Simulations of Molecular Ordering and Charge-Transport of Oligo

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Simulations of Molecular Ordering and ChargeTransport of Oligo-Didodecylquaterthiophenes (DDQT) Ilhan Yavuz, Lei Zhang, Alejandro L. Briseno, and K. N. Houk J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp510567d • Publication Date (Web): 15 Dec 2014 Downloaded from http://pubs.acs.org on December 22, 2014

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The Journal of Physical Chemistry

Simulations of Molecular Ordering and Charge-Transport of Oligo-Didodecylquaterthiophenes (DDQT) Ilhan Yavuz1*, Lei Zhang2, Alejandro L. Briseno2 and K. N. Houk1† 1

Department of Chemistry and Biochemistry, University of California, Los Angeles, 90095 CA, United

States 2

Department of Polymer Science and Engineering, Conte Polymer Research Center, University of

Massachusetts, Amherst, 01003 MA, United States.

ABSTRACT

Semiconductor poly(3,3’’-didodecyl-quaterthiophene) (PQT-12) polymer, for which the hole mobility exceeds 0.1 cm2/Vs, exhibits promising charge-transport characteristics as an organic thin-film transistor. A family of its oligomeric analogs, DDQT-n (3,3’’didedocylquaterthiophene-n) has been synthesized (with n=1−6) and extensively characterized [Zhang et al., J. Am. Chem. Soc. 2013, 135, 844-854]. Through atomistic molecular

dynamics

and

charge-transport

simulations,

we

have

studied

the

morphologies and electronic properties of crystalline di-dodecylquaterthiophenes (DDQT-1, DDQT-2 and DDQT-3). The morphologies are characterized by molecular ordering and paracrystallinity, while charge-transport is characterized by electroniccoupling, reorganization energy, energetic disorder and hole mobility, calculated with VOTCA. We observed increasing transport efficiency with increasing molecule size, as the morphologies evolve from oligomeric to polymeric packing arrangements. The trend is related to decreasing hole reorganization energy, energetic disorder and increasing efficacy of transport topology. We also elucidate a direct link between molecular ordering and charge-carrier mobility of different DDQT-n oligomers.

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I.

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INTRODUCTION

Conducting conjugated-polymers based on thiophene chains are an important class of materials for high performance, air stable organic electronic devices such as transistors and photovoltaics. Charge-carrier mobilities exceeding 0.1 cm2/Vs have been reported.13

Despite

recent

advances

in

oligo/polymeric

thiophene

semiconductors,

structure/charge mobility relationships are still mysterious due to their complicated polymorphologies.

Poly(3,3”-didodecyl-quaterthiophene) (PQT-12), is a promising polymer semi-conductor as an alternative to one of the highly studied poly(3-hexylthiophene) (P3HT) and poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]-thiophene) (PBTTT) conducting polymers. Upon controlled ordering of lamellar π−stacking, OTFT mobility of PQT-12 up to 0.2 cm2/Vs has been achieved4. Lower molecular weight (i.e., oligomeric) PQT-12s have also exhibited high charge-carrier mobility.5,6 Briseno and coworkers performed a systematic experimental study of the charge-transport characteristics of low-molecular weight DDQT oligomers up to DDQT-6 (up to 24 thiophene units) and observed that the thin film morphology of DDQT-n evolves from oligomeric to polymer-type packing arrangement.6,7 There is decreasing crystallinity (hence decreasing mobility) with increasing chain length. It was concluded that, the chain-length scaling of chargetransport depends not on increasing molecular-weight but on the degree of crystallinity. On the other hand, the mobility converges around 10−4 cm2/Vs which is roughly three orders of magnitude lower than that found for PQT-127. This is attributed to random orientations of lamellar packing with respect to the substrate plane, hindering charge transportation.


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Figure 1. Molecular structures of oligo-(3,3’’-di-dodecylquaterthiophene) (DDQT-n) studied here.

The crystal structures of DDQT-1, DDQT-2 and DDQT-3 with 4, 8 and 12 thiophene units have been refined.7-9 According to XRD measurements, DDQT-1 and DDQT-3 exhibit lamellar-type π-stacking. DDQT-1 forms slipped π − π overlap and DDQT-3 forms brick-like π−stacking. On other hand, DDQT-2 forms herringbone type lamellar packing. The strong π − π overlap is clearly beneficial to charge-transport, but the degree of charge percolation must be quantified in order to identify the transport efficiency. Strong π−stacking with one-dimensional overlap is less beneficial than weak stacking with multidimensional overlap. This is because the former is prone to chargetrapping.10 DDQT-3 DDQT-1

DDQT-2 b c b

c a

c

Figure 2. Crystal structure, unit cell and side-chain interdigitation of (a) DDQT-1, (b) DDQT-2 and (c) DDQT-3.

No hole mobility is observed for DDQT-1, but DDQT-2 and DDQT-3 exhibit thin-film mobilities of 0.001-0.0043 cm2/Vs and 0.0017-0.0026 cm2/Vs, respectively.7 The 3 ACS Paragon Plus Environment


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observed thin-film mobilities are related to the size and the orientations of the crystallites with respect to substrate, which is crucial in charge-transport. The single-crystal DDQT3 shows a mobility 0.01-0.04 cm2/Vs, which is roughly an order of magnitude higher than that of thin-film DDQT-3, owing to the high level of crystallinity and absence of defects.67

Even so, the mobility observed for single-crystal DDQT-3 is an order of magnitude

lower than that of highly-crystalline thin-film of PQT-12.1

Due to the weak inter/intra molecular interactions of molecules in solids, the materials can easily undergo morphologic changes and can form polymorphs.11 The role of conformational polymorphism is discussed in detail in ref. [6].

For backbone

polymorphism in thiophene-based systems, all-trans confirmation is typically observed for side-chain unsubstituted molecules and these oligomers always show herringbone packing motifs. The polymorphs give rise to herringbone packing with a different number of molecules in the unit cell (two and four) and a small different tilt angle of the molecular long axis. But, the backbone conformational changes can be significantly influenced by side-chain substitutions, side-chain position, and crystallization conditions (solvent polarity, solvent pressure, etc.). The energy barrier between the polymorphs is very small. Therefore, it is difficult to predict the polymorphs in the oligothiophenes with substitutents. In principle, for long side-chain oligothiophenes, lamellar packing is likely, due to the interdigitation between the long side-chains. Therefore, the solvents, which greatly affect the conformation of the side chains in the solution, play important role on the polymorphs. For example, in polarized solvents, the side-chain is bent, it is likely to form herringbone packing; in non-polarized solvent, the side-chain is straight and the crystal packing likely form lamellar. However, it should be noted that the density and position of the alkyl chains, the length of the backbone should be considered as well.

As presented in Fig. 2, we observed all-trans conformation for DDQT-1 molecules in solid.7 However for DDQT-2 and DDQT-3, terminal thiophenes exhibits synconformation and the remaining rings are in trans-conformation. Also, the side-chains of DDQT-2 exhibits a gauche-conformation of terminal alkyl chains.7


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These results prompted us to investigate the interplay between morphology, molecular packing and charge-transport properties of DDQT-n, and to elucidate the factors responsible for charge-carrier mobility from a small (DDQT-1) to a larger one (DDQT-3).

II.

MODELING MORPHOLOGIES

In order to study molecular ordering and morphologies of DDQT-n, we employ atomistic molecular dynamics (MD) simulations. The initial configurations of crystals have been constructed from successive duplicates of the unit cells along three crystallographic axes. A supercell containing 15x11x9=1485 molecules for DDQT-1, 6x14x17=1428 molecules for DDQT-2 and 12x14x8=1344 molecules for DDQT-3 have been used. All MD simulations were performed using GPU version of Amber12.12 Molecular mechanics parameters were prepared using GAFF force-field following a recommended procedure described elsewhere.13,14 However, the force-field parameters of the dihedral angles between thiophene-thiophene units were reparameterized using the values given in ref. [15]. Partial charges of ground-states were generated via Merz-Singh-Kollman scheme16,17, using HF/6-31G(d) method based on B3LYP/6-31G(d,p) optimized geometries, as implemented in Gaussian0918. Periodic boundary conditions (PBC) were employed. The packing geometry was energy minimized in 1000 MD steps restraining all heavy atom coordinates to their initial values. Each system was heated and equilibrated at 300 K for 0.5 ns, while regulating heat bath temperature at 300 K using Langevin thermostat19 with a weak collision parameter (5.0 ps−1). Additional 1 ns relaxation was carried out with Langevin barostat19 turned on to relax the system at 1 atm. The final production runs lasted for 2 ns while maintaining heat bath temperature at 300 K and time averaged pressure at 1 atm.

Fig. 3 shows the MD snapshots of the DDQT-1 to DDQT-3 after 2 ns of equilibration. DDQT-1 forms a lamellar-type packing. Also, the two adjacent in-plane backbone units are in close contact through outermost thiophene units. In other words, only two thiophenes in neighboring backbones are in contact. In the third lamellar direction, the adjacent backbones are isolated due to pronounced side-chain interdigitation. The sidechains of DDQT-1 morphology are mobile, but largely maintain their initial regular 5 ACS Paragon Plus Environment


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configurations. DDQT-2 forms a herringbone-type lamellar packing motif. Through π − π overlap, 8 units of the backbone is in direct contact with those of adjacent monomer, similar to DDQT-1. However, along the tilted-packing direction only half of the thiophene units of the backbones are in contact. Similar to DDQT-1, backbones along the third lamellar direction are isolated with side-chains. For DDQT-2, the side-chains are again interdigitated, but, this time, apparently to prevent steric interactions, there is a gauche conformation at the end of each terminal side-chain. This is observed in the XRD structures7. A brick-like packing arrangement along π−stacking results in rather complicated backbone ordering for DDQT-3.9 Through π-stacking, the dimers form cofacial packing slipped along longitudinal direction of the backbone. We also observed that the side-chains of DDQT-3 are mobile as for DDQT-1.


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DDQT-1

DDQT-2

DDQT-3 Figure 3. Representative MD snapshots of morphologies equilibrated at 300K.



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In order to quantify the degree of backbone ordering along a given crystallographic axis, we calculate the paracrystalline order parameter, g. 20,21 If dhkl is the spacing between two conjugated units of the neighboring backbones, projected onto [hkl] direction and ∆ is the variance of dhkl, then g parameter is given as

g hkl =

∆ < d hkl >

(1)

where stands for ensemble average. Here, we should keep in mind that the order parameter comprises the contribution from the torsional modes of the monomer units, gi , and the breathing modes of the entire backbone, g b . We simplify (1) to:

g hkl = gi + gb .

(2)

We calculated the π-stacking paracrystallinity g of the equilibrated morphologies and found that it is 4.5, 4.3 and 4.2% for DDQT-1, DDQT-2 and DDQT-3, respectively. According to a set of XRD measurements, the room temperature g parameter of lowmolecular weight PQT-12 is found to be 6-8%.22 Therefore, our simulated results are roughly 40-90% lower than the experimental measurements of PQT-12 polymer. The differences indicate the differences between the simulated structural regularity and those present in thin-films of DDQT-n. When we also take into account the spacing between the intermolecular centroid distances, the paracrystal order parameters (i.e., gb) are 2.3, 1.7 and 0.6%, respectively. The results for gb suggest that there is an increasing trend in backbone order along the π−stacking direction with increasing molecular size. However, the gb and g − gb = gi parameters for DDQT-1 indicate that the torsional modes of the thiophene units and the breathing modes of the entire backbone contribute almost equally to the disorder (i.e., 2.3 and 2.2%, respectively), for DDQT-2 the torsional modes of the thiophene units slightly dominate and for DDQT-3 they are the main contributor to the g parameter. This distinct behavior of DDQT-3 could be related to the average distance between thiophene units along the π-stacking direction. For DDQT-1 and DDQT-2, the average distances are 0.47 nm for both, but for DDQT-3 the average 8 ACS Paragon Plus Environment

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distance is 0.40 nm. This indicates that DDQT-3 molecules resemble relatively dense packing and the stretching of backbone is largely restrained by intermolecular nonbonded interactions.

III.

CHARGE-TRANSPORT SIMULATIONS III.

1. Transport mechanism

Here we employ the charge-transport simulations procedure implemented in VOTCA package developed by Andrienko and coworkers.23,24

Based on the assumption that charges are localized on a single molecule and chargetransfer reactions take place via an intersite hopping mechanism, the charge-hopping rate is evaluated as the non-adiabatic, high-temperature limit of the Marcus rate25,26

2π 2 kij = J ij h

 ( ∆E − λ ) 2  ij  exp  −   4 k T λ 4πλ k BT B   1

(3)

where T is the temperature, J ij = φi Hˆ φ j is the electronic coupling element (or transfer integral) between initial φi

and final φ j

states. λ is the reorganization energy and

∆Eij = ε i − ε j is called the site energy difference between initial i and final j states. Recently, there has been an ongoing debate on the applicability of the Marcus hopping model for organic crystals.27,28 One particular reason is that in some promising organic crystals, the electronic coupling and the reorganization energy are comparable. In such case one can question the validity of localizing the charge-carrier in a single molecule, and hopping transport. However, there is a consensus that hopping is the dominating transport mode around room temperature for these types of molecules.29 The reorganization energy λ is the sum of two terms: the inner (λin) and outer sphere (λout) reorganization energy. Since the geometries of the neighboring molecules do not 9 ACS Paragon Plus Environment


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change much, in the solid, during a charge-transfer reaction, λout is often neglected.30 So, one can write λ≅λin. We therefore calculated the reorganization energy λ from adiabatic potential energy surfaces of neutral and cationic states of compounds, using the following expression:

λ = ( Eqn − Eqn ) + ( Eqc − Eqc c

n

n

c

)

(4)

where Eqnn ( Eqcn ) is the energy of the neutral n (charged c) state of the molecule in its optimized neutral geometry and Eqnc ( Eqcc ) is the energy of the neutral n (charged c) state of the molecule in its optimized charged geometry. We perform Density Functional Theory (DFT) calculations, implemented in Gaussian0918, to calculate λ for an isolated molecule. We employ the B3LYP hybrid density functional31 with the 6-31G(d) basis set. TABLE I: Reorganization energy λ calculated with B3LYP/6-31G(d). The energies are in units of meV.

λ

DDQT-1

DDQT-2

DDQT-3

635

359

256

The DFT calculated λ of compounds DDQT-1, DDQT-2 and DDQT-3 are given in Table I. DDQT-1 has a considerably high λ value of 635 meV. However, λ decreases with increasing molecular size owing to the extended conjugation length. Even with this straightforward analysis, we can state that DDQT-1 may not be a feasible material for efficient charge-transport, since a monomer by itself will involve large self-trapping due to the huge reorganization energy, λ.

In order to evaluate the electronic-coupling and site energies that enter Marcus rates, the knowledge of the materials morphology, the hopping sites and ”neighbor list” are necessary. A pair of molecules of which the intermolecular centroid distances are within a certain interval are classified as interacting neighbors and added to a neighbor list to calculate the intersite hopping rates. In this study we use a fixed cut-off of 0.8 nm, 0.5


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and 0.4 nm for DDQT-1, DDQT-2 and DDQT-3, respectively. The charge-transport simulations were performed using VOTCA package.23,24

From the neighbor list, the electronic coupling Jij for each molecular dimer with diabatic states of φi and φ j are calculated using semi-empirical ZINDO method.32,33 Here, the Frozen Orbital Approximation is used. Namely, it is assumed that the occupation of orbitals of molecule i and j only differ by the occupation of the HOMO.

Site-energies include the contributions from Coulombic and polarization interactions due to the interactions of oligomers in the crystals and the contributions from external electric field. External electric field contributions are calculated using the expression r r r r ∆Eext = −eF .d ij . Here F is the field-vector and d ij is the position-vector between molecules i and j. Coulombic and polarization contributions to site energies are calculated self-consistently using Thole Model.24,34-37 Partial charges of neutral and charged states are generated via Merz-Singh-Kollman scheme16,17, using HF/6-31G(d) method based on B3LYP/6-31G(d,p) optimized geometries, as implemented in Gaussian0918. Isotropic atomic polarizabilities of the neutral and charged states are reparameterized for each species as to reproduce the molecular polarizabilities obtained from B3LYP/6-31G(d,p) method18. By fitting the histogram of site-energy differences to a Gaussian-distribution function,

f (ε , σ ) =

 ε2  exp  − 2  , 2π σ  2σ  1

(5)

the standard deviation and hence the energetic disorder σ is evaluated.

For charge-carrier dynamics simulations, we employ rate-based Kinetic-Monte Carlo methods for a single-charge carrier in an applied external electric field, as implemented in VOTCA23, 24. Hole mobilities are evaluated using velocity-averaging38. We performed a series of charge-transport simulations, for DDQT-n system, in different field directions and report the maximum mobility, since the mobilities in solids are often anisotropic. The reported mobilities are the averages over 100 stochastic realizations.



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III. 2. Charge-transport in ideal crystals of DDQT-n Figure 4. shows the unique transport pathways of the crystals of DDQT-n, and Table II presents the corresponding transfer-integral elements and intermolecular centroid distances of the entire backbones (d) and the thiophene units (dc). For DDQT-1, there are four unique transport pathways. Among them, P is along the slightly slipped πstacking direction. The strong π−π overlap results in high transfer integral of 26 meV comparing with other transport paths. DDQT-2 has two unique molecular stacking, one being tilted (or T-shaped) packing and the other one being the slipped π-stacking. The calculated transfer-integrals of DDQT-2 show that the electronic couplings are comparable along either of the two transport pathways, but are weaker than JP of DDQT-1. DDQT-3 forms brick-like packing arrangement with two unique π−π overlaps. P1 is a slightly slipped cofacial packing, and for P2 only the side-edges of adjacent backbones are overlapping. As a result, P1 is 40 times stronger than P2.

Figure 4. Main transport pathways of DDQT-1, DDQT-2 and DDQT-3 crystals. Side-chains are replaced by green spheres for clarity.


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Table II. Transport paths, electronic coupling elements (J), intermolecular centroid distances (d) and mobilities (µcrys) for DDQT-1, DDQT-2 and DDQT-3 crystals as found from ZINDO. Hole mobilities µ are evaluated using velocity-averaging. dc represents the shortest intermolecular thiophene - thiophene distances.

DDQT-1

DDQT-2

DDQT-3

J(meV)

d(nm)

dc(nm)

J(meV)

d(nm)

dc(nm)

J(meV)

d(nm)

dc(nm)

JP=26

dP=0.56

0.43

JP=6

dP=0.46

0.46

JP1=4

dP1=1.91

0.43

JT1=1

dT1=1.44

0.54

JT1=3

dT1=1.63 0.50

JP2=0.1

dP2=1.39

0.54

JT2=0.2

dT2=1.23

0.67

JT1=0.2

dT1=3.20

0.67

JT3=10-4

dT3=1.25

0.96

µ = 0.0038 cm2/Vs

µ = 0.011 cm2/Vs

µ = 0.038 cm2/Vs

For systems we studied here, the ratio between the electronic coupling and the reorganization energy is so small that charge transport should predominantly occur by hopping.27,28 Marcus Theory is appropriate to calculate the transfer rates of these systems. The simulated crystal mobilities of compounds are also given in Table II, for main transport directions. We observe a systematic increase in mobility with increasing system size. Although the J2 (as in Marcus rate) of DDQT-1 along π-stacking direction is roughly 40 times higher than that of DDQT-3, the mobility is an order of magnitude lower owing to considerably higher λ of DDQT-1. Similarly, the J2 of DDQT-2 along π-stacking direction is slightly higher than DDQT-3, but the relatively lower mobility of DDQT-2 is due to its relatively lower λ.

III. 3. Site-energies, energetic disorder and electronic-coupling in equilibrated morphologies of DDQT-n The presence of local positional disorder due to thermal fluctuations results in broadening of site-energy distributions and cause evident energetic disorder σ. A high level of energetic disorder σ results in high energetic barriers amongst adjacent hopping 13 ACS Paragon Plus Environment


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sites and limits charge-drift diffusion. Figure 5 shows the probability distributions of siteenergy differences and the corresponding σ of DDQT-1, DDQT-2 and DDQT-3. DDQT-1 has a slightly higher σ of 76 meV which may be attributed to its higher backbone paracrystallinity (4.5%) arising from thermal fluctuations of torsional and stretching modes of backbones. The σ of DDQT-2 and DDQT-3 are energetically less disordered, and the σ is 69 meV for both, which correlates with slightly lower paracrystal order parameter.

Figure 5. Probability distributions of site-energy differences and corresponding fits to Gaussian distribution functions (solid lines). Inset shows the n-scaling of energetic disorders of DDQT-n.


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Figure 6. Distributions of squared electronic-coupling elements of the equilibrated morphologies. Vertical lines present the corresponding ideal crystal electronic-coupling elements

Figure 6 shows the distributions of direction-resolved electronic-coupling elements of equilibrated morphologies of DDQT-1, DDQT-2 and DDQT-3. In this figure, the positions of ideal-crystal electronic-couplings are also indicated by vertical lines. The broadening of electronic-couplings, due to thermal fluctuations, is in analogy with that of site-energy differences. The peak positions of distributions in some cases coincide with the position of the electronic-coupling of crystal morphology. However, especially for DDQT-3, the equilibrated electronic-coupling along either of the two π-stacking directions are, quite remarkably, enhanced roughly by 2-3 orders of magnitude over those of crystal DDQT-3. This may, to a first order approximation, be explained by shortening of the distance between the overlapping thiophene units of the neighboring backbones, since studies 15 ACS Paragon Plus Environment


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have

shown

that

electronic-coupling

increase

exponentially

Page 16 of 24

with

increasing

intermolecular spacing.

One thing also evident from the electronic-coupling distribution is that in all cases there are tail distributions of weak electronic-couplings that are partly responsible for chargetrapping. Figure 6 shows that the tail of weak π−π overlap of DDQT-3 is shorter comparing with those of DDQT-1 and DDQT-2, owing to its relatively high backbone order as identified from paracrystal order parameter, g.

III. 4. Hole mobility of equilibrated morphologies of DDQT-n The simulated charge-carrier mobilities for equilibrated morphologies are given in Table III. For comparison, experimental thin-film and single-crystal mobilities are also given7. With the presence of thermal fluctuations in structural order, the mobility of DDQT-1 decreases by two orders of magnitude and becomes 4.1x10-5 cm2/Vs. Despite the fact that the reorganization energy is considerably large, the relatively small mobility of DDQT-1 arises from its higher energetic disorder and, more importantly, due to the poor transport connectivity. Herringbone-type packing with π-π overlap, as in DDQT-2, has been known to be beneficial for charge-transport, owing to diminishing trap-states arising from high dimensional percolation network. However, an order of magnitude decrease in mobility of DDQT-2 is due to the presence of energetic disorder and extensive tail of weak electronic-couplings. Quite remarkably, the equilibrated mobility of DDQT-3 is increased roughly by a factor of two relative to its calculated ideal crystal mobility, owing to 2-3 orders of magnitude enhanced electronic coupling elements (see Figure 6). Also, studies have shown that brick-like packing arrangement (as in DDQT-3) in morphologies are most beneficial for charge-transport, again due to the ability of charge-carriers to bypass trap-states.39,40


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Table III. Calculated paracrystal order parameter g, energetic disorder σ (in meV), ideal crystal µcrys, equilibrated µequi hole mobilities of DDQT-n (n = 1, 2, 3). For comparison, experimental single-crystal µsc 2

and thin-film µtf mobilities are also given. Mobility units are in cm /Vs.

DDQT-1

DDQT-2

DDQT-3

g[%]

4.5

4.3

4.2

σ

76

69

69

µcrys

3.8x10-3

1.1x10-2

3.8x10-2

µequi

4.1x10-5

1.2x10-3

9.1x10-2

µsc (exp.)7

n/a

n/a

(1.0-4.0)x10-2

µtf (exp.)7

~0.0

(1.0-4.3)x10-3

(1.7-2.6)x10-3

The zero experimental thin-film hole mobility of DDQT-1 has been attributed to its large crystalline disorder7. However, as our results suggest even for the highly regular DDQT1 the hole mobility is quite low. We recently introduced a comprehensive benchmark study that uses the Marcus hopping model to calculate hole mobilities for a diverse set of 22 organic semiconductors. We assumed that single crystal morphologies are devoid of structural and energetic disorder, but that thin-film morphologies do have such disorder. We neglected other factors influencing mobility in crystals and thin films materials such as purity, the presence of defects or grain boundaries, charge concentration, polymorphism, and choice of substrate, and did short MD and found good agreement between our calculations and experimental macroscopic hole mobilities typically within an order of magnitude.41 Based on this analysis, we see that the simulated µequi=1.2x10-3 cm2/Vs of DDQT-2 is in agreement with experimental thin-film mobility. Also, for DDQT-3 the simulated ideal-crystal mobility 3.8x10-2 cm2/Vs is in agreement with the experimental single-crystal transistor mobility. However, the simulated µequi=9.1x10-2cm2/Vs of DDQT-3 is more than an order of magnitude higher than the thin-film transistor mobility. This deviation from the experiment is larger than we typically observed in our benchmark study.41 More interestingly, the simulated mobility µequi of DDQT-3, as a relatively high molecular weight oligomer, is very close to experimental thin-film mobility of ordered PQT-12 polymer, i.e. µtf ~ 0.2 cm2/Vs, and this



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Page 18 of 24

value is even an order of magnitude higher than defect-free single-crystal transistor mobility of DDQT-3.1,4

IV.

The

CONCLUSIONS

molecular

ordering

and

charge-transport

properties

of

oligo-didodecyl

quaterthiophenes (DDQT) were studied. The molecular order was characterized by paracrystallinity through atomistic molecular dynamics simulations. We found that the πstacking paracrystal order parameters of DDQT-1, DDQT-2 and DDQT-3 is qualitatively similar, and in close agreement with experimental order parameter of PQT-12 polymer.

Thermal fluctuations in molecular conformations result in broadening of site energies (yielding non-zero energetic disorder) and electronic-coupling elements. The peak positions of electronic-coupling distributions mostly coincide with the electronic-coupling elements of ideal crystals. However, for DDQT-3, electronic coupling along π-stacking direction has been enhanced by 2-3 orders of magnitude comparing with that of ideal crystal DDQT-3. The π-stacking also exhibits relatively short tail of weak electroniccoupling elements. Although π−π overlap of DDQT-1 is relatively high, its equilibrated mobility was found to be quite low due to a combination of properties; high λ and energetic disorder and, more importantly, unbeneficial transport connectivity. DDQT-2 packs in herringbone-type, which is beneficial for charge-transport, and its calculated equilibrium mobility is in agreement with experimental thin-film hole mobility. DDQT-3 forms two-dimensional brick-like packing arrangement. The equilibrated hole mobility is found to be more than an order of magnitude higher than corresponding thin-film mobility, and it approaches that of the experimental thin-film mobility of PQT-12 polymer.


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V. Author information * Permanent address: Department of Physics, University of Marmara, Istanbul, 34722, Turkey.

† Corresponding author: [email protected]

Notes: The authors declare no competing financial interest.

VI. Acknowledgments The authors are grateful for the financial support from National Science Foundation (Grants: DMR-1335645 and DMR-1112455). I.Y. thanks Marmara University, Turkpetrol Foundation and Turkish Higher Education Council (YOK) for supporting a portion of this research. We thank Jiyong Park and Blanton N. Martin for helpful comments. All calculations were performed on the Hoffman2 cluster at UCLA.

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  0.0038 cm2 / Vs

  0.011 cm2 / Vs

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  0.038 cm2 / Vs

Simulations of Molecular Ordering and Charge-Transport of Oligo

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