MM Study of Static and Dynamic Energetic Disorder in the

Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 1329−1334

pubs.acs.org/JPCL

QM/MM Study of Static and Dynamic Energetic Disorder in the Emission Layer of an Organic Light-Emitting Diode Piotr de Silva† and Troy Van Voorhis* Department of Chemistry, 77 Massachusetts Avenue, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States

J. Phys. Chem. Lett. 2018.9:1329-1334. Downloaded from pubs.acs.org by EASTERN KENTUCKY UNIV on 01/24/19. For personal use only.

S Supporting Information *

ABSTRACT: Static and dynamic energetic disorder in emission layers of organic lightemitting diodes (OLEDs) is investigated through combined molecular dynamics and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. The analysis is based on a comparison of ensemble and time distributions of site energies of guest and host components in an emission layer. The law of total variance is applied to decompose the total disorder into its static and dynamic contributions. It is found that both contributions are of the same order of magnitude. While the dynamic disorder is not affected by intermolecular interactions, the static disorder for both guests and hosts is determined by the polarity of host molecules. The amount of static disorder affects charge-transport properties and exciton formation pathways, which consequently influence the overall efficiency of an OLED device. The simulations indicate that the amount of static disorder induced by the host should be considered for the optimization of the emission layer.

O

diagonal disorder, while the latter gives rise to the dynamic diagonal disorder. Widely used disorder models like the Gaussian Disorder Model (GDM)13 as well as its extensions and modifications14−16 do not make an explicit distinction between these two sources of variability. While there exist studies that analyze the role of the two types of disorder,17−20 many charge-transport simulations use parametrizations that assume all of the disorder to be static.21−24 Because static and dynamic disorder have, in general, different effects on chargehopping and trapping processes, this lack of distinction appears as a possible source of errors. The problem of separating and quantifying static and dynamic contributions to the energetic disorder of organic semiconductors has been undertaken only very recently.25,26 Because the emission layer of an OLED is an amorphous host−guest system, there is an additional source of static disorder compared with single-component solids. Guests are impurities that may affect the distribution of energy levels in their vicinity. The relative level alignment of guests and hosts as well as the degree and character of disorder determine the efficiency of charge transport and viable paths for final localization of excitons on emitter molecules. In this work, we employ molecular dynamics (MD) and hybrid quantummechanics/molecular-mechanics (QM/MM) to study the site energy distributions for both hole and electron transport in emission layers of OLEDs. As a guest molecule we choose PICTRZ2,27 which is an all-organic emitter exhibiting thermally activated delayed fluorescence (TADF). It is a particularly interesting molecule as the gap between the first singlet and

rganic light-emitting diodes (OLEDs) are composed of several layers of organic materials that are sandwiched between the electrodes and deposited on a glass substrate.1,2 These organic layers are typically vapor-deposited amorphous films of relatively small organic molecules. The crucial part of an OLED is the emission layer, which is a host−guest material composed of organic emitter molecules dispersed in an organic matrix.3,4 Low doping (∼5−10%) prevents undesired bimolecular processes, like triplet−triplet annihilation,5 which are detrimental for the device’s efficiency.6 While the final lightemitting exciton is localized on a guest molecule, the host matrix plays an important role in charge and exciton migration as well as in tuning of emitter’s properties.7 There are two principal pathways to localize an exciton on the emitter. Hole and electron can recombine directly on a guest8,9 and form an intramolecular charge-transfer state, which then relaxes to the ground state by emitting a photon. Alternatively, charges recombine on a host with subsequent energy transfer to the emitter.10,11 In either scenario, charges in the emission layer are transported through sequential hops between molecules until they recombine or get trapped on either a guest or a host molecule. In the weak coupling regime, charge-hopping rates are mostly affected by the alignment of electronic transport levels of individual sites (site energies).12 In any given instant of time, there is a distribution of instantaneous site energies, which is a manifestation of the energetic (diagonal) disorder. In a material that is not a perfect crystal, the lack of translational symmetry results in sites that experience permanently different local steric or electrostatic environments, which is the first source of variability in site energies across the materials. The second source is the intra- and intermolecular vibrations, which modulate energies of individual sites with some characteristic frequencies. The first phenomenon is the source of the static © 2018 American Chemical Society

Received: January 5, 2018 Accepted: March 1, 2018 Published: March 1, 2018 1329

DOI: 10.1021/acs.jpclett.8b00040 J. Phys. Chem. Lett. 2018, 9, 1329−1334

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The Journal of Physical Chemistry Letters

Figure 1. Distributions of IPs (solid lines) and EAs (dashed lines) of host (blue) and guest (red) components in (a) PIC-TRZ2 in mCP and (b) PIC-TRZ2 in UGH2. Solid black line is a Gaussian fit to the data.

Figure 2. Time distributions of IPs, EAs, and TGs for 20 host and guest molecules in (top) PIC-TRZ2@mCP and (bottom) PIC-TRZ2@UGH2.

triplet excited states is nearly vanishing, which is a desired feature for an efficient up-conversion in the TADF process. For the host matrix we consider two different materials, mCP28 and UGH2,29 which have been used in conjunction with PICTRZ2. This particular selection is motivated by the differences in their permanent dipole moments and polarizabilities, which we expect to affect the densities of states of both hosts and guests. As a first step, we carried out MD simulations to sample realistic trajectories of thin films of PIC-TRZ2 dispersed in

mCP and UGH2. After initial heating, annealing, and equilibration phases, snapshots were sampled every 20 ps from a 2 ns trajectory. Subsequently, QM/MM calculations of site energies were carried out for all 20 emitter molecules present in the simulation box and 20 randomly selected host molecules. To account for polarization of the environment upon electron addition or removal, our QM/MM scheme used a polarizable force field based on the Drude oscillator model.30 The number of considered molecules (20 guests and hosts) was limited by the computational cost because the polarization of all 1330

DOI: 10.1021/acs.jpclett.8b00040 J. Phys. Chem. Lett. 2018, 9, 1329−1334

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The Journal of Physical Chemistry Letters

Table 1. Total, Static, and Dynamic Disorder for Hole and Electron Levels in PICTRZ2@mCP and PIC-TRZ2@UGH2 (Standard Deviations in eV) IP PIC-TRZ2@mCP PIC-TRZ2@UGH2

guest host guest host

EA

σT

σd

σs

σT

σd

σs

0.163 0.157 0.100 0.102

0.070 0.070 0.070 0.079

0.147 0.140 0.072 0.064

0.160 0.154 0.103 0.096

0.075 0.069 0.079 0.081

0.142 0.138 0.066 0.051

shown in Figure 2. It is apparent that there is significant static disorder in PIC-TRZ2@mCP material as DOS of sites of both components are centered around different mean values, leading to a significant variance of mean site energies. This variance is much smaller for TGs, which means that interactions giving rise to static disorder shift hole and electron levels in the same direction. Comparison of time distributions for PIC-TRZ2@ mCP and PIC-TRZ2@UGH2 reveals that there is significantly less static disorder in the second material. Interestingly, this applies to not only the host but also guest time distributions, which are much closer to each other when UGH2 is used as a host matrix. Because UGH2 has no permanent dipole moment, its random geometric orientation has less effect on the variance of energy levels of neighboring sites. On the contrary, despite being less polar, UGH2 has significantly larger polarizability that results in larger stabilization of charged states and reduction of the PIC-TRZ2 transport gap in solid state. Contrary to the time distribution of a single site, which reflects only dynamic disorder, the ensemble distribution arising from sampling multiple site energies at a particular moment of time reflects both static and dynamic disorder. To separate the two sources of disorder, we partition the variance of the total distribution into its dynamic and static components

of the molecules in the simulation box was accounted for explicitly. To quantify the energetic disorder in the OLED emission layers we focus on distributions of site energies, where the variability results from sampling 20 different host and guest sites and their time evolution over 100 snapshots. This gives rise to empirical distributions, which are plotted in Figure 1 using the kernel density estimator. The distributions of site energies appear to be well represented by Gaussians, where possible discrepancies are likely to result from the relatively small sample of 20 sites limiting the applicability of the central limit theorem. In the case of PIC-TRZ2@mCP, the probability densities of electron affinities (EAs) for both components are well separated, while ionization potentials (IPs) overlap significantly. This means that electrons are efficiently trapped on guest molecules, whereas holes are free to hop between guests and hosts. In UGH2, which is a wide bandgap host, the distributions of PICTRZ2 levels are completely nonoverlapping, which leads to effective trapping of both charge carriers. The choice of the host significantly affects mean values of PIC-TRZ2 site energies, where replacing mCP with UGH2 results in 0.4 eV lower IP and 0.2 eV higher EA (see Table S1 in the SI). Intrestingly, the choice of the host matrix also determines the degree of disorder in site energies for both guest and host components. Using mCP as a host results in standard deviation of electron levels in the range 0.15 to 0.16 eV, while standard deviations when UGH2 is used are only 0.10 eV. These results show that the choice of the host affects transport properties of OLED emission layers not only through different average host levels but also through shifting guest levels and influencing the energetic disorder in the entire system. By accounting for different physical effects it can be shown that the position of the distributions is determined by polarizability of the environment, while their shapes are determined by the local electrostatic environment (see the SI). The observation that the host changes the disorder in the energy levels is central to this paper as it motivates the rest of the investigation. The first question to ask is how the choice of the host influences the disorder in the emission layer in relation to its charge-transport properties. The distributions in Figure 1 result from a convolution of both static and dynamic disorder. When an individual site is followed over the length of the simulation, site energies oscillate due to coupling to molecular vibrations. These variations contribute to the dynamic energetic disorder in the material that can be characterized by variances of time distributions of individual molecules. If only the dynamic disorder was present in the system, then the distributions of individual sites would be just overlapping gaussians. On the contrary, if the gaussians do not overlap completely, then the sites are not energetically equivalent and some degree of static disorder is also present. Such time distributions of IPs, EAs, and transport gaps (TGs) of individual guest and host sites are

σT2 = σd2 + σs2

(1)

To be able to this formally, we set up a probabilistic model for DOS distributions and make use of the law of total variance (see the SI). This allows us to decompose the total variance the following way σT2 =

⎞ 1 2 ⎛⎜ 1 2 σi + μi − μT2 ⎟ ⎝ ⎠ N N

(2)

σ2i

where μi and are the mean and the variance of the ith site energy and μT is the mean of the total distribution. The first term on the right-hand side of eq 2 is dynamic and the second is the static component of the total disorder. Table 1 contains standard deviations of IPs and EAs corresponding to total, dynamic and static disorder of guest and host components in PIC-TRZ2@mCP and PIC-TRZ2@ UGH2 emission layers. It becomes apparent that larger disorder present in the PIC-TRZ2@mCP film is caused by the increase in the static component. The dynamic disorder of PIC-TRZ2 in both hosts does not differ noticeably, but there is an approximately two-fold increase in the static part when UGH2 is compared with mCP. For host energy levels, UGH2 has a slightly larger contribution to the dynamic disorder compared to mCP but over two times smaller static disorder. This comparison indicates that static disorder is controlled by polarity of the molecules in the material, while dynamic disorder remains largely unaffected by the environment. There are no significant differences in disorder between hole and electron energy levels. Another important conclusion for 1331

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Figure 3. Scatter plots of energy levels versus interaction energies. Each color represents a different site, and different points of the same color correspond to different snapshots.

where on/off means whether partial charges on guest molecules were set to 0 in the MM part of the Hamiltonian (of f) or kept at the parametrized force-field values (on). The premise for such choice is that hosts that are closer to a guest will interact stronger, while the sign of the reaction coordinate indicates if the interaction is stabilizing or destabilizing. In a recent work,32 it has been shown that there is a weak trend if energy levels in the emission layer of a phosphorescent OLED are plotted against such defined reaction coordinate. Figure 3 shows a scatter plot of IP/EA versus ΔIP/ΔEA for 20 host molecules traced over 100 snapshots. There is no global correlation between these values, which suggests that there is no particular level alignment of hosts with respect to the distance to a guest molecule. This is somewhat expected because inherent static disorder due to the host material electrostatics is the dominant source of variability in the energy levels. However, no trend is apparent even for individual molecules, which means that even dynamic disorder is stronger than any possible level alignment effect. The static disorder is reflected in the structure of the scatter plots, where data points corresponding to different sites form well-separated clusters for mCP. For UGH2 the dynamic disorder is even slightly larger than static, so no such clustering takes place and data points corresponding to different sites are distributed more uniformly. The energetic disorder and, in particular, the distinction between its static and dynamic components have been largely ignored in the design and modeling of OLEDs. Our simulations show that dynamic disorder is non-negligible and should be accounted for whenever the static disorder is accounted for. Extending existing disorder models to account for both

development of disorder models and charge-transport simulations is that both types of disorder have comparable magnitudes for disordered organic materials. This finding is in line with results obtained by Tummala et al.,25 who simulated both types of disorder for fullerene-based electronaccepting materials. A similar analysis can be carried out for disorder of transport gaps, which is related to the covariance between IPs and EAs. The main conclusion is that electron and hole levels are more correlated in polar hosts through increase in the static covariance, while dynamic covariance is small and mostly unaffected by the environment (see the SI for details). In an OLED emission layer, guest molecules can be treated as impurities because of their low concentration. It is interesting to check if such impurity affects the levels of neighboring host molecules in any systematic way. Considering that one of the viable pathways for localization of an exciton on the emitter begins with charge trapping, any systematic effect on host levels could lead to a level alignment that either facilitates or hinders charge migration to the guest. This is by analogy to band bending at interfaces, which can, for instance, facilitate exciton breakup in organic solar cells.31 In disordered molecular materials, the geometrical distance is not a good measure of molecules proximity because molecular sizes are on the same order. Instead, for a charge-transfer reaction coordinate we use energies of electron or hole electrostatic interaction with guest molecules ΔIP = IP(on) − IP(off ) ΔEA = EA(on) − EA(off )

(3) 1332

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QM calculations were done at the density functional theory (DFT) level (PBE0/6-31+G*), while an OPLS force field augmented with the Drude oscillator model was used to describe the environment at the polarizable MM level. Drude parameters were distributed on selected heavy atoms and fitted to reproduce molecular polarizabilities calculated at the DFT level. In each case, QM region comprised one guest or host molecule that was centered in the middle of the simulation box, while all of the remaining molecules were described by the MM Hamiltonian. HOMO and LUMO levels (IPs/EAs) were calculated as differences of total energies for neutral and charge species.

contributions seems to be a natural strategy, especially that the dynamic component appears to be relatively constant, so it may be possible to include it in some form of a correction. Because the energetic disorder in the emission layer has an effect on electron and hole mobilities, it will also influence the efficiency of charge recombination. Therefore, it is also expected that disorder contributes to the overall electroluminescence efficiency of an OLED device. In particular, large static disorder negatively affects charge transport and can lead to charge trapping and subsequent degradation of molecules. Furthermore, the polarity and polarizability of the host is expected to have a similar influence on the optical levels in the emission layer, which can be probed experimentally through singlemolecule spectroscopy.33 Their disorder affects energy transport as well as the efficiency of radiative relaxation of excitons. This work provides a conceptual and computational framework for further studies of the dynamic and static disorder of the excited states and its role in electroluminescence efficiency. We have analyzed the distribution of electron and hole site energies in two OLED emission layers composed of an TADF emitter PIC-TRZ2 dispersed in mCP and UGH2 matrices. Using the law of the total variance we partitioned the total disorder into the static and dynamic component. The analysis revealed that the choice of host matrix significantly affects both the average value of site energies as well as the amount of static disorder not only for the hosts but also for the guests. The static and dynamic disorder are of the same magnitude, where in a polar host mCP the former is twice as large as the latter, while for nonpolar UGH2 they are comparable. We conclude that polarity is the dominant factor for static disorder, while dynamic disorder does not depend significantly on intermolecular interactions. The difference in mean values of guests’ site energies is determined by polarizability of the host rather than its polarity, as reorientation of permanent dipoles is suppressed in the solid state as opposed to solutions, where solvent molecules are free to rotate and align with electric fields. Finally, we have not observed any level alignment of host and guest levels in the investigated materials, as the effect of an external field of the guest is completely suppressed by both static and dynamic disorder. The specific selection of the host and guest molecules, together with the choice of the 6% doping level, make this work a case study inspired by a particular experimental setup;34 however, the conclusions are not specific to the particular choice of the emission layer components but are expected to be valid for a broad class of host−guest materials where electrostatic interactions determine the energetic landscape for charge transport.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b00040. Parameters of total distributions for energy levels and transport gaps, analysis of effects affecting energy level distributions, probabilistic model for the density of states, analysis of covariance between ionization potentials and electron affinities. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Piotr de Silva: 0000-0002-4985-7350 Present Address †

P.d.S.: Department of Energy Conversion and Storage, Technical University of Denmark, Fysikvej, Bldg. 309, 2800 Kgs Lyngby, Denmark.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by a grant from the US Department of Energy, Basic Energy Sciences (BES ER46474).

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REFERENCES

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COMPUTATIONAL METHODS MD Simulations. The simulation box consisted of 20 guest molecules and 432 or 297 host molecules for mCP and UGH2, respectively. The initial configuration was assembled using PACKMOL35 program and was followed by molecular mechanics calculations with OLPS 36 force field using GROMACS37 package. The MD calculations consisted of four steps (i) energy minimization of initial configuration, (ii) heating the system to 500 K during 2 ns and equilibrating for another 2 ns, (iii) cooling to 300 K during 1 ns, and (iv) running the simulation for another 4 ns in the NPT ensemble. The last 2 ns of the simulations were subsequently used for sampling of snapshots for QM/MM calculations. QM/MM Calculations. A QChem38 and CHARMM39 interface40 was used to perform QM/MM calculations. The 1333

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