Origin of the High Carrier Mobilities of Nonperipheral Octahexyl

Oct 6, 2015 - Selective crystal growth of polymorphs and crystal-to-crystal thermal phase transition of non-peripherally alkyl-substituted phthalocyan...
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Origin of the High Carrier Mobilities of Nonperipheral Octahexyl Substituted Phthalocyanine Makoto Yoneya,*,† Ayano Miyamoto,† Yo Shimizu,‡ Akihiko Fujii,§ and Masanori Ozaki§ †

National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan National Institute of Advanced Industrial Science and Technology, 1-8-31 Midorioka, Ikeda, Osaka 563-8577, Japan § Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan ‡

S Supporting Information *

ABSTRACT: The carrier transport properties of nonperipheral octahexyl substituted phthalocyanine H2Pc(C6H13)np 8 in its crystal and columnar (Col) liquid crystal (LC) phase were investigated using density functional theory (DFT) calculations in combination with molecular dynamics (MD) and kinetic Monte Carlo (KMC) simulations. In the crystal phase, we found that the nonperipherally substituted chains of H2Pc(C6H13)np 8 , that interpenetrate adjacent phthalocyanines (Pcs), significantly alter the Pc-core stacking such that higher hole mobilities are observed for this system than for the nonsubstituted H2Pc. This chain interpenetration was found to be inherited by the column stacking in the Col phase and hindered the Pc-core in-plane rotations between adjacent Pcs. This rotational hindrance further caused a nonuniform distribution of the adjacent dimer Pc-core in-plane orientation configurations. The relatively high carrier mobility in the Col phase in this system can be rationalized by the nonuniform distribution of the dimer configurations that give relatively high electronic coupling between the adjacent dimers. Our results show the remarkable effects of nonperipheral substitutions on the carrier transport properties in both the crystal and Col LC phases.

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phase with time-of-flight (TOF) measurements.5 In its columnar (Col) liquid crystal (LC) phase, TOF mobilities of the order of 10−1 cm2 V−1 s−1 have been reported,5 which is the same order of magnitude reported values for their octaoctyl analogue (H2Pc(C8H17)8np).6 Correlated with these high mobilities, a high solar-cell efficiency of up to 4.1% has been reported with a binary mixture of H2Pc(C6H13)np 8 with the fullerene derivative 1-(3-methoxy-carbonyl)-propyl-1-1-phenyl(6,6)C61 (PCBM).7 However, the origin of the high carrier mobilities of these nonperipheral octaalkyl substituted Pcs is not well understood.6 The Norwich group reported an exceptionally large intercore distance normal to the Pc-core (i.e., 0.85 nm), in the crystalline phase of H2Pc(C6H13)np 8 based on their X-ray crystallographic study.8 They also suggested that the intercore distance in the

INTRODUCTION Organic electronic materials have the potential to significantly change several electronic applications (e.g., printable and/or flexible devices) because of their flexible design.1 However, to realize the potential of these materials, some basic design principles for various applications must first be clarified. Phthalocyanine (Pc) derivatives are one type of organic electronic material that has been extensively investigated.2 For example, a triclinic phase II crystal of titanyl phthalocyanine (αTiOPc) is reported to show high field-effect mobility (μFET) of ca. 3.3 cm2 V−1 s−1 in organic thin-film transistor operations.3 Using density functional calculations, ultraclose (ca. 0.31 nm) π-stacking of the α-TiOPc is found to be the origin of the observed high mobility.3,4 However, more data are required to provide a comprehensive set of design principles even for the relatively well-examined Pc materials. Recently, Miyake et al. reported a high carrier mobility up to 1.4 cm2 V−1 s−1 in metal-free nonperipheral octahexyl substituted Pc (H2Pc(C6H13)np 8 , see Figure 1) in its crystal © 2015 American Chemical Society

Received: July 22, 2015 Revised: September 29, 2015 Published: October 6, 2015 23852

DOI: 10.1021/acs.jpcc.5b07085 J. Phys. Chem. C 2015, 119, 23852−23858

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The Journal of Physical Chemistry C

performed with the Becke3-Lee−Yang−Parr (B3LYP) hybrid XC functional and a polarized double-ζ STO basis set (DZP). We had chosen these XC functionals and basis sets by checking the dependency of the calculated λ and Vij values on these. The details are presented in the Supporting Information. For the case of crystals with translational symmetries, the diffusion constant D of the hopping is approximated by the following equation: D=

Pj =

9

Col phase would be larger (0.4−0.5 nm ) than the more commonly observed values in the Col phase (ca. 0.35 nm) based on the X-ray diffraction data. However, these larger intercore separations contradict the existence of high carrier mobilities, because such separations are known to degrade the mobilities. Previously, we investigated the Col phase structure of H2Pc(C6H13)np 8 with molecular dynamics (MD) simulations and showed that the intercore distance would be similar to the common value (i.e., 0.36 nm).10 This may partly resolve the contradiction noted above, but it does not explain the high carrier mobilities. In this study, the origin of the high carrier mobilities of the nonperipheral octahexyl substituted phthalocyanine H2Pc(C6H13)np 8 in its crystal and LC phase was investigated using density functional theory (DFT) calculations. The effects of the nonperipheral substitutions on the carrier transport properties were investigated in detail.

kij ∑j kij

pi , i − 1 =

METHODS The charge transport in condensed phases of organic molecules near room temperature can be described as a hopping transport. In this hopping regime, the rate of charge hopping between specific dimers, kij, can be estimated by the Marcus model4,11 expressed as follows:

(4)

ki , i − 1 ki , i − 1 + ki , i + 1

(5)

where ki,i−1 and ki,i+1 are the hopping rates calculated using eq 1. Then, a random number is generated between 0 and 1 and is compared with pi,i−1. If the random number is lower than pi,i−1, the charge hops to the molecules i − 1; otherwise, the charge hops to the molecules i + 1. The time t and coordinate x are updated as t = t + ki,i−1−1 and x = x − di,i−1, respectively, for the case of hopping from i to i − 1. Here, di,i−1 is the center-of-mass distance between the molecules i and i − 1. For the case of hopping from i to i + 1, the time t and the coordinate x are updated as t = t + ki,i+1−1 and x = x + di,i+1, respectively. After a sufficient number of MC steps (e.g., >1012 steps in this study), the diffusion constant DKMC of the 1-D random hopping is obtained from the mean-squared-displacement ⟨x2(t)⟩ as

(1)

where kB is Boltzmann’s constant, ℏ is Planck’s constant, T is the temperature, λ is the reorganization energy, and Vij is the electronic coupling matrix element (hereafter simply referred to as “electronic coupling”), respectively. Vij is defined as Jij − Sij(εi + εj)/2 1 − Sij 2

(3)

j

In contrast to the crystal phase, the columnar LC phase displays structural disorder, and then, there are no translational symmetries as in the crystal phase. These structural disorders in the LC phase can be captured with MD simulations. Basically, we follow the joint method of MD/kinetic Monte Carlo (KMC) as described in Olivier et al.14 to estimate the mobility in the Col LC phase. In this method, one-dimensional (1-D) mobility along the column axis is evaluated by performing 1-D KMC random hopping on a column selected from the MD snapshots. In this KMC scheme, the charge is initially localized on a given molecule i at the 1-D coordinate x = 0 and hops to either an adjacent molecule i − 1 or i + 1, which is chosen on the basis of the probability pi,i−1:

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Vij =

∑ dij 2kijPj

where N is the spatial dimensionality, dij is the center-of-mass distance between the molecules in the dimer, and Pj is the hopping probability along the jth hopping path defined as

Figure 1. Nonsubstituted (R = R′ = H), peripheral (R = CnH2n+1, R′ = H), and nonperipheral (R = H, R′ = CnH2n+1) octaalkyl substituted phthalocyanine.

1/2 ⎛ |Vij|2 ⎛ π ⎞ λ ⎞ kij = ⎜ ⎟ exp⎜ − ⎟ ℏ ⎝ λkBT ⎠ ⎝ 4kBT ⎠

1 2N

DKMC =

(2)

Here, Jij, Sij, εi, εj are the transfer integral, the spatial overlap integral, and the site energies, respectively.12 These values (i.e., Jij, Sij, εi, εj) between the dimer were obtained with the “fragment approach” implemented in the Amsterdam density functional (ADF) package.13 The calculations were performed using the generalized gradient approximation (GGA) and the Perdew and Wang 91 (PW91) exchange-correlation (XC) functional with a polarized triple-ζ Slater-type orbital (STO) basis set (TZP). Optimization of the monomer geometries and the calculations of the reorganization energies λ were

x 2(t ) 2t

(6)

In this study, the DKMC value was further averaged over 128 independent hoppings with different random number seeds. We note that the diffusion constant DKMC obtained using eq 6 for the molecules with identical values of k and d (1-D crystal case) agrees with the 1-D diffusion constant obtained using eq 3,

D=

1 2 dk 2

(7)

within statistical error. 23853

DOI: 10.1021/acs.jpcc.5b07085 J. Phys. Chem. C 2015, 119, 23852−23858

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The Journal of Physical Chemistry C Table 1. Calculated and Experimental Mobilities of the Investigated Pc Systems λ (eV)

system H2Pc(C6H13)np 8

H2Pc

path

0.09928

0.04736

a b c a+b b+c a+c a+b+c a/2 − b/2 b c a/2 + b/2

d (nm)

4.507 × 2.192 × 6.526 × ca. 0.0 5.155 × ca. 0.0 4.000 × 8.694 × 1.328 × 3.243 × 8.596 ×

0.9267 0.9732 1.9991 1.2730 2.0502 2.1863 2.1912 1.0213 0.4731 1.4813 1.2955

1 di , i + 12ki , i + 1 2

10 10−5 10−5 2.318

1.15

0.1265

0.05−0.119

−6

10

10−5 10−4 10−2 10−5 10−5

(8)

i

In contrast, Alexander et al. averaging form,

2 −1 −1 μexp s ) hole (cm V

−2

adjacent molecular stacking between H2Pc and H2Pc(C6H13)np 8 is shown in Figure 2. As shown, the Pc-core stackings differ

If we consider average diffusion constant of 1-D transport systems with different ki,i+1 and di,i+1 values, it may simply be Davr1 =

2 −1 −1 μcalc s ) hole (cm V

|Vij| (eV)

15

theoretically derived a different

−1

Davr2

1 = 2

1 di , i + 12ki , i + 1

i

(9)

We will compare these Davr1 and Davr2 values with the DKMC in the later section. Finally, the charge mobility μ can be estimated from the diffusion constant D by the Einstein relation: e μ= D kBT (10) where e is the elementary charge.

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Figure 2. Comparison of adjacent molecular stacking between (a) the nonsubstituted Pc (H2Pc) and (b) the nonperipheral octahexyl substituted Pc (H2Pc(C6H13)np 8 ).

RESULTS AND DISCUSSION Mobility in the Crystal Phase. We first calculated the mobility of the H2Pc(C6H13)np 8 system in its crystal phase, based on the crystal structure obtained by an X-ray crystallographic study.8 The mobility of the nonsubstituted H2Pc crystal16 was also calculated for comparison. The calculated hole mobilities, μhole, at room temperature (i.e., T = 293 K) are shown in Table 1 with the corresponding experimental values. Good agreements were obtained between the calculated and experimental mobilities in both Pc systems. The hole mobility of the H2Pc(C6H13)np 8 system was 1 order of magnitude larger than that of the H2Pc system for both the calculated and experimental values. From the hopping rate expression in eq 1, it is seen that higher carrier mobilities are obtained via smaller reorganization energies, λ, and larger electronic couplings, |Vij|. From the results in Table 1, the larger electronic coupling |Vij| of H2Pc(C6H13)np 8 relative to H2Pc makes its mobility higher than that of H2Pc, even though it has a smaller reorganization energy, λ. In both Pc systems, the hopping path with the shortest distance d (i.e., the a-axis for H2Pc(C6H13)np 8 and the baxis for H2Pc) showed the largest electronic coupling, |Vij|, whereas the other paths possessed almost negligible couplings. Actually, the shortest hopping paths alone give essentially identical calculated mobilities, μcalc hole. Next, we compared the stacking structures of both Pc systems along the shortest distance path. A comparison of the

largely in two ways; that is the difference in the Pc-core normal tilt θ from the column axis and the Pc-core central H−H vector in-plane azimuth ϕ from the column axis: (θ, ϕ) ∼ (45°, 45°) for H2Pc and (θ, ϕ) ∼ (65°, 15°) for H2Pc(C6H13)np 8 . The intercore distance normal to the Pc-cores, dc, can be evaluated from θ and the corresponding molecular center-of-mass distance d as dc = d cos (θ) . These values are dc ∼ 0.33 nm and dc ∼ 0.39 nm for the H2Pc and the H2Pc(C6H13)np 8 systems, respectively. This result means that the origin of the higher mobility of H2Pc(C6H13)np 8 than that of H2Pc could not occur because of a short intercore distance. Here, we note that our result of an intercore distance of dc ∼ 0.39 nm for H2Pc(C6H13)np 8 is far shorter than the previously reported value of 0.85 nm.8 This value (i.e., 0.85 nm) would be estimated based on Figure 2 of ref 8, in which the two alkyl chains that are staggered out from the Pc-core plane act as spacers between the molecules. However, as shown in Figure 4b, these two staggered chains do not act as spacers but instead interpenetrate the adjacent molecules. To further clarify the relationship between mobilities and the stacking configurations of the Pc-cores, we calculated the mobilities of the nonsubstituted Pc (H2Pc) dimer as a function of (θ, ϕ). We note that only the shortest hopping path was considered in these mobility calculations because this 23854

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The Journal of Physical Chemistry C approximation has been shown to be satisfactory, as described above. The Pc-core tilt θ was changed while the intercore distance normal to the cores dc = 0.34 nm was kept constant. Then, the distances between the dimer were varied as d = 0.34 × cos−1 θ. Figure 3 shows the θ−ϕ mapping of the hole mobilities of the H2Pc dimers. Figure 3 shows the complicated dependency

Figure 4. (a) Snapshot of a representative column (ID 22 in Table 2) viewed from perpendicular to the column axis (dashed line). (b) The corresponding view of the column along the a-axis (dashed line) in the crystal phase. Note that the scales are different between snapshots a and b.

Table 2. Calculated Hole Mobilities (cm2 V−1 s−1) of Six Randomly Selected Columns column ID 4 9 15 19 22 31 av

Figure 3. θ−ϕ mapping of the hole mobilities for nonsubstituted Pc (H2Pc). The symbols + and × correspond to the configuration for H2Pc and H2Pc(C6H13)np 8 , respectively.

μKMC 1.101 2.020 1.766 1.223 4.383 1.228 1.266

× × × × × × ×

10−3 10−2 10−1 10−1 10−1 10−3 10−1

μavr1 9.812 9.149 1.228 7.470 2.799 1.414 1.347

× × × × × × ×

μavr2 10−1 10−1 100 10−1 100 100 100

1.486 2.277 1.737 1.367 4.426 1.114 1.297

× × × × × × ×

10−3 10−2 10−1 10−1 10−1 10−3 10−1

μavr1, and μavr2, correspond to the mobility values calculated with the diffusion constants from the KMC (eqs 6, eq 8, and eq 9, respectively). The average value of μKMC (1.266 × 10−1 cm2 V−1 s−1) agrees well with the corresponding value from TOF measurements of 2.0 × 10−1 cm2 V−1 s−1.5 We also found that the μavr2 values agree well with the μKMC values, but the μavr1 values were 1 order of magnitude larger than the μKMC values. The results show that the averaged diffusion expression (eq 9) by Alexander et al.15 could be a good alternative to the diffusion constant by KMC. Figure 5 shows the plots of the standard deviations, σ, divided by the corresponding mean value, m, of the electronic

of the mobilities on the dimer configuration (θ, ϕ), especially when θ > 30°. We can see that the stacking configuration (θ, ϕ) ∼ (45°, 45°) of H2Pc essentially corresponds to the basin of the 2 −1 −1 mobility mapping (i.e., μcalc s ). In contrast, hole = 0.3767 cm V calc higher mobilities (i.e., μhole = 2.985 cm2 V−1 s−1) are corresponded for the configuration (θ, ϕ) ∼ (65°, 15°) for H2Pc(C6H13)np 8 . From these results, it is clear that the relatively higher crystalline mobilities of H2Pc(C6H13)np 8 versus H2Pc originate because of differences in the Pc-core stacking configurations (θ, ϕ). This difference is caused by the novelty of the H2Pc(C6H13)np 8 crystal structure, that is two of the eight nonperipheral substituted chains stagger out of the Pc-core plane whereas the remaining six chains reside in the Pc-core plane.8 The two staggered chains interpenetrate the adjacent Pcs and significantly alter the Pc-core stacking configurations (from (θ, ϕ) ∼ (45°, 45°) to (65°, 15°)), which increases the mobility of H2Pc(C6H13)np 8 relative to H2Pc. Mobility in the Col Phase. For the Col LC phase, we conducted KMC simulations with DFT-derived charge hopping rates between each adjacent molecular pair within the column. The column structures were obtained as snapshots from our previous MD simulations.10 Specifically we used the snapshot after a 60 ns MD run with 432 H2Pc(C6H13)np 8 molecules at 438 K, which is at the middle of the Colh LC temperature range of 434−443 K, under normal pressure. Details can be found in our previous study (Supporting Information S2).10 Figure 4a shows a snapshot of a representative column viewed from perpendicular to the column axis. For comparison, the corresponding view of the crystal a-axis column is shown in Figure 4b. The calculated hole mobilities at 438 K are shown in Table 2 for six randomly selected columns (from a total of 36 columns in the system investigated). In this table, three values, μKMC,

Figure 5. σ/m of the electronic coupling |Vij| within a column vs the column hole mobility μ. The broken line is drawn solely as a visual aid. 23855

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The Journal of Physical Chemistry C coupling, |Vij|, within each column and the μcalc hole of each column. Figure 5 shows a negative correlation between the parameters investigated, i.e., larger σ/m values lead to smaller values of μcalc hole. We note that σ/m is a measure of the electronic disorder mediated via charge localization.17 If so, then the data of Figure 5 indicate that the localization being stronger, the smaller mobility. Large σ/m values mostly occur for the columns with molecular pairs that possess very small |Vij| values. In Figure 6,

Figure 7. Rotational-autocorrelation functions of the H2Pc(C6H13)np 8 system. The solid, dashed, and long dashed lines correspond to the Pccore normal vector rotation, the Pc-core in-plane vector rotation, and the relative in-plane rotation between adjacent Pcs.

different from the Colh results by Olivier et al. and highlights the novelty of the Colh phase of the H2Pc(C6H13)np 8 system. The weakly hindered Pc-core normal vector rotation indicates that the Pc-core tilt orientations of H2Pc(C6H13)np 8 are highly disordered in time. For the carrier hopping between Pcs, Pc-core in-plane relative rotation between adjacent Pcs would be more important than the rotations relative to the absolute coordinates above. Additionally, we also evaluated the following rotational autocorrelation functions for the relative in-plane angles Δϕ between adjacent Pcs within the same columns:

Figure 6. Time variations of |Vij| for the smallest value pairs within each column (+, column ID 4; ×, 9; *, 15; ○, 19; □, 22; △, 31).

we plot the time evolution of |Vij| for the smallest value pairs at the initial state. In this figure, the initial state corresponds to the snapshot at t = 60 ns (i.e., textended = 0 corresponds to t = 60 ns). As shown, the |Vij| values vary over an order of magnitude within a time scale of sub-ps (i.e., comparable time scale of the local molecular motions). Next, we investigated the rotational dynamics in the Col phase because it is known to affect carrier transport.14 Olivier et al. reported that the in-plane vector rotation of the Pc-core is hindered in low temperature (tilted-core) Colr phase, but it is fast (on the order of tens of nanoseconds) in high temperature (nontilted-core) Colh phase. These were clarified from rotational autocorrelation functions, C(t ) =

v(t0) ·v(t ) |v(t0)||v(t )|

t0

C(t ) = cos(Δϕ(t0) − Δϕ(t ))

(12)

t0 18

The functional form of eq 12 readily gives C(t=0) = 1, as eq 11. The function is plotted in Figure 7 with a long dashed line and shows hindered behavior. The origin of this rotational hindrance is the interpenetration of the nonperipherally substituted alkyl chains between the adjacent Pcs mentioned in the previous section. From the results of our previous MD simulations,10 the crystal a-axis becomes the column axis in the Colh phase, and the column stacking structures in the Colh phase (Figure 4a) may inherit the crystal a-axis stacking structures (Figure 4b). Actually, some of the chain interpenetrations shown in Figure 4b are similar to the ones found in Figure 4a. If we look closely at the interpenetrated (staggered out) chains in Figure 4b, the two chains are almost parallel to the vector normal to the Pc-cores, whereas the remaining six chains make approximately right angles to the Pc-core normal vectors. Figure 8 shows the calculated population distributions of angle θ, which is the angle between the terminal chain direction (i.e., the vectors between C2 to C6 in the inlet) with the Pc-core normal vector for both the crystal phase and the Colh phase structure (i.e., the snapshot after 60 ns of MD simulation). In the crystal phase (dashed line), the peak at θ ∼ 5° with a normalized population of approximately 0.25 corresponds to the two staggered out terminal chains from a total of eight chains per molecule, whereas the θ ∼ 79° and 83° correspond to the remaining chains. The distribution of the Colh phase (solid line) with low θ populations, even less than

(11)

in their MD simulations of a peripherally tetraalkoxy substituted metal-free Pc system.14 They also reported that the normal vector rotation of the Pc-core is hindered in both of the Colr and Colh phases. It would be noteworthy to compare these to the current nonperipheral octahexyl substituted Pc (H2Pc(C6H13)np 8 ) system because we found that the Col phase of this system is the tilt orientationally disordered Colh phase; that is, the Pc-cores are tilted as in the Colr phase, but their orientational disorder makes the hexagonal 2-D column arrangements like those in the Colh phase.10 Figure 7 shows the rotational-autocorrelation functions of the H2Pc(C6H13)np 8 system. Figure 7 shows that the Pc-core inplane vector rotations (dashed line) are fast in the Colh phase of the H2Pc(C6H13)np 8 system, which is similar to the Colh phase observed in Olivier et al.14 However, the Pc-core normal vector rotations (solid line) are only weakly hindered. This result is 23856

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Figure 8. Normalized population distributions of the angle θ between the Pc-core normal vector and the terminal chain C2−C6 vectors for the Col LC phase (solid line) and the crystal phase (dashed line).

Figure 10. Normalized population distributions of the mapped electronic coupling |Vij| values of the adjacent dimer stacking configurations (× symbols in Figure 9).

20°, corresponds to the staggered out (and interpenetrated) chains. This indicates that the column stacking structures in the Colh phase inherit the interpenetration of the substituted chains between adjacent Pcs from the crystal stacking structures. It is probable that the rotational hindrance may cause nonuniform distribution of adjacent dimer configurations. This dimer configuration in the Colh LC phase possesses an additional degree of freedom than those in the crystal phase (i.e., the single azimuth ϕ in Figure 2), and it can be specified with independent azimuth angles, ϕ1 and ϕ2, for each molecule in the dimer. Figure 9 shows the ϕ1−ϕ2 mapping of the

these plots (× symbols) for the mapped electronic coupling |Vij| values of Figure 9. The distribution has a peak around |Vij| ∼ 0.011 eV and an average value of ca. 0.033 eV. The latter value corresponds well to the average value of 0.027 eV for all of the calculated dimers in Table 2. This suggests that the relatively high carrier mobility in the Colh phase for this system can be rationalized by the nonuniform distribution of dimer configurations present in Figures 9 and 10.

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CONCLUSIONS The origin of the high carrier mobilities of nonperipheral octahexyl substituted phthalocyanine H2Pc(C6H13)np 8 in its crystal and Colh phase was investigated theoretically. The calculated hole mobilities of both the crystal and Colh phase correspond well to the experimental mobility values. We found that the larger crystal hole mobilities of H2Pc(C6H13)8np relative to nonsubstituted H2Pc originate from differences in the Pc-core stacking configurations. The nonperipherally substituted chains of H2Pc(C6H13)8np that interpenetrate the adjacent Pcs significantly alter the Pc-core stacking to effect a high hole mobility relative to H2Pc. Moreover, our results indicate that Pc-core stacking configurations superior to the H2Pc(C6H13)np 8 crystal are possible (e.g., (θ, ϕ) ∼ (60°, 47°) in Figure 3). If such configurations could be realized by judicious substitution, for example, then more higher mobilities would be achieved. The chain interpenetration may alter the rotational dynamics of Pcs, which is known to affect carrier transport. We found that the relative Pc-core in-plane rotations between adjacent Pcs were hindered in the Colh phase. Additionally, we found that the column stacking structures in the Colh phase inherit the chain interpenetration from the crystal stacking structures. Further, we found that nonuniform distribution of adjacent dimer Pc-core in-plane orientation configurations gives a relatively high carrier mobility in the Colh phase for this system. We think that this nonuniform distribution is mediated by the rotational hindrance caused by the chain interpenetrations. Our results highlight the remarkable effects of nonperipheral substitutions on the carrier transport properties of both crystal and Colh LC phases.

Figure 9. |Vij| mapping as a function of in-plane orientations ϕ1, ϕ2 for a Pc dimers. Adjacent dimer stacking configurations for the last 1 ns of the MD simulation were overlaid with × symbols.

electronic coupling |Vij| for H2Pc dimers. In this mapping, the Pc-core tilt θ is fixed to the average value of 53° because the tilt is much less sensitive than the azimuth. Adjacent dimer stacking configurations within the six columns in Table 2 were overlaid on this mapping (with × symbols) for the last 1 ns (t = 59−60 ns) of the MD simulation with time slices of 100 ps. These plots (× symbols) distribute nonuniformly over the ϕ1−ϕ2 configuration. Figure 10 shows the population distributions of 23857

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Transport Dynamics in Liquid-Crystalline Phthalocyanine Stacks. J. Phys. Chem. B 2009, 113, 14102−14111. (15) Alexander, S.; Bernasconi, J.; Schneider, W.; Orbach, R. Excitation Dynamics in Random One-Dimensional Systems. Rev. Mod. Phys. 1981, 53, 175. (16) Matsumoto, S.; Matsuhama, K.; Mizuguchi, J. Metal-Free Phthalocyanine. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1999, 55, 131−133. (17) Ando, M.; Kehoe, T. B.; Yoneya, M.; Ishii, H.; Kawasaki, M.; Duffy, C. M.; Minakata, T.; Phillips, R. T.; Sirringhaus, H. Evidence for Charge-Trapping Inducing Polymorphic Structural-Phase Transition in Pentacene. Adv. Mater. 2015, 27, 122−129. (18) van der Spoel, D.; Berendsen, H. Molecular Dynamics Simulations of Leu-Enkephalin in Water and DMSO. Biophys. J. 1997, 72, 2032. (19) Westgate, C.; Warfield, G. Drift Mobility Measurements in Metal-Free and Lead Phthalocyanine. J. Chem. Phys. 1967, 46, 94−97.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07085. Dependency of λ and Vij on calculation methods (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Prof. Hiroyuki Ishii of Tsukuba University and Dr. Kazuhiko Seki of AIST for valuable discussions. We also thank Dr. Kento Mori of Ryoka Systems Inc. for his help on the ADF program. This work was supported by the Japan Science and Technology Agency (JST-ALCA project).

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REFERENCES

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DOI: 10.1021/acs.jpcc.5b07085 J. Phys. Chem. C 2015, 119, 23852−23858