT) where the solubilizing alkyl side chains on the TBT unit are removed to enhance solid state packing and promote planarization. Previous work has shown that photovoltaic performance of devices incorporating polymers with TBT moieties are significantly enhanced relative to the more soluble analogues with additional alkyl side chains. This is attributed to morphological differences within the active layer.54-57 Block copolymers were cast onto quartz substrates and steady state absorbance and photoluminescence spectra were measured. In the solid state, a linear combination of the homopolymer absorbance and emission (550 nm excitation) spectra is able to mostly describe the block copolymer spectra (Figure S7, Supporting Information). Differences in molecular orientation and intermolecular coupling of chains in the block copolymer films, compared to the pristine homopolymer films, will alter the energetics and therefore the optical spectra.54 Imperfections in representing the solid state spectra are attributed to variations in solid state packing of the block copolymer films relative to the homopolymer films. Exciton dissociation to a charge transfer state is quantified using an analogous method as the block copolymer solutions. We thus expect some error in our calculation from the imperfect representation of block copolymer spectra. We estimate this error will be no more than 20%. As shown in Figure 5, charge transfer state yields are significantly enhanced in the solid state relative to the isolated chains in solution for all of the block copolymers, demonstrating more favorable conditions for CT state formation.


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1

Solution,  = 2.24 0

0.8

CT state yield

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


Solution,  = 4.81 0

Solution,  = 9.93 0.6

0

Film

0.4 0.2 0 P3HT-bP3HT-bPCPDT12BT/ PCT6BT/ PCDTBT PCPDTBT

P3HT-bPFT6BT/ PFTBT

P3HT-bPPT6BT/ PPDTBT

Figure 5. CT state yield of the block copolymers in solution (grey bars) and film (black bars). Solution measurements are performed on block copolymers with additional side chains on the TBT unit (R = C6H13 or C12H25), designed to enhance solubility. Film measurements are performed on block copolymers without additional side chains on the TBT unit (R = H) that are designed to enhance solid state packing. Charge transfer is significantly enhanced in the block copolymer films. Unfortunately, in going from isolated block copolymer chains to a polymer film, we lose much of the simplicity of our model system. To this end, it may not be possible to accurately characterize the energetic driving force for charge transfer in the block copolymer films. Through careful material design, the driving force for hole transfer is the main pathway available for exciton dissociation in our isolated block copolymer chains. Moreover, molecular orientation at the donor-acceptor interface is established by the covalent linkage between the blocks. These properties do not hold true in block copolymer films. From the data available, it is not possible to determine which pathways are leading to charge transfer and what the associated energy levels are. Nevertheless, CT state yields in the film are significantly enhanced relative to isolated chains in solution in all materials tested. In some materials, the difference in CT state yield going from isolated chains to a film is larger than the variation over the entire energy range of polymers in solution (-0.2 to 0.5 eV) and CT state yields over 75% are measured. While the energetics will certainly change in going from isolated chains in solution to films, our results from the isolated chains indicate such a large enhancement 15 ACS Paragon Plus Environment


Page 16 of 25

in CT state yield would necessitate an enthalpic driving force significantly greater than 0.5 eV, which is unexpected. Furthermore, after accounting for uncertainty of the fitting parameters, our model in Figure 3 suggests the CT state yield is unlikely to exceed approximately 62% for any enthalpic driving force. Altogether, these results imply that energetics alone cannot fully explain the high CT state yields observed in block copolymer films. We propose the increase in CT state yield in block copolymer thin films is at least in part the result of an enhanced entropic driving force. We can support this hypothesis by measuring the temperaturedependence of photoluminescence from our polymer films. Figure 6 shows that the photoluminescence from P3HT, PPDTBT, and P3HT-b-PPDTBT films (the block copolymer for which we observe the largest CT state yield) increases with decreasing temperature, as expected due to diminished molecular motion at low temperatures. Using the homopolymer spectra as a reference, we quantify the CT state yield by measuring quenching of block copolymer photoluminescence intensities from 90 K to 294 K. We relate the CT state yield to the charge transfer rate kCT and emission rate kR with CT state yield = kCT/(kCT + kR). Using kR = Φ/τ (see Supporting Information), assuming an excited state lifetime (τ) at 294 K of approximately 500 ps,58-59 and a fluorescence quantum yield (Φ) on the order of 0.05 for films near room temperature60, we calculate values for kR. We assume that τ is proportional to 𝑇 and that Φ increases with temperature according to the increase in integrated emission.59 Having estimated kCT, we use the Eyring equation61 to calculate the contributions of enthalpy (ΔH‡) and entropy (ΔS‡) to the barrier for charge transfer (Figure 6d):

𝑘𝐶𝑇

( )=

𝑙𝑛

𝑇

― ∆𝐻 ‡ 𝑘𝐵𝑇

𝑘𝐶𝑇𝑘𝐵

( )+

+𝑙𝑛

ℎ

∆𝑆 ‡ 𝑘𝐵

(1)

Where kB is the Boltzman constant and h is Planck’s constant. Fitting to the data shown in Figure 6e suggests a minimal enthalpic barrier, ΔH‡ = -0.02 eV, and more significant entropic barrier, TΔS‡ = 0.27 eV at 294


Page 17 of 25

K. Thus, we interpret these results as a signature of an entropic-driven process for charge transfer and CT

6 4 2

(a)

P3HT 294 K 255 K 210 K 165 K 90 K

PL emission (a.u.)

PL emission (a.u.)

state formation.

0

40

(b)

PPDTBT 294 K 255 K 210 K 165 K 90 K

30 20 10 0

600 700 800 900 Wavelength (nm)

600 700 800 900 Wavelength (nm)

B CT

8 (c) P3HT-b-PPDTBT 294 K 6 255 K 210 K 4 165 K 90 K 2

ln(k /T * (h/k ))

-4 PL emission (a.u.)

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


(d)

-6 -8 -10 -12 -14

0

0

600 700 800 900 Wavelength (nm)

0.005 0.01 -1 1/T (K )

Figure 6. PL emission as a function of temperature from (a) P3HT films, (b) PPDTBT films, and (c) P3HTb-PPDTBT films. (d) Fit of charge transfer rate kCT to Eyring equation as a function of temperature to obtain energetic (enthalpic) and entropic contributions to the barrier for charge transfer. We suspect that the stronger importance of entropy for CT state formation is due to an increase in the number of accessible sites for exciton dissociation or enhanced delocalization. In polymer films, intermolecular interactions introduce pathways for intermolecular charge transfer, increasing the number of accessible states. Furthermore, the increase in effective conjugation length observed as polymers pack in a solid state film will enhance delocalization. Although, recent work on the mechanism of polaron formation in P3HT suggests significant intermolecular delocalization may not be necessary; even in a twodimensional lattice, polarons are about the width of two thiophene rings and tend to localize on single chains.62 Thus, we conclude that an increased entropic driving force in the solid state can enhance exciton dissociation due to the greater number of accessible states. Furthermore, it is possible that the enhanced entropic driving force in films, compared to isolated block copolymer chains, may be able to compensate for low energetic driving forces and facilitate efficient charge transfer in systems with a low energetic offset. 17 ACS Paragon Plus Environment


Conclusions Our study makes use of conjugated block copolymers as ideal model materials to systematically investigate energetic and entropic contributions to the driving force for exciton dissociation to a CT state. We examine intramolecular charge transfer in isolated chains where the number of states available for charge transfer is reduced with respect to a polymer film. The energetic driving force can be precisely tuned using different molecular structures and dielectric environments. Hole transfer from acceptor to donor within individual block copolymer chains was quantified as the energetics of the singlet exciton and charge transfer state were selectively tuned. In a model system, where exciton dissociation occurs via hole transfer from one donor to one acceptor, a significant energetic offset of about 0.3 eV is critical for significant charge transfer, although we predict that CT state yields are not maximized until a driving force of about 0.7 eV is achieved. Entropic effects were investigated by examining block copolymers in solid state films, which introduces intermolecular interactions and increases the number of states available for exciton dissociation. While it is not straightforward to precisely characterize the relevant energetic driving forces for charge transfer, in all cases exciton dissociation is more efficient than in isolated chains. According to our model for exciton dissociation within isolated block copolymer chains, altered energetics alone cannot account for the dramatic increase in exciton dissociation in block copolymer films versus isolated chains. Altogether, our results suggest that both an energetic driving force and an entropic driving force are important to facilitate efficient photocurrent generation. This entropic driving force is likely crucial to maximize photocurrent in low energetic offset systems and thereby simultaneously maximize photocurrent and photovoltage in organic solar cell devices.

Acknowledgement Financial support from the Office of Naval Research under Grant N000141410532 is gratefully acknowledged.


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Supporting Information NMR spectra, polymer molecular weights, driving force for electron transfer, dynamic light scattering results, absorbance and photoluminescence spectra of polymer solutions, CT state yields predicted from Marcus Theory, absorbance and photoluminescence spectra of polymer films, temperature dependence of photoluminescence quenching.

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