Estimating the Magnitude of Exciton Delocalization in ... - UAkron Blog

Subscriber access provided by Georgetown University | Lauinger and Blommer Libraries

Article

Estimating the Magnitude of Exciton Delocalization in Regioregular P3HT Michael Heiber, and Ali Dhinojwala J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp403396v • Publication Date (Web): 23 Sep 2013 Downloaded from http://pubs.acs.org on October 7, 2013

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

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

Page 1 of 28

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

The Journal of Physical Chemistry

Estimating the Magnitude of Exciton Delocalization in Regioregular P3HT Michael C. Heiber∗ and Ali Dhinojwala∗ Department of Polymer Science, The University of Akron, Akron, Ohio 44325, USA E-mail: [email protected],Phone:(815)2898184; [email protected],Phone:(330)9726246

∗

To whom correspondence should be addressed

1 ACS Paragon Plus Environment


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

Abstract Exciton delocalization has been proposed to have a strong impact on the performance of organic solar cells. For example, large exciton delocalization estimates have promoted the theory of long-range charge transfer as a mechanism for efficient charge separation. Here, two new computational modeling techniques for analyzing femtosecond transient absorption spectroscopy experiments are developed in order to estimate the magnitude of exciton delocalization in semiconducting polymers. The developed techniques are then used to analyze previously published experimental data for regioregular poly(3-hexylthiophene) (P3HT). Based on modeling both the exciton-exciton annihilation behavior in a pure P3HT film and the exciton dissociation dynamics in a P3HT:PCBM blend film, the exciton delocalization radius in regioregular P3HT is estimated to be in the range of 1-2 nm, which is significantly smaller than estimated in a number of previous studies. These results suggest that exciton delocalization is not likely to be a significant contributing factor to efficient charge separation.

Keywords: Organic Solar Cells, Dynamic Monte Carlo, Polymers, and Exciton Annihilation, Exciton Dissociation

Introduction Understanding the fundamental mechanisms that occur in bulk heterojunction devices has been of significant interest to researchers studying organic solar cells. In particular, several excellent reviews of this field have been recently published. 1,2 By understanding these processes, scientists hope to be able to tailor materials properties and bulk heterojunction morphologies to increase the power conversion efficiency. Explaining the unexpectedly high charge separation yield observed in optimized polymer:fullerene devices has been particularly challenging. In an attempt, several concepts have been proposed including interfacial dipoles, 3–5 hot charge separation, 6–8 charge delocalization, 7,9 exciton delocalization, 8,10,11 and interfacial disorder. 12 2 ACS Paragon Plus Environment

Page 2 of 28

Page 3 of 28

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


Among these, exciton delocalization has been indicated to have a strong impact on charge separation. Previously, Guo et al. have investigated exciton delocalization behavior in regiorandom and regioregular poly(3-hexylthiohpene) (P3HT) using femtosecond transient photoinduced infrared absorption spectroscopy, and found that excitons in regioregular P3HT are more delocalized. 13 In a subsequent study, Guo et al. showed that free charge carrier generation was much more efficient in regioregular P3HT, and proposed that the magnitude of exciton delocalization affects the charge separation efficiency. 10 Using this concept in a dynamic Monte Carlo simulation, we have previously shown that the magnitude of the exciton delocalization radius could have a strong impact on the geminate recombination for a model donor-acceptor system. 8 Subsequently, Caruso and Troisi proposed a similar longrange charge transfer model as a method for increasing the separation yield. 11 To understand the role of exciton delocalization further, it is imperative to have a more accurate estimate for the magnitude of exciton delocalization in P3HT and other semiconducting polymers used in organic photovoltaic devices. Exciton delocalization in conjugated polymers is thought to occur when the exciton wavefunction is not confined to a single monomer unit but is instead extended over multiple monomer units along the backbone of the chain and possibly even to portions of adjacent polymer chains. The first studies attempting to experimentally measure exciton delocalization in conjugated polymers have used measurements of the excess polarizability of excitons to estimate the delocalization volume. Excess polarizability measurements on PPVs and poly(alkylthiophenes) were performed in dilute solution and on solid films. 14–17 The delocalization length in solution was estimated at 4-5 nm, but in solid films, delocalization volumes were measured to be several times larger potentially due to intermolecular delocalization. However, studies of this nature have not yet estimated the exciton delocalization size for regioregular P3HT films, in which significant intermolecular delocalization is expected due to high crystallinity. In addition, several experimentally measured phenomena have been attributed to exciton



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

delocalization and have been used to estimate the magnitude of exciton delocalization. The first one is the observation of significant exciton-exciton annihilation when films are placed under high intensity illumination. Based on exciton-exciton annihilation modeling, several groups have estimated the exciton-exciton annihilation radius, which can be used as an upper bound estimate of the exciton delocalization radius. Estimates for the exciton-exciton annihilation radius have ranged from 2.5-8.5 nm. 13,18–20 The second piece of evidence for exciton delocalization is observed in the exciton dissociation dynamics in P3HT:PCBM blends. Using femtosecond transient absorption spectroscopy, Guo et al. measured two different timescales for exciton dissociation and have associated them with two distinct mechanisms. First, excitons created near the donor-acceptor interface undergo ultra-fast dissociation on the sub-100 fs timescale. Second, excitons created further away from the interface must undergo diffusion prior to dissociation that occurs on the 10 ps timescale. Similar exciton dynamics have also been observed in several additional studies. 18,20–22 The fraction of excitons able to undergo immediate dissociation should be directly related to the exciton delocalization radius and the P3HT domain size, and Guo et al. have concluded that their previously estimated delocalization radius of 4.3-6.7 nm derived from exciton-exciton annihilation modeling is consistent with their observation of 50% immediate dissociation for domains sizes of 13-15 nm. 10 Conversely, recently Kaake et al. have proposed that ultrafast dissociation of highly delocalized (>20 nm) excitons is the dominant mechanism occurring in many donor-acceptor blends, including P3HT:PCBM. 23,24 Here, to obtain a more refined estimate of the exciton delocalization radius in P3HT and other semiconducting polymers, we have developed two computational modeling techniques to analyze the exciton-exciton annihilation behavior and exciton dynamics measured by femtosecond transient absorption spectroscopy. First, we construct a course grain lattice model for simulating exciton-exciton annihilation behavior in a pure film, and then implement a more complex dynamic Monte Carlo simulation technique to simulate the exciton dissociation dynamics for a model bulk heterojunction film. While several simplifying assumptions


Page 4 of 28

Page 5 of 28

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


have been made in this work, the modeling techniques developed here are far more rigorous than previously implemented models and can readily be applied to characterize new materials.

Methodology Exciton-Exciton Annihilation Modeling Here, femtosecond transient absorption spectroscopy measurements performed by Guo et al. are modeled. 13 In these experiments, a 100 nm P3HT film was prepared on a glass substrate and a 100 fs excitation pulse was applied to create excitons in the film. Since absorption of 400 nm light in P3HT is relatively independent of the magnitude of crystallinity, 25–27 we assume that excitons are created uniformly throughout both the amorphous and crystalline regions. As a result, the delocalization radius estimated here represents the average behavior from excitons formed in both the amorphous and crystalline regions. To simulate the exciton-exciton annihilation behavior, a simple lattice model is constructed in which a cubic lattice is constructed to represent a 100 by 100 by 100 nm section of the film. Several tests were also performed on lattices of 150 by 150 by 100 nm and 200 by 200 by 100 nm, but no significant changes were observed. In this model, excitons are assumed to behave as hard spheres, such that excitons cannot overlap each other. As a result, as the lattice is populated with excitons, the lattice sites become filled up. To control the magnitude of exciton delocalization, the number of sites in the lattice is adjusted. For example, in a 100 by 100 by 100 site lattice, each site represents a 1 nm3 volume which can hold an exciton with a diameter of 1 nm. In a 50 by 50 by 50 site lattice, each site can hold an exciton with a diameter of 2 nm. The pump pulse excitation is simulated by calculating the number and distribution of excitons created in the section under the given conditions. Since the pump pulse is very short, it is assumed that all photons in the pump pulse strike the sample instantaneously. The 5 ACS Paragon Plus Environment


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

number of excitons created in the lattice is calculated by first converting the pump energy into a number of photons and then calculating the fraction of photons absorbed using the BeerLambert law. Thin film interference was not included because there is minimal reflection at the P3HT-glass interface. The refractive index for P3HT was taken from spectroscopic ellipsometry measurements, resulting in a value of 1.7 at 400 nm. 28 The imaginary portion of the refractive index was calculated from the absorption coefficient. Absorption coefficient measurements for P3HT at 400 nm range from 4.5 × 104 to 6.5 × 104 cm−1 depending on regioregularity and film preparation conditions. 28–32 Here we assume an absorption coefficient of 5.5×104 cm−1 , resulting in an estimation of 42% photon absorption. The absorbed excitons are then randomly placed on the lattice with an exponential distribution. Details about the photon absorption calculations and the exciton probability distribution can be found in the supporting information. Once the lattice is populated, a small fraction of the excitons undergo immediate dissociation into polarons. Experimental measurements of the initial polaron yield range from approximately 2-30% depending on the measurement technique and excitation wavelength used. 13,18,20,33–36 Most studies agree that the yield is on the low end of this range and Guo et al. have measured a 6% initial polaron yield at 400 nm excitation. 13 As a result, we assume that 6% of the excitons created in the lattice undergo dissociation immediately after creation. When executing dissociation, the exciton is replaced on the lattice site with a polaron pair. All remaining excitons are then checked for exciton-exciton annihilation. In the excitonexciton annihilation mechanism, the energy of one exciton is transferred to another nearby exciton, resulting in the quenching of the first exciton and the creation of a hot exciton. In this model, we assume that only nearest neighboring excitons can undergo ultrafast annihilation. As a result, if an exciton is positioned in one of the 6 nearest neighbor sites of another exciton, the pair is deemed able to undergo annihilation. To simulate the annihilation process, the entire lattice is scanned and all exciton pairs able to undergo annihilation


Page 6 of 28

Page 7 of 28

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


are placed into a list. One exciton pair is randomly chosen from the list and annihilation is executed. The hot excitons which are formed after each exciton-exciton annihilation event are then able to either relax back to the singlet state or dissociate immediately into a polaron pair. It has been observed that hot excitons have an increased probability of ultrafast dissociation into polarons based on the measurement of increased polaron yield under high intensity excitation. 13,20,37 In addition, higher energy excitons formed by higher energy excitation have also been shown to have increased polaron yield, which is consistent with the concept of hot exciton autoionization. 13,20,33 Guo et al. have measured a large overall initial polaron yield under high intensity excitation, up to 50%. 13 However, the polaron yield of hot excitons formed by exciton-exciton annihilation has not been specifically quantified. Here, to start, we assume that the hot excitons have a 50% dissociation yield. Once this process is complete, the list of possible annihilation pairs is updated. This execution and updating cycle continues until all possible exciton-exciton annihilation events have been executed, and then the final exciton concentration is calculated. In addition, it is assumed that no exciton-polaron annihilation occurs within the 100 fs timescale simulated here. This assumption is justified further in the Results and Discussion section. The experimental data showing the relationship between the optical density of the exciton absorption peak as a function of pump intensity was extracted from the figure previously published by Guo et al. 13 The raw data was normalized so that the linear regime of the experimental data fits the linear regime of the simulated curves. As a result, the original experimental data published in arbitrary units was converted to an absolute measurement of exciton density.

Exciton Dissociation Dynamics Modeling To simulate the exciton dissociation dynamics, a dynamic Monte Carlo (DMC) simulation technique is used, as described in detail in our previous work. 8 In the DMC technique, all 7 ACS Paragon Plus Environment


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

Page 8 of 28

fundamental mechanisms occurring in an organic solar cell can be simulated. However, in this study, the only mechanisms included are exciton creation, diffusion, dissociation, and relaxation. For exciton creation events, we set the simulation to approximate the performance of P3HT:PCBM blends under low intensity 400 nm excitation. Under this condition, it is assumed that excitons are only created in the P3HT regions and that excitons are created uniformly throughout the crystalline and amorphous domains. In addition, the intensity of the pump pulse is assumed to be low enough such that exciton-exciton annihilation and exciton-polaron quenching can be disregarded. The effects of hot excitons are also not included because the excitons are assumed to undergo vibrational relaxation to the S1 singlet state before exciton hopping occurs. Also, this study ignores the possible formation of triplet state excitons because regioregular P3HT does not exhibit significant triplet formation. 13 For exciton diffusion, an isotropic diffusion process is implemented through a Förster resonance energy transfer mechanism. 38 While excitons are also thought to be able to migrate by Dexter electron exchange, 39 the Förster mechanism is almost always assumed to dominate and has become the standard model for describing singlet exciton diffusion. 40 Any potential anisotropy caused by molecular or crystallite orientation is not included. Simulated exciton diffusion deviates from a true random walk through the incorporation of energetic disorder using the Gaussian disorder model. 41 When excitons are near the donor-acceptor interface, exciton dissociation is enabled and implemented through a charge transfer process from the donor site to any nearby acceptor sites that are adjacent to the interface. The rate of an exciton dissociation event is calculated based on Miller-Abrahams theory, 42

Rexd = R0,exd exp (−2γex dij )

(1)

where R0,exd is the exciton dissociation coefficient, γex is the inverse exciton localization


Page 9 of 28

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


parameter, and dij is the distance from the center of the exciton to the destination acceptor site. A Boltzmann term is not included here because, in this study, exciton dissociation is always energetically favorable. As the exciton localization parameter decreases, the exciton can effectively dissociate farther from the interface and has a larger interaction radius. Here, the exciton delocalization radius is defined as the average distance between the center the exciton and the interface when the excitons dissociate. As a result, the magnitude of exciton delocalization is tuned by adjusting the inverse exciton localization parameter, γex . If an exciton does not dissociate within its lifetime, exciton relaxation occurs and the exciton is removed from the lattice. Exciton dissociation within the P3HT domains is assumed to be negligible and is also not included. In this study, a kinetic model is applied to describe the ultrafast dissociation of excitons created near the donor-acceptor interface on the sub-100 fs timescale. It is important to note that electronic mechanisms occurring on this timescale may be subject to quantum effects that are not included in this kinetic model. As a result, using this technique to distinguish the dynamics of different processes occurring on the sub-100 fs timescale may not be adequate. Here, the key assumption is that the Miller-Abrahams model explained above adequately describes both the time and distance dependence of the charge transfer process that occurs when ultrafast exciton dissociation takes place. We emphasize that the kinetic model is used here to simply distinguish the ultrafast exciton dissociation mechanism from the much slower exciton hopping mechanism. Given the two very distinct timescales present, a kinetic model should be adequate for describing the exciton dissociation dynamics of interest in this study. To simulate the exciton dissociation dynamics in a bulk heterojunction film, a model bulk heterojunction morphology is implemented using the Ising model. 43 It has been previously shown that the P3HT domains in P3HT:PCBM blends are approximately 13-15 nm. 44,45 To test this range, five morphologies were generated with donor domain sizes ranging from about 12 to 16 nm. The average domain size present in each morphology was calculated using the



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

Table 1: DMC Simulation Parameters Lattice length, l 80 sites Lattice width, w 80 sites Lattice height, d 100 sites Lattice spacing, a 1 nm Exciton generation rate, G 10 nm−3 s−1 Energetic disorder, σ 0.07 eV Exciton lifetime, τex 330 ps Dissociation rate, R0,exd 1 × 1016 s−1 pair-pair correlation method. 46 More details about the morphology generation procedure can be found in the supporting information. Data for the exciton dissociation dynamics is obtained by recording the lifetime of each simulated exciton, one at a time. Excitons are created and data is collected until 2000 excitons have been dissociated. To construct an exciton decay curve, for each time point on the curve, the fraction of excitons which have a lifetime that is greater than the time point is calculated. In this way, a time averaging technique is used on a small volume to calculate the performance that would be expected from an experiment on a large volume sample. This technique can only be applied when the experimental exciton density resulting from the pump pulse is low enough such that exciton-exciton annihilation is negligible. To fit the experimental data, the inverse exciton localization parameter, γex , and the exciton hopping coefficient, R0,exh , are manually adjusted until a best fit is obtained. For a given set of parameters, the exciton delocalization radius is determined by calculating the average effective interaction radius. To calculate the average effective interaction radius, a separate DMC simulation test is performed in which exciton creation is limited to sites which are greater than 5 nm from the donor-acceptor interface. After creation, the excitons are allowed to undergo standard behavior, and when each exciton dissociates, the distance between the center of the exciton and the interface is recorded. Data is recorded until 1000 excitons have dissociated, and the average effective interaction radius is then calculated for the given set of parameters.


Page 10 of 28

Page 11 of 28

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


To simulate exciton behavior in the P3HT phase, simulation parameters were taken from experimental characterization of neat P3HT. The energetic disorder was set to 0.07 eV 47,48 and the exciton lifetime was set to 330 ps. 13 A complete list of simulation parameters is shown in Table 1. To obtain a representative experimental exciton decay curve, data has been extracted and analyzed from the figures published by Guo et al. 10 Several points were selected from the exciton decay curve and renormalized. With the condition that the exciton fraction is equal to 0.5 at 100 fs, the data was converted from units of optical density to a measurement of the exciton fraction. Error bars for the reference experimental curve were calculated from the estimated variance of the original experimental data.

Results and Discussion Exciton-Exciton Annihilation Modeling Using the data gathered from the exciton-exciton annihilation simulation, the exciton concentration is plotted as a function of the pump power in Figure 1. Simulated curves were generated for exciton delocalization radii, r, of 1.52, 1.79, and 2.08 nm. In comparison with the normalized experimental data, the best fit is obtained for an exciton delocalization radius of 1.79 nm. Due to the scatter of the experimental data and the resolution of the fitting procedure, the uncertainty of the extracted exciton radius for a given set of parameters is estimated at ±0.05 nm. The other potential sources of uncertainty are the magnitude of the absorption coefficient, hot exciton dissociation yield, and initial polaron yield. Tests were also performed varying each of these parameters within the experimentally indicated ranges, but these variations were found to have only a small (∼0.1 nm) impact on the estimated delocalization radius. Further discussion of these source of uncertainty can be found in the supporting information. As a result, based on the exciton-exciton annihilation modeling performed here, 11 ACS Paragon Plus Environment


19

10

Exciton Concentration (cm−3)

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

18

10

r = 1.52 nm r = 1.79 nm 17

r = 2.08 nm

10

Experiment −6

10

−5

10

−4

10

Pump Intensity (J/cm2)

Figure 1: Simulated Exciton Concentration vs. Pump Intensity compared to normalized experimental data for exciton delocalization radii of 1.52 nm (solid), 1.79 nm (dash), and 2.08 nm (dash-dot). the final upper limit estimate for the exciton delocalization radius is around 2 nm, which is significantly smaller than many estimates in previous studies. It should be noted that this estimate describes the exciton delocalization behavior on the sub-100 fs timescale and that exciton delocalization on the picosecond timescale could be even smaller due to presence of dynamic localization that occurs on the picosecond timescale. 13 Previous estimates based on modeling exciton-exciton annihilation behavior have used a much simpler model that relies on determination of the onset point of exciton-exciton annihilation. Guo et al. and Zhang et al. have defined the onset point as the intersection point between two lines, one drawn though the linear regime with a slope of 1, and one drawn through the data measured at high intensity. 13,20 However, this method depends critically on how the line is drawn through the high intensity data. In reality, the determination of an finite onset point has little physical meaning. In the experimental data shown in Figure 1, close inspection reveals that there does not appear to be an abrupt transition where excitonexciton annihilation begins. Rather, as the excitation intensity increases, the data becomes gradually less and less linear until eventually reaching a plateau at high intensity. Furthermore, the assumed exciton distribution at the measured onset point has a sig12 ACS Paragon Plus Environment

Page 12 of 28

Page 13 of 28

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


nificant impact on the estimated delocalization radius in previous studies. Simple models assume that excitons in a film form a homogeneous, ordered distribution. At the onset point, it is assumed that the exciton concentration has reached the point where the excitons are just beginning to "touch" each other. To approximate this state, the excitons are assumed to be spheres with a radius, r, that are packed into a finite volume. For a given exciton concentration, there are several ways to assume how the excitons are arranged in the volume of the film. A close packed arrangement is most dense, followed by a cubic arrangement, and finally random packing. In reality, the excitons are more accurately described as being randomly distributed in the film, and random close packed structures have been shown to have packing densities which are much lower than close packed structures. 49 This difference is expected to cause exciton-exciton annihilation to occur more frequently at lower exciton concentrations, resulting in a smaller delocalization estimate compared to models which assume a close packed arrangement. In addition, when populating the volume randomly, excitons always have a chance to be placed next to each other, yielding a small amount of annihilation even at low exciton concentrations. As a result, an abrupt onset of exciton-exciton annihilation is not simulated here using the random populating algorithm. While some order is impemented here by using a cubic lattice, this underlying lattice order has little effect on the random population of the lattice when the lattice is mostly empty. In the worst case, at the high end of the pump intensity, when simulating a pump power of 1 × 10−4 J/cm2 , the lattice is initially only 39% full. When the lattice is mostly empty, randomly populating the cubic lattice is almost equivalent to truly random positioning. Finally, we justify the simplification of not including exciton-polaron annihilation. Several experimental studies have indicated the prevalence of exciton-polaron annihilation in conjugated polymers. 36,50 In P3HT films, Ferguson et al. have measured a reduced polaron yield on the nanosecond timescale at high excitation intensity and have attributed this phenomenon to the quenching of excitons by polarons. 36 However, Guo et al. have measured



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

seemingly opposite behavior, with a higher polaron yield on the 100 fs timescale at high excitation intensity. 13 The important difference between these two measurement, though, is the timescale of each measurement. We hypothesize that exciton-polaron annihilation is minimal on the 100 fs timescale, but plays a much larger role on the picosecond to nanosecond timescale. However, we also performed simulations including exciton-polaron annihilation, which are shown in the supporting information. We find that if exciton-polaron annihilation is competitive with exciton-exciton annihilation on the 100 fs timescale, we would expect two behaviors to be observed. First, the overall polaron yield would not continue to increase at high excitation intensity, and second, the exciton concentration would not plateau at high excitation intensity. Rather, the increased polaron concentration due to dissociation of hot excitons would lead to further exciton quenching, resulting in a lower exciton concentration at the highest intensities simulated. The experimental measurements modeled here do not demonstrate either of these behaviors, suggesting that exciton-polaron annihilation is insignificant on the 100 fs timescale, and even if it was significant, our results indicate that it would only lead to a slightly smaller exciton delocalization radius estimate.

Exciton Dissociation Dynamics Modeling The simulated exciton dissociation dynamics is dictated by four main parameters: the exciton dissociation rate, domain size, inverse exciton localization parameter, and exciton hopping rate. In order for excitons adjacent to the interface to dissociate within 100 fs, the exciton dissociation process must be very fast. As a result, the exciton dissociation rate coefficient is fixed at a constant value of 1 × 1016 s−1 . This reduces the problem to only three important parameters, and for simulations on a given morphology, the domain size is also constant, leaving only the inverse exciton localization parameter and the exciton hopping rate. To demonstrate the effects of these two parameters, simulations using a fixed domain size of 13.8 nm are discussed first. 14 ACS Paragon Plus Environment

Page 14 of 28

Page 15 of 28

Figure 2 shows how the simulated exciton decay behavior is affected by the inverse exciton localization parameter. The magnitude of the inverse exciton localization parameter has a significant effect on the magnitude of the initial decay (1 ps). As expected, the magnitude of the initial decay is inversely proportional to the inverse exciton localization parameter. For this morphology, a best fit is obtained when the inverse exciton localization parameter equals 1.7 nm−1 . 1 Experiment

0.9

γex = 1.5 nm−1

0.8 Exciton Fraction

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


γex = 1.7 nm−1 γex = 1.9 nm−1

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

5

10

15

20 25 Time (ps)

30

35

40

Figure 2: The effect of the inverse exciton localization parameter on simulated exciton decay curves compared to the experimental data. 10

The second aspect to fitting the experimental exciton decay curve is the exciton hopping rate. As shown in Figure 3, the exciton hopping rate mainly affects the exciton decay curve at longer timescales (>1 ps) and has no effect on the magnitude of the initial decay. However, in order for excitons created away from the interface to reach the interface within the 10 ps timescale, the exciton hopping rate must be fairly fast. For this morphology, the best fit is obtained using an exciton hopping rate of 4 × 1012 s−1 . In an independent exciton diffusion simulation, given an exciton lifetime of 330 ps and an exciton hopping rate of 4 × 1012 s−1 , we obtain an average diffusion length of 20 nm. This magnitude for the exciton diffusion length is significantly larger than estimated by most previous studies that have found the



exciton diffusion length to be less than 10 nm for P3HT. 19,51–54 However, Cook et al. have estimated an exciton diffusion length of 27±12 nm based on modeling exciton annihilation behavior measured by time resolved photoluminescence. 55 It is plausible that excitons created in the crystalline regions undergo fast exciton diffusion until reaching an amorphous boundary or a defect where trapping or slow diffusion would occur. This concept would allow for fast short range diffusion while preventing a large diffusion length. Anisotropic diffusion could also potentially explain this behavior. In this case, it is likely that the exciton decay due to diffusion would also be dependent on regioregularity as well as film fabrication and annealing conditions. Regardless, since the initial decay is independent of the exciton hopping rate used, the estimation of the exciton delocalization radius is independent of the exciton hopping rate used and the details of the exciton diffusion process. 1 Experiment

0.9

Rhop = 6 × 1012 s−1

0.8 Exciton Fraction

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

Page 16 of 28

Rhop = 4 × 1012 s−1 Rhop = 2 × 1012 s−1

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

5

10

15

20 25 Time (ps)

30

35

40

Figure 3: The effect of exciton hopping rate on simulated exciton decay curves compared to experimental data. 10 Similar curve fitting was performed for all five morphology sets with domain sizes ranging from 12-16 nm to calculate the effect of the domain size on the fitted inverse exciton localization parameter and the exciton hopping rate. In addition, the average effective interaction radius was also calculated for each set of parameters to estimate the exciton delocalization


Page 17 of 28

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


Table 2: Exciton Decay Fitting Results Morphology M1 M2 M3 M4 M5

Domain Size (nm) γex (nm−1 ) 12.1 1.9 13.0 1.8 13.8 1.7 14.9 1.6 15.8 1.5

R0,exh (s−1 ) 3 × 1012 4 × 1012 4 × 1012 5 × 1012 6 × 1012

Delocalization Radius (nm) 2.0 2.1 2.3 2.5 2.7

radius. Table 2 shows all of the data extracted from exciton decay curve fitting and the corresponding exciton delocalization radius. Given a domain size in the range of 13-15 nm for real P3HT:PCBM films, the average exciton delocalization radius is estimated to be 2.3 nm. To estimate the uncertainty in this calculation, we look at two factors: uncertainty in the experimental data analysis and uncertainty in the morphology. Experimental data uncertainty is mainly attributed to the quantification of 50% dissociation at 100 fs. Given the lack of sub-100 fs resolution of the initial decay, the determination of exactly 50% initial dissociation is not possible. While keeping the domain size constant, if we assume that the initial dissociation uncertainty is ±5%, this leads to a variation in the estimate delocalization radius of about ±0.5 nm. While keeping the initial dissociation constant, if we assume that the domain size uncertainty is ± 2 nm, the uncertainty of the exciton delocalization radius is ±0.4 nm. Additional discrepancies may also be expected due to other morphological factors including domain shape and domain purity. As the domain shape changes, the interfacial area to volume ratio will also change, which could have an impact on the fitted exciton delocalization radius. To investigate this effect, simulations have also been performed on an extreme case of a vertically-aligned checkerboard morphology with 14 nm wide square pillars. In cases where P3HT domains form fibrillar crystals, 44 the true morphology may behave in a similar manner to a checkerboard morphology. Even though the long axis of the P3HT crystals is typically randomly oriented in the plane of the film, domain orientation does not effect the exciton decay behavior in this model. With the checkerboard morphology, a best fit to the experimental data was obtained using an inverse exciton localization of 2.2 nm−1 and an 17 ACS Paragon Plus Environment


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

exciton hopping coefficient of 3 × 1012 s−1 , resulting in an estimated exciton delocalization radius of 1.5 nm. In this extreme example, the fitted exciton delocalization radius was found to be even smaller than the value estimated for the model bulk heterojunction morphology. In addition, if the domain interfaces are not sharp and there is mixing of the acceptor into parts of the donor phase, as indicated by the presence of a mixed P3HT:PCBM phase between pure P3HT and pure PCBM domains, 56 the effective domain size will decrease, resulting in an even smaller estimate of the exciton delocalization radius. To investigate this effect, a model bulk heterojunction morphology was created with 14 nm donor domains and then modified to include an 3 nm wide interfacial region containing 20% acceptor as shown in Figure 4. Using this morphology, a best fit to the experimental data was obtained using an inverse exciton localization of 2.7 nm−1 and an exciton hopping coefficient of 4 × 1012 s−1 , resulting in an estimated exciton delocalization radius of only 0.9 nm.

Figure 4: Cross-sectional image of a model BHJ morphology with 14 nm donor domains and a 3 nm wide diffuse interface consisting of 20% acceptor. While the model bulk heterojunction morphologies used here certainly have differences when compared to experimentally measured morphologies, overall, given the domain size constraints imposed by previous experimental measurements, the exciton delocalization radius estimated from this experimental data is relatively small and in the range of 1 to 2 nm. Only 18 ACS Paragon Plus Environment

Page 18 of 28

Page 19 of 28

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


the presence of much larger pure P3HT domains or the presence of a significantly greater proportion of ultrafast dissociation would result in a large exciton delocalization estimate similar to previous studies. As morphological models become more fine-tuned to accurately represent experimentally measured morphologies, the delocalization radius estimated here can be refined. Conversely, recently Kaake et al. have proposed that ultrafast dissociation of highly delocalized (>20 nm) excitons is the dominant mechanism occurring in many donor-acceptor blends, including P3HT:PCBM. 23,24 However, our analysis leads to a significantly different picture. Our conclusions are supported by several key experimental observations. First, annealing of P3HT:PCBM blends introduces an enhanced presence of exciton diffusion limited polaron formation, indicating that domain size and purity have a significant impact on the exciton dissociation dynamics. 10,22 Second, decreasing the amount of PCBM in the blend, thereby creating larger P3HT domains, also slows down the exciton dissociation dynamics. 10 These two observations point to an exciton dissociation process that is sensitive to relatively small changes in domain size. Along with our conclusions, these experimental trends refute the idea that exciton dissociation is dominated by highly delocalized excitons on the sub-100 fs timescale. At least in the P3HT:PCBM system, diffusion limited exciton dissociation is readily observed, which indicates that the exciton declocalization length must be significantly smaller than the domain size.

Conclusions Overall, we have developed two techniques that make use of femtosecond transient absorption spectroscopy and computational modeling to extract an approximation of the exciton delocalization radius in semiconducting polymers. These techniques were subsequently applied to estimate the exciton delocalization radius in regioregular P3HT. Results from our rigorous modeling efforts strongly support the notion that the exciton delocalization radius in



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

regioregular P3HT is significantly smaller than previously estimated values. In addition, we have highlighted the sources of uncertainty and characterized the sensitivity of the extracted estimates to input parameter variation. While there is some uncertainty in each modeling technique, the two estimates derived from modeling two separate experiments both support the conclusion that the effective exciton delocalization radius in regioregular P3HT is likely to be in the range of 1-2 nm. Quantifying this behavior is particularly important for understanding the effect of delocalization on the fundamental mechanisms in organic solar cells. In particular, exciton delocalization effects have been proposed to be a major factor for reducing geminate recombination in polymer:fullerene devices. 8,10,11 The small exciton delocalization radius estimated here suggests that exciton delocalization is not likely to be the main factor aiding charge separation and reducing geminate recombination. However, characterization of the magnitude of exciton delocalization as demonstrated here will allow researchers to investigate charge separation behavior as a function of delocalization magnitude for different semiconducting polymers in further detail. To facilitate this effort, the computational tools used to perform the modeling described here are now freely available online. 57,58

Acknowledgement We thank the LORD corporation and the National Science Foundation grant NSF-DMR 0512156 for funding, Prof. Mesfin Tsige for valuable discussions and simulation help, and Dr. Carsten Deibel for insightful advice.

Supporting Information Available The supporting information contains additional details about the methodologies used and more detailed uncertainty calculations.

This material is available free of charge via the

Internet at http://pubs.acs.org/.


Page 20 of 28

Page 21 of 28

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


References (1) Deibel, C.; Strobel, T.; Dyakonov, V. Role of the Charge Transfer State in Organic Donor-Acceptor Solar Cells. Adv. Mater. 2010, 22, 4097–4111. (2) Clarke, T. M.; Durrant, J. R. Charge Photogeneration in Organic Solar Cells. Chem. Rev. 2010, 110, 6736–6767. (3) Arkhipov, V. I.; Emelianova, E. V.; Bässler, H. Dopant-Assisted Charge Carrier Photogeneration in Conjugated Polymers. Chem. Phys. Lett. 2003, 372, 886–892. (4) Arkhipov, V. I.; Heremans, P.; Bässler, H. Why is Exciton Dissociation So Efficient at the Interface between a Conjugated Polymer and an Electron Acceptor? Appl. Phys. Lett. 2003, 82, 4605–4607. (5) Aarnio, H.; Sehati, P.; Braun, S.; Nyman, M.; de Jong, M. P.; Fahlman, M.; Österbacka, R. Spontaneous Charge Transfer and Dipole Formation at the Interface Between P3HT and PCBM. Adv. Energy Mater. 2011, 1, 792–797. (6) Peumans, P.; Forrest, S. R. Separation of Geminate Charge-Pairs at Donor-Acceptor Interfaces in Disordered Solids. Chem. Phys. Lett. 2004, 398, 27–31. (7) Bakulin, A. A.; Rao, A.; Pavelyev, V. G.; van Loosdrecht, P. H. M.; Pshenichnikov, M. S.; Niedzialek, D.; Cornil, J.; Beljonne, D.; Friend, R. The Role of Driving Energy and Delocalizaed States for Charge Separation in Organic Semiconductors. Science 2012, 335, 1340–1344. (8) Heiber, M. C.; Dhinojwala, A. Dynamic Monte Carlo Modeling of Exciton Dissociation in Organic Donor-Acceptor Solar Cells. J. Chem. Phys. 2012, 137, 014903. (9) Deibel, C.; Strobel, T.; Dyakonov, V. Origin of the Efficient Polaron-Pair Dissociation in Polymer-Fullerene Blends. Phys. Rev. Lett. 2009, 103, 036402.



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

(10) Guo, J.; Ohkita, H.; Benten, H.; Ito, S. Charge Generation and Recombination Dynamics in Poly(3-hexylthiophene)/Fullerene Blend Films with Different Regioregularities and Morphologies. J. Am. Chem. Soc. 2010, 132, 6154–6164. (11) Caruso, D.; Troisi, A. Long-range Exciton Disocciation in Organic Solar Cells. Proc. Natl. Acad. Sci. 2012, 109, 13498–13502. (12) McMahon, D. P.; Cheung, D. L.; Troisi, A. Why Holes and Electrons Separate So Well in Polymer/Fullerene Photovoltaic Cells. J. Phys. Chem. Lett. 2011, 2, 2737–2741. (13) Guo, J.; Ohkita, H.; Benten, H.; Ito, S. Near-IR Femtosecond Transient Absorption Spectroscopy of Ultrafast Polaron and Triplet Exciton Formation in Polythiophene Films with Different Regioregularities. J. Am. Chem. Soc. 2009, 131, 16869–16880. (14) Liess, M.; Jeglinski, S.; Vardeny, Z. V.; Ozaki, M.; Yoshino, K. Y.; Ding, Y.; Barton, T. Electroabsorption Spectroscopy of Luminescent and Nonluminescent π-Conjugated Polymers. Phys. Rev. B 1997, 56, 712–724. (15) Warman, J. M.; Gelinck, G. H.; Piet, J. J.; Suykerbuyk, J. W. A.; de Haas, M. P.; Langeveld-Voss, B. M. W.; Janssen, R. A. J.; Hwang, D.-H.; Holmes, A. B.; Remmers, M.; Neher, D.; Müllen, K.; Bäuerle, P. Time-Resolved Microwave Measurements of the Polarizability of Photoexcitations on Conjugated Polymer Chains. Proc. SPIE 1997, 3145, 142–149. (16) Gelinck, G. H.; Piet, J. J.; Wegewijs, B. R.; Müllen, K.; Wildeman, J.; Hadziioannou, G.; Warman, J. M. Measuring the Size of Excitons on Isolated Phenylene-Vinylene Chains: From Dimers to Polymers. Phys. Rev. B 2000, 62, 1489–1491. (17) van der Horst, J. W.; Bobbert, P. A.; de Jong, P. H. L.; Michels, M. A. J.; Siebbeles, L. D. A.; Warman, J. M.; Gelinck, G. H.; Brocks, G. Predicting Polarizabilities and Lifetimes of Excitons on Conjugated Polymer Chains. Chem. Phys. Lett. 2001, 334, 303–308. 22 ACS Paragon Plus Environment

Page 22 of 28

Page 23 of 28

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


(18) Piris, J.; Dykstra, T. E.; Bakulin, A. A.; van Loosdrecht, P. H. M.; Knulst, W.; Trinh, M. T.; Schins, J. M.; Siebbeles, L. D. A. Photogeneration and Ultrafast Dynamics of Excitons and Charges in P3HT/PCBM Blends. J. Phys. Chem. C 2000, 113, 14500–14506. (19) Wang, H.; Wang, H.-Y.; Gao, B.-R.; Wang, L.; Yang, Z.-Y.; Du, X.-B.; Chen, Q.D.; Song, J.-F.; Sun, H.-B. Exciton Diffusion and Charge Transfer Dynamics in Nano Phase-Separated P3HT/PCBM Blend Films. Nanoscale 2011, 3, 2280–2285. (20) Zhang, W.; Hu, R.; Li, D.; Huo, M.-M.; Ai, X.-C.; Zhang, J.-P. Primary Dynamics of Exciton and Charge Photogeneration in Solvent Vapor Annealed P3HT/PCBM Films. J. Phys. Chem. C 2012, 116, 4298–4310. (21) Marsh, R. A.; Hodgkiss, J. M.; Albert-Seifried, S.; Friend, R. H. Effect of Annealing on P3HT:PCBM Charge Transfer and Nanoscale Morphology Probed by Ultrafast Spectroscopy. Nano Lett. 2010, 10, 923–930. (22) Howard, I. A.; Mauer, R.; Meister, M.; Laquai, F. Effect of Morphology on Ultrafast Free Carrier Generation in Polythiophene:Fullerene Organic Solar Cells. J. Am. Chem. Soc. 2010, 132, 14866–14876. (23) Kaake, L. G.; Moses, D.; Heeger, A. J. Coherence and Uncertainty in Nanostructured Organic Photovoltaics. J. Phys. Chem. Lett. 2013, 4, 2264–2268. (24) Kaake, L. G.; Jasieniak, J. J.; Ronald C. Bakus, I.; Welch, G. C.; Moses, D.; Bazan, G. C.; Heeger, A. J. Photoinduced Charge Generation in a Molecular Bulk Heterojunction Material. J. Am. Chem. Soc. 2012, 134, 19828–19838. (25) Zhokhavets, U.; Erb, T.; Gobsch, G.; Al-Ibrahim, M.; Ambacher, O. Relation Between Absorption and Crystallinity of poly(3-hexylthiophene)/Fullerene Films for Plastic Solar Cells. Chem. Phys. Lett. 2006, 418, 347–350.



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

(26) Vanlaeke, P.; Swinnen, A.; Haeldermans, I.; Vanhoyland, G.; Aernouts, T.; Cheyns, D.; Deibel, C.; D’Haen, J.; Heremans, P.; Poortmans, J.; Manca, J. V. P3HT/PCBM Bulk Heterojunction Solar Cells: Relation between Morphology and Electro-Optical Characteristics. Sol. Energ. Mat. Sol. C. 2006, 90, 2150–2158. (27) Lee, W. H.; Chuang, S. Y.; Chen, H. L.; Su, W. F.; Lin, C. H. Exploiting Optical Properties of P3HT:PCBM Films for Organic Solar Cells with Semitransparent Anode. Thin Solid Films 2010, 518, 7450–7454. (28) Ng, A. M. C.; Cheung, K. Y.; Fung, M. K.; Djuri˘sić, A. B.; Chan, W. K. Spectroscopic Ellipsometry Characterization of Polymer-Fullerene Blend Films. Thin Solid Films 2008, 517, 1047âĂŞ1052. (29) Al-Ibrahim, M.; Roth, H.-K.; Schroedner, M.; Konkin, A.; Zhokhavets, U.; Gobsch, G.; Scharff, P.; Sensfuss, S. The Influence of the Optoelectronic Properties of poly(3alkylthiophenes) on the Device Parameters in Flexible Polymer Solar Cells. Org. Electron. 2005, 6, 65–77. (30) Kim, Y.; Choulis, S. A.; Nelson, J.; Bradley, D. D. C.; Cook, S.; Durrant, J. R. Composition and Annealing Effects in Polythiophene-Fullerene Solar Cells. J. Mater. Sci. 2005, 40, 1371–1376. (31) Kim, Y.; Cook, S.; Tuladhar, S. M.; Choulis, S. A.; Nelson, J.; Durrant, J. R.; Bradley, D. D. C.; Giles, M.; McCulloch, I.; Ha, C.-S.; Ree, M. A Strong Regioregularity Effect in Self-Organizing Conjugated Polymer Films and High-Efficiency Polythiophene:Fullerene Solar Cells. Nature Mater. 2006, 5, 197–203. (32) Morfa, A. J.; Barnes, T. M.; Ferguson, A. J.; Levi, D. H.; Rumbles, G.; Rowlen, K. L.; van de Lagemaat, J. Optical Characterization of Pristine Poly(3-Hexyl thiophene) Films. J. Polym. Sci., Part B: Polym. Phys. 2011, 49, 186–194.


Page 24 of 28

Page 25 of 28

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


(33) Dicker, G.; de Haas, M. P.; Siebbeles, L. D. A.; Warman, J. M. Electrodeless TimeResolved Microwave Conductivity Study of Charge-Carrier Photogeneration in Regioregular poly(3-hexylthiophene Thin Films. Phys. Rev. B 2004, 70, 045203. (34) Dicker, G.; de Haas, M. P.; Siebbeles, L. D. A. Signature of Exciton Annihilation in the Photoconductance of Regioregular poly(3-hexylthiophene). Phys. Rev. B 2005, 71, 155204. (35) Sheng, C.-X.; Tong, M.; Singh, S.; Vardeny, Z. V. Experimental Determination of the Charge/Neutral Branching Ratio η in the Photoexcitation of π-Conjugated Polymers by Broadband Ultrafast Spectroscopy. Phys. Rev. B 2007, 75, 085206. (36) Ferguson, A. J.; Kopidakis, N.; Shaheen, S. E.; Rumbles, G. Quenching of Excitons by Holes in Poly(3-hexylthiophene) Films. J. Phys. Chem. C 2009, 112, 9865–9871. (37) Stevens, M. A.; Silva, C.; Russell, D. M.; Friend, R. Exciton Dissociation Mechanisms in the Polymeric Semiconductors poly(9,9-dioctylfluorene) and poly(9,9-dioctylfluoreneco-benzothiadiazole). Phys. Rev. B 2001, 63, 165213. (38) Förster, T. Zwischenmolekulare Energiewanderung und Fluoreszenz. Ann. Phys. 1948, 437, 55–75. (39) Dexter, D. L. A Theory of Sensitized Luminescence in Solids. J. Chem. Phys. 1953, 21, 836–859. (40) Brédas, J.-L.; Norton, J. E.; Cornil, J.; Coropceanu, V. Molecular Understanding of Organic Solar Cells: The Challenges. Acc. Chem. Res. 2009, 42, 1691–1699. (41) Bässler, H. Charge Transport in Disordered Organic Photoconductors. Phys. Stat. Sol. (b) 1993, 175, 15. (42) Miller, A.; Abrahams, E. Impurity Conduction at Low Concentrations. Phys. Rev. 1960, 120, 745–755. 25 ACS Paragon Plus Environment


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

(43) Watkins, P. K.; Walker, A. B.; Verschoor, G. L. B. Dynamical Monte Carlo Modelling of Organic Solar Cells: The Dependence of Internal Quantum Efficiency on Morphology. Nano Lett. 2005, 5, 1814–1818. (44) van Bavel, S. S.; Sourty, E.; de With, G.; Loos, J. Three-Dimensional Nanoscale Organization of Bulk Heterojunction Polymer Solar Cells. Nano Lett. 2009, 9, 507–513. (45) van Bavel, S. S.; de With, M. B. G.; Hoppe, H.; Loos, J. P3HT/PCBM Bulk Heterojunction Solar Cells: Impact of Blend Composition and 3D Morphology on Device Performance. Adv. Func. Mater. 2010, 20, 1458–1463. (46) Lyons, B. P.; Clarke, N.; Groves, C. The Relative Importance of Domain Size, Domain Purity and Domain Interfaces to the Performance of Bulk-Heterojunction Organic Photovoltaics. Energy Environ. Sci. 2012, 5, 7657–7663. (47) Mozer, A. J.; Sariciftci, N. S.; Pivrikas, A.; Österbacka, R.; Ju˘ska, G.; Brassat, L.; Bässler, H. Charge Carrier Mobility in Regioregular poly(3-hexylthiophene) Probed by Transient Conductivity Techniques: A Comparative Study. Phys. Rev. B 2005, 71, 035214. (48) Deibel, C.; Mack, D.; Gorenflot, J.; Schöll, A.; Krause, S.; Reinert, F.; Rauh, D.; Dyakonov, V. Energetics of Excited States in the Conjugated Polymer poly(3hexylthiophene). Phys. Rev. B 2010, 81, 085202. (49) Scott, G. D.; Kilgour, D. M. The Density of Random Close Packing of Spheres. J. Phys. D: Appl. Phys. 1969, 2, 863. (50) Howard, I. A.; Hodgkiss, J. M.; Zhang, X.; Kirov, K. R.; Bronstein, H. A.; Williams, C. K.; Friend, R. H.; Westenhoff, S.; Greenham, N. C. Charge Recombination and Exciton Annihilation Reactions in Conjugated Polymer Blends. J. Am. Chem. Soc. 2010, 132, 328–335.


Page 26 of 28

Page 27 of 28

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


(51) Kroeze, J. E.; Savenije, T. J.; Vermeulen, M. J. W.; Warman, J. M. Contactless Determination of the Photoconductivity Action Spectrum, Exciton Diffusion Length, and Charge Separation Efficiency in Polythiophene-Sensitized TiO2 Bilayers. J. Phys. Chem. B 2003, 107, 7696–7705. (52) Lüer, L.; Egelhaaf, H.-J.; Oelkrug, D.; Cerullo, G.; Lanzani, G.; Huisman, B.-H.; de Leeuw, D. Oxygen-Induced Quenching of Photoexcited States in Polythiophene Films. Org. Electron. 2004, 5, 83–89. (53) Goh, C.; Scully, S. R.; McGehee, M. D. Effects of Molecular Interface Modification in Hybrid Organic-Inorganic Photovoltaic Cells. J. Appl. Phys. 2007, 101, 114503. (54) Shaw, P. E.; Ruseckas, A.; Samuel, I. D. W. Exciton Diffusion Measurements in Poly(3hexylthiopene). Adv. Mater. 2008, 20, 3516–3520. (55) Cook, S.; Liyuan, H.; Furube, A.; Katoh, R. Singlet Annihilation in Films of Regioregular Poly(3-hexylthiophene): Estimates for Singlet Diffusion Lengths and the Correlation between Singlet Annihilation Rates and Spectral Relaxation. J. Phys. Chem. C 2010, 114, 10962–10968. (56) Pfannmöller, M.; Flügge, H.; Benner, G.; Wacker, I.; Sommer, C.; Hanselmann, M.; Schmale, S.; Schmidt, H.; Hamprecht, F. A.; Rabe, T.; Kowalsky, W.; Schröder, R. R. Visualising a Homogeneous Blend in Bulk Heterojunction Polymer Solar Cells by Analytical Electron Microscopy. Nano Lett. 2011, 11, 3099–3107. (57) Heiber, M. C. Exciton Annihilation Simulator. 2013; https://nanohub.org/ resources/annihilate. (58) Heiber, M. C. Exciton Dynamics Simulator. 2013; https://nanohub.org/ resources/exdynamics.



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

Graphical TOC Entry


Page 28 of 28

Estimating the Magnitude of Exciton Delocalization in ... - UAkron Blog

Recommend Documents