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Liquid Crystals

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Structure-electronics relations of discotic liquidcrystals from a molecular modelling perspective

Suhana Mohd Said, Mohamad Syafie Mahmood, Mohammad Noh Daud,Mohd Faizul Mohd Sabri & Nor Asrina Sairi

To cite this article: Suhana Mohd Said, Mohamad Syafie Mahmood, Mohammad NohDaud, Mohd Faizul Mohd Sabri & Nor Asrina Sairi (2016): Structure-electronics relationsof discotic liquid crystals from a molecular modelling perspective, Liquid Crystals, DOI:10.1080/02678292.2016.1209792

To link to this article: http://dx.doi.org/10.1080/02678292.2016.1209792

Published online: 27 Jul 2016.

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INVITED ARTICLE

Structure-electronics relations of discotic liquid crystals from a molecularmodelling perspectiveSuhana Mohd Saida, Mohamad Syafie Mahmooda,b, Mohammad Noh Daudc, Mohd Faizul Mohd Sabrid

and Nor Asrina Sairic

aDepartment of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia; bFaculty of Applied Science,MARA University of Technology, Shah Alam, Malaysia; cDepartment of Chemistry, Faculty of Science, University of Malaya, Kuala Lumpur,Malaysia; dDepartment of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia

ABSTRACTDiscotic liquid crystals (DLCs) have been researched for their potential in electronics applications,such as organic field-effect transistors, organic light-emitting diodes and organic photovoltaics.These molecules generally comprise a rigid planar core surrounded by aliphatic chains, and self-organise into columnar phases. Charge transfer is enabled along these columns, as the spatialoverlap of the stacked π orbitals within the columns lead to a quasi-one-dimensional conductiv-ity. An understanding of charge transfer and electronics orbitals in the field of DLCs is valuable forrational design of future DLC molecules in electronics applications. This paper provides aperspective that a range of molecular modelling tools may bring into our understanding onthe structure, dynamics and electronics properties of DLCs. Whilst the description of chargetransfer of DLCs has been substantially investigated, the understanding on the molecular orbitalshad been relatively less explored. We introduce a multiscale molecular mechanics and quantummechanics approach to understanding the relationship between the bandgap and density ofstates (DOS) and the structural parameters of a DLC. This investigation is expected to be thestarting point for situations where knowledge of DOS for DLCs are of the essence, in applicationssuch as current rectification and thermoelectricity.

ARTICLE HISTORYReceived 2 May 2016

KEYWORDSDiscotic liquid crystals;molecular modelling; chargetransport; charge mobility;density of states

1. Introduction to discotic liquid crystals

1.1. Basic discotic liquid crystal structures

Discotic liquid crystals (DLCs) are attractive candidatesfor molecular electronics devices, given their low cost,ease of processability and potential for self assembly.DLCs are defined by their overall disc-shaped molecu-lar structure, which comprises of a rigid planar central

core surrounded by 6–8 aliphatic side chains whichserve to stabilise the liquid crystalline phase.[1,2]

The binding between molecules is in most casesmainly due to van der Waals forces.[3] The core–coreand tail–tail van der Waals interactions are responsiblefor the formation of the columnar phase. These pack-ing structures are a function of the symmetry of col-umns and also intracolumnar van der Waals forces.

CONTACT Suhana Mohd Said smsaid@um.edu.my Department of Electrical Engineering, Faculty of Engineering, University of Malaya, KualaLumpur 50603, Malaysia

LIQUID CRYSTALS, 2016http://dx.doi.org/10.1080/02678292.2016.1209792

© 2016 Informa UK Limited, trading as Taylor & Francis Group

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Furthermore, the tail–tail interactions determine therigidity of the columns. The high entropy and disorderof the flexible aliphatic chains on the periphery of thecentral rigid core prevents the formation of a 3D crys-tal and is crucial to the formation of a liquid crystallinephase. There are also tilted columns where the cores ofthe disks are tilted with respect to the column axis,better known as oblique columnar phases.[4,5] A col-umn’s order is a function of temperature, whereas theyare bound within core–core interaction where thecolumnar arrangement is preferred.[2] The packing ofthe DLC phase can be categorised according to theirtwo dimensional (2D) packing structures, such ascolumnar hexagonal (Dh) and columnar rectangular(Drd).[6,7] These packing structures are a function ofthe symmetry of columns and also intracolumnar vander Waals forces. X-ray studies suggest that withinthese columns, a long range intracolumnar helicalorder exists as studied by Fontes et al. and Malthêteet al.[8,9] This helical order is proposed to be thecompetition between the attraction of the cores andthe steric repulsion of the alkyl side chains.

The self assembly of these DLCs can be exploitedas molecular nanowires. For example, 2,3,6,7,10,11-hexapentyloxytriphenylene (HAT5) can sponta-neously form well aligned, micrometre long, yetonly tens of nanometres thick, nanowires on solidsurfaces.[10] A shorter side chain is also found to bemore beneficial for columnar stability.[11] Solventsalso influence the arrangement and order by actingon spontaneous self-organisation of discotic liquidcrystals (LCs).[10,12,13]

Due to the liquid crystalline nature of these col-umns, they do not exhibit true 1D order and areinstead defined as 1D-fluids where there is a degreeof liquid-like dynamic disorder within the mesophase.[2,14] Hence, the ‘columnar’ configuration, which isthought to be useful for charge transfer, is not perfect.It is a stochastical average in terms of its positional andorientational order. However, instead of viewing thefluid-like behaviour of DLCs as a liability, this liquid-like property of DLCs allows self healing of defects andcharge traps within the columns, which are able toaverage out over a temporal scale [15].

Common classes of DLCs are listed in Table 1, suchas triphenylenes, porphyrins, perylenes, thiophenes andhexa-peri-benzocoronenes. Amongst the classes ofDLCs, triphenylenes were amongst the first synthe-sised. In particular, HAT derivatives have formed thebuilding blocks for many DLC systems in a range ofmolecular electronic applications, given their ability toaccept electrons, and have a rigid, planar core whichencourages π–π stacking. Porphyrins, on the other

hand, with their fused six member rings providedeven larger π–π overlap. To our knowledge, metal–porphyrin complexes were first invented by Bruceet al.,[16] whilst other coordination complexes includephtalocyanines and n-aryl Schiff bases.[17–19] Latermetallomesogens have shown spin crossover beha-viour, which are useful for potential applications indye-sensitised solar cells and memory devices.[20–22]Hexa-peri-benzocoronenes were synthesised by Mullerand Spiess et al. in 1999, and exhibited highly orderedcolumnar structures. Thiophenes came into the picturein 2002, when Eichhorn et al. developed di-, tri- andtetra-catenar LCs carrying thiophene cores.

This paper is not intended as a review for DLCs, asthere have been several excellent articles on this subjectmatter. In particular, a review by Cammidge et al.provided a comprehensive overview of the synthesisof multifunctional triphenylenes, either through theassembly of the triphenylene core with appropriatepositioned substituents, and functionalisation throughsimple electrophilic aromatic substitution.[28] Also ofnote in the review by Kumar on the role of nanopar-ticles on the supramolecular order of DLCs, whichserve to improve the conductivity of the system andhence has positive impact as semiconducting materialsfor device applications.[37] Of further interest is thereview of polar columnar LCs by Takezoe and Araoka,which demonstrates Ising polarisation, which gives riseto interesting potential applications as piezoelectric andferroelectric devices.[38] Rather, it is meant to be aperspective to draw a picture of the structure, dynamicsand electronics of DLCs which is provided throughmolecular modelling investigations and the under-standing it provides when analysed in conjunctionwith experimental data. In particular, it is intended todraw the reader’s attention through the strong correla-tion which exists between the DLC’s molecular struc-ture and its electronic behaviour. This perspective firstprovides an introduction to DLCs and the powerfulpotential it possesses in molecular electronics, as 1Dmolecular wires due to stacking of its π–π orbitals. Anoverview of the experimental techniques used to probethe structural and electronic characteristics is thenprovided. The potential applications of DLCs are thenaddressed, and correspondingly, the challenges whichremain in order to realise the full potential of theseapplications. The bulk of the paper discusses the rangeof molecular modelling approaches which have beenused in conjunction with experimental techniques inorder to provide a picture of DLC structure, dynamicsand charge transfer. We then identify the gaps in ourunderstanding which remain, and our efforts to fillthese gaps with our contribution to describing the

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Table 1. Common classes of DLC molecule core structure and its chain substituents.Core Examples of substituents

R

R

R

R

R

R

Triphenylene

R = O(CH2)5CH3 (HAT5) [10]R = O(CH2)6CH3 (HAT6) [23,24]R = S(CH2)6CH3[25–27]R = O-n-hexyl [28]

N

NN

RS SR

SRRS

N N

N

N N

SRRS

RS SR

M

Porphyrin

M = Cu, R = (CH2)3N3

M = Cu, R = (CH2)3C≡CH [29]

R R

R R

Perylene

R = COOC2H5

R = COOC3H7 [30]

S

RO OR

S

RO OR

N N

S

HO OH

X X

Thiophene

R = TetrahydropyranX = H, Br, CN [31]

(Continued )

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electronic configuration of DLCs as a function of struc-tural parameters. Our efforts are expected to providethe starting point for applications where this informa-tion is vital: thermoelectrics, current rectification andmagnetic-based sensors.

1.2. Electronics properties of DLCs

1.2.1. Charge transfer in DLCs1D charge transfer is enabled along these columns, andthese columnar liquid crystals have been described asmolecular wires. In terms of electronic charge transfer,DLCs are seen to be advantageous over amorphousconjugated polymers as their 1D order allows overlapof the highest occupied molecular orbital (HOMO) to alarger extent. The spatial overlap of π� orbitals of

adjacent aromatic rings in the DLC core is expectedto lead to quasi one-dimensional conductivity [39](illustrated in Figure 1), as there is sufficient proximitybetween the cores, approximately 3.5 Å for hexakis(n-alkoxy)triphenylene (HATn).[15] Hexa-peri-hexaben-zocoronene derivatives are able to produce high elec-tronic charge carrier mobility up to 1.1 cm2 V−1 s−1,which is comparable to amorphous silicon, and chargemobility for 2,3,6,7,10,11-hexahexyloxytriphenylene(HAT6) is 2 × 10–3 cm2 V−1 s−1.[24,40] The exchangeof charge carriers between neighbouring columns isstrongly hindered due to the insulating alkyl chains.DLCs are characterised by anisotropic charge transferalong and perpendicular to the columns, where chargemobility along the columns have been found to bearound 1000 times higher than that across the columns.

Table 1. (Continued).

Core Examples of substituents

R

R

R

R

R

R

Hexa-peri-hexabenzocoronene

R= C8F17 [32],

R=

C8F17

[32],

R= C12H25 [33].

N

N

NC

NC

R

R

R1

R1

Azatriphenylene

R = R1 = C10H21 [34]R = C10H21 R

1 = C6H13 [35]

N

N

N

N

R

R

R

R

R

R

Tricycloquinoxaline

R = C3H7

R = C5H11 [36]

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The relatively high mobilities along the stacking direc-tion of the columns in the liquid crystalline phase havebeen explained by liquid-like self-healing of structuraldefects on a time scale faster than hopping of chargecarriers.[41]

1.2.2. Charge mobility in DLCsCharge mobility is a macroscopic characteristic ofDLCs which is related to the fundamental charge trans-fer on DLCs. There have been many investigations onthe experimental and theoretical aspects on mobility inDLCs, given its premise for molecular electronicsapplications. A comprehensive list of charge mobilitiesfor DLCs, measured through different experimentalmethods has been compiled by Wohrle et al.[2] Forexample, the HAT derivative, 2,3,8,9,14,15-hexakisde-cylsulfanyl and 2,3,8,9,14,15-dodecylsulfanyl of5,6,11,12,17,18-hexaazatrinaphthylene have shown amobility of 0.9 cm2 V−1 s−1 using the pulse-radiolysistime-resolved microwave conductivity (PR-TRMC).[17] These compounds are relatively small, and mobilityis a function of side-chain length. On the other hand, formolecules, such hexabenzocoronenes mobilities in theLC phase are independent of the side chains. Synthesisof a series of self-organising n-type hexaazatrinaphthy-lenes [42] such as that illustrated in Figure 2, withvarious bay-located side have the ability to form long-range molecular columns with well-defined growthdirections. One particular variant of perpendicular tosubstrate columnar configuration exhibited mobilitiesof up to 103 cm2 V−1 s−1 using the time of flight(TOF) method. This provides some clues on the chemi-cal structure required for fast mobility: in this case, theelectron deficiency of the HAT core, coupled with long-range columnar order. The charge transfer mechanismwill be elaborated in Section 2.4.

1.2.3. Improving charge transfer in DLCsIn undoped DLCs, the core–core distance rather large,due to van der Waals forces being the main bindingforce. The direct electronic wave function overlap fromone molecule into the positive core of the adjacentmolecule is very weak, as the positive core is wellscreened in the ground state. For example, in HATn,we have a HOMO-lowest unoccupied molecular orbital(LUMO) gap which is ~4 eV or more.[3]

Doping will further improve the charge transfercharacteristics of DLCs. When a charge is injectedinto a DLC system, the extra charge in the LUMOband is weakly bound and hence its wave function ismore extended in space. Thus, the overlap of the elec-tron cloud is increased, which provides a potential forthe electron to transfer to the next molecule.Consequently, a bias field that promotes tunnellingresonance transfer to the neighbouring molecule isinduced.[3]

DLCs are generally good electron acceptors. The lowoxidation potential of HAT6 facilitates formation ofradical cations; when electron acceptors are introduced,they will become good conductors. Vaughan et al. [25]doped 2,3,6,7,10,11-hexakishexathioltriphenylene withiodine, which increased the conductivity by severalorders of magnitude. Boden et al. used HAT5 withAlCl3, [43] which transformed the insulating HAT5into a p-doped semiconductor, in which the conduc-tion along the columns was three orders of magnitudegreater than in the perpendicular direction.[1] Dopingwith gold nanoparticles or quantum dots has also beenshown to improve charge mobility without disturbingits mesomorphic structure/organisation.[37,44] BinaryDLC mixtures such as two triphenylene derivatives,HAT 6 and 2,3,6,7,10,11-hexakis–4-n-nonylphenyl-tri-phenylene in a 1:1 stoichiometry has been shown toincrease the structural robustness of the discotic mix-ture and better order. This has been proposed to be due

Figure 1. A schematic of one dimensional charge conductionthrough the columnar axis of a stack of DLCs. Figure 2. Structure of HATNA and its alkyl substituents which

provide long-range molecular order for good charge mobility.[42]

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to the favourable enthalpy of intercalation between thestacks of the two different DLCs. The charge mobilityin the hexagonal columnar mesophase has also beenshown to benefit from this binary mixing, where up tothree orders of magnitude higher mobility than a singleHAT6 composition has been shown.

Charge injection is also induced through contactwith a metal surface in actual devices. This results ineither a stronger or weaker coupling (depending on theorientation of the molecule at the substrate) betweenthe π electrons in the core of the DLC and the s-elec-trons on the metal surface.[3]

1.3. Experimental approaches to studyingelectronic properties in DLCs

In this section, specific experimental methods whichhave been useful to shed light on the molecular andelectronic characteristics of DLCs, and used in con-junction with molecular mechanics (MM) methodsfor discussion in this paper, will be elaborated.

1.3.1. Quasielastic neutron scatteringQuasielastic neutron scattering (QENS) has the advan-tage of identifying molecular motion on the picosecondtime scale, which is the time scale at which intermole-cular charge transfer occurs. In this experiment, neu-trons are described by the temporal and spatialcharacteristics of atomic motion through interactionwith the atomic nuclei. By selectively deuterating thehydrogen atoms in the HAT6 core, QENS was used toseparately obtain core and chain dynamics, and itsresults correlated with Molecular Dynamics (MD)simulations to provide an understanding of liquid crys-tal dynamics. It has been especially useful tool to elu-cidate core–tail correlation dynamics in DLCs, whichwill be explained further in Section 2.3. The liquidcrystal behaviour was evaluated using QENS by anelastic incoherent structure factor (EISF), which is

defined as the limit of the incoherent intermediatescattering function at infinite time:

EISF Qð Þ ¼ limt!1 Iinc Q; tð Þ (1)

The EISF is calculated by taking the Fourier transformof the QENS data, which is expressed as

Sinc Q;ωð Þ ¼ EISF Qð Þδ ωð Þ þ S0inc Q;ωð Þ (2)

where the EISF is the amplitude of the elastic line in themeasured spectrum, and the Q-dependence is a measureof the space confinement of the motions of the scatteringatom. However, in the liquid state, there is no elasticscattering in the sense of EISF because there is no spaceconfinement of the motion of the scattering atom.

1.3.2. TOF measurementsThe TOF method is the most commonly used methodto measure photoconductivity and hence charge mobi-lity.[45] It allows separate measurement of hole andelectron mobility. The experimental setup as shown inFigure 3, comprises of a typical liquid crystal cell,where a thin layer of liquid crystal is sandwichedbetween two transparent electrodes. This cell is thenirradiated with a laser to induce charge separation, anda bias voltage applied to drive the charge carriers totheir respective terminals. The photocurrent from theelectrons and holes are measured at their respectiveterminals after the application of the bias voltage, andobserved as a function of time. The nature of thecharge transit can be deduced from the photocurrentdecay profile. For relatively low charge carrier densi-ties, the TOF profile can show a well-defined Gaussiandistribution. However, in a DLC system, the presenceof defects and deviations from an ideal columnar struc-ture such as lateral slide of the columnar stacks wouldregister as a lower reading of the TOF compared to theidealised case.

Figure 3. Schematic diagram of time-of-flight (TOF) experiment. The incident irradiation is a narrow beam-width short pulse laser.Reprinted with permission from Ref. [45]. Copyright 2007 Springer.

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1.3.3. PR-TRMCConcurrent to the TOF method outlined above, PR-TRMC utilises a nanosecond ionising irradiation pulseto induce charge separation of a known concentrationuniformly in the DLC. The DLC does not need to bealigned.Microwaves are used as a contactless probe of thechange of the charge carrier concentration in the DLCbulk. The mobility is deduced from the tail end of thephotocurrent profile, as shown in Figure 4. In PR-TRMC,the hole and electron mobilities cannot be differentiatedand thus the measured mobility is a sum of the respectivemobilities of holes and electrons. Hence, mobilitiesobtained using PR-TRMC are generally higher thanTOF, and are not indicative of the anisotropic nature ofthe DLC as the measurement is not directional.

1.3.4. Ultraviolet photoelectron spectroscopyUltraviolet photoelectron spectroscopy (UPS) is themeasurement of the kinetic energy spectra of photo-electrons of molecules which have absorbed ultravioletphotons. It provides an insight into the molecularorbital (MO) energy of the valence region. It is anexperimental means of correlating experimental andtheoretical MO energies, and is useful in determiningthe work function of a material.[46] The high resolu-tion of the measurements also allows observation of thevibrational levels of the molecular ions, and the assign-ment of these peaks to bonding, nonbonding or anti-bonding MOs. In the field of DLCs, this technique hasbeen further refined to understand the describe intra-molecular band dispersion in a quasi-one-dimensionalmolecular chain and intermolecular band dispersionusing angle-resolved UPS.[47] This method provides apowerful link in providing experimental informationon the physical origin of charge mobility, which in turnwill be a powerful tool in improving charge carriermobility through molecular design and engineering.

1.4. Applications of DLCs

Given their charge transfer characteristics mentionedabove, DLCs find applications in electronics such as

light emitting diodes, photovoltaic devices and organicfield-effect transistors (OFET).[44,48] Organic light-emitting diodes (OLEDs), e.g. have been fabricated byBock et al. through devices comprising of aluminium/perylene (as electron transporter)/triphenylene (as holetransporter)/indium tin oxide.[49] However, the liquidcrystalline properties were not exploited for these roomtemperature devices, and, currently, device lifetime is aparticular issue. On the other hand, organic photovol-taics (OPVs) containing DLCs are thought to have theadvantages of being stable and robust, with the particu-lar characteristics of liquid crystals providing self-assem-bly and self-healing abilities. In theory, DLCs have thefollowing advantages for application in OPVs: largediffusion length, large charge carrier mobilities, andlarge solar absorption windows. They can be highlytuned to match the energy levels of dopants and electro-des, and their solution processability allows large areafabrication. A blend of electron-acceptor perylene tetra-carboxdiimide and electron-donor hexa-peri-hexaben-zocoronene (HBC) achieved a photovoltaic responsewith an external quantum efficiency up to 29.5% at460 nm and an open circuit voltage of 0.70 V.[50]

In sensing applications, exposed DLC films have beenshown to undergo electronic coupling or charge transferreactions upon exposure to gases which induce conforma-tional change. This can be measured in terms of the con-ductivity or polarisation response, and may be useful todetect weakly interacting nonpolar gases such as benzene,pentane, hexane, and heptane gases.[3] Furthermore, self-organised MD prefer to keep charged and unchargedimpurities near the free surface of the liquid crystal.Directionality of alignment is of essence in such electronicdevices which exploit one-dimensional charge transferalong the columns: unidirectional planar alignment isideal for OFET [51] while the homeotropic alignment isideal for OPV or OLED applications [52].

Other less known applications forDLCs include organicmagnetoresistance (OMAR) devices, OTE (organic ther-moelectric) devices, current rectifiers andmemory devices.

OMAR refers to the change in electrical resistivityfor sandwiched structures of nonmagnetic and organic

Figure 4. Deduction of mobility from the tail end of the photocurrent profile of PRTRMC. Reprinted with permission from Ref. [42].Copyright 2007 Springer.

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materials, when subjected to a magnetic field. HAT-CNderivatives have been shown to exhibit this effect. Suchdevices hold potential for in 2012, Saragi and cow-orkers reported the first magnetoresistive field-effecttransistors sensitive to ultrasmall magnetic fields(0.5 mT).[53] They employed a charge transport layercomprising of a mixture of HAT-CN (as electronacceptor) and 2,20,7,70-tetrakis-(N,N-di-p-methylphe-nylamino)-9,90-spirobifluorene as electron donor.

Thermoelectricity, on the other hand, is a solid stateconversion of a temperature gradient to electric poten-tial. It is currently being intensively explored for itspotential in waste heat energy harvesting applications.OTE materials are fast closing the gap with inorganicmaterials.[54] Some preliminary work has been doneon DLCs for thermoelectricity,[55,56] but the tunabil-ity of the DLC’s density of states (DOS) is expected tohave a direct impact on the OTE’s Seebeck coefficient,i.e. its ability to generate electrical potential per degreeKelvin of temperature difference (ΔV/ΔT) [57] which isa point of further investigation.

In terms of memory devices, the first structurallystable Ferroelectric DLC was synthesised by Miyajimaet al. in 2012, with fan-shaped dendrons which have asupramolecular conical arrangement as shown inFigure 5.[38,58] If the switching speeds can beimproved, they are promising for high-density memoryapplications, where each individual column may serveas an electrically addressable memory. On the otherhand, current rectification has been demonstrated byTsuji et al. [59] in stacked structures of donor (hydro-quinone)–acceptor (quinone) cyclophane materials.Their investigations included calculations of electrontransport in these materials based on density functionaltheory (DFT).[60] They have observed nearly

symmetrical current–voltage (I–V) characteristicsresulting in limited rectification.

The above examples illustrate the different ways thatthe DLCs can be utilised in applications: applicationssuch as OPVs and OLEDs exploit the quasi-one-dimensional charge transfer characteristics and relyon the fact that higher charge mobility DLCs poten-tially make better performing devices. Others, such asOMAR rely on exploitation of its magnetic properties,whilst OTEs rely on the information of the electronicDOS. Thus, in terms of development of DLCs forapplications, some challenges remain. Unlike inorganicdevices, the spectral sensitivity of organic materials islimited. One of the major limitations is their narrowabsorption window. The diffusion length of excitons tothe donor–acceptor interface is much shorter than theoptical absorption length. Direct electronic wave func-tion overlap from one molecule into the positive coreof a neighbouring molecule in the ground state istypically weak. The liquid crystalline nature of DLCs,whilst promising in terms of self-assembly, also containspatial and temporal perturbation which act as barriersto charge transfer. Variations in terms of core–corespacing, twist and lateral slide may disturb the chargetransfer process. In the next sections, our understand-ing of DLC structure, dynamics and electronic proper-ties will be provided from a molecular modellingperspective.

2. Molecular modelling of DLCs

2.1. Overview of molecular modelling approachesin DLC research

Molecular modelling is defined to encompass all theo-retical and computational approaches to emulate thebehaviour of molecules. For the purpose of this paper,the different types of molecular modelling approacheswhich have been useful in DLC research will be sum-marised in this section. MM, e.g. uses Newtonianmechanics to describe atoms as point charges with anassociated mass. The interactions between the atomsare then described by van der Waals forces and elec-trostatic interactions. The van der Waals forces arequantified uisng the Lennard-Jones potentials, whilstelectrostatic interactions are quantified uisngCoulomb’s law. These terms are collected to describethe system’s internal energy (U) through a potentialfunction. Minimisation of energy to deduce a system’sequilibrium position is obtained through techniquessuch as steepest descent; this approach is elaboratedfurther within the context of the potential energy sur-face in Section 2.2.

Figure 5. Example of fan shaped dendrons studied by Miyajimaet al. Reprinted with permission from Ref. [58]. Copyright 2007AAAS.

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The behaviour of such as system as a function oftime is known as MD. The trajectories of atoms ormolecules are solved using Newton’s laws of motion,which are then solved using numerical methods.Typically results from MD simulations are correlatedwith experiments which measure MD, such as nuclearmagnetic resonance (NMR) spectroscopy.

Complementary to the MD approach, Monte Carlo(MC) molecular modelling is an approach heavilyrelied upon in the charge transfer studies outlined inSection 2.4.2. The fundamental difference between thisand MD approaches is that the MC approach relies onequilibrium statistical mechanics. States are generatedbased on Boltzmann probabilities through a Markovchain procedure. The MD and MC approach provide apreliminary understanding of energy minima, and toaddress the effect of force, i.e. the contribution of vander Waals and electrostatic forces.

In contrast to the Newtonian-based approachesdescribed above, the electronic structure of the mole-cule is solved through the quantum mechanical (QM)approach. A molecule’s chemical properties can thenbe extracted through our understanding of its electro-nic structure. The first step is to solve the Schrödingerequation with the electronic molecular Hamiltonian.Since an exact solution of the Schrödinger equationcan only be obtained for hydrogen atoms, solutions toother systems may be obtained through an approxima-tion. For example, in the MO approach, the electronsare not assigned to individual bonds, but as under theinfluence of the molecule’s nuclei. Thus, the MOs ofthese electrons are defined by the spatial and energeticproperties of these electrons. The positions of theseorbitals are approximated by the DFT or Hartree–Fock (HF) models to solve the Schrödinger equation.In particular, the DFT is favoured for its relative speedof computation and accuracy. It describes the electronpopulation in terms of electronic density instead ofwavefunctions using the Kohn–Sham method andallows an understanding of charge transport. In thisapproach, the density functional is split into (i) theKohn–Sham kinetic energy, (ii) an exchange potential,(iii) exchange energies and (iv) correlation energies.

2.2. Modelling of DLC structure

Simulation of liquid crystal systems using molecular mod-elling approaches has been instrumental in understandingand predicting liquid crystal behaviour, either throughMM, MC or QM approaches, or a combination thereof.There has been an established body of work, especiallyrelated to calamitic (rod-like) liquid crystals. In the caseof DLCs, molecular modelling techniques are not as

established. For example, QM allows quantification of LCorder, identification of LC packing, and prediction ofcharge carrier mobility.[61] MC simulation based on idea-lised models of discs portraying the Gay–Berne potentialhas been used to study phase formation in DLCs.[62] MMpotentials have been used to establish the phase diagramsof DLCs mixtures.[63] An early MD work on understand-ing of the molecular properties and order of DLCs was putforward by Ono and Kondo, through their studies of thedisc-like hexakispentyloxytriphenylene (HAT5) molecule.[64] The early models did not pay fine attention to theexact structural packing or chemical structure. This wasimproved upon by refining the model according to theunderstanding of the liquid crystalline structure affordedby XRD analysis; furthermore hybrid classical/QM calcu-lations have been applied to cases such as rigid columnarstructures subjected to an explicitly described energeticdisorder.[65] Investigations on DLC molecular structureand its correlation with FTIR has also been explored.[66]

Mulder et al. developed an all-atom molecule forfour atoms within a discotic column, to investigatethe dynamics of HAT6, in the columnar and isotropicliquid phases.[67] On the other hand, charge transportparameters of semiconducting LCs, e.g. charge mobilityof triphenylene molecules, have been determined fromband structure calculations.[68,69] Later, DFT approaches have been used to study charge transfer in tri-phenylene derivatives. In particular, Bredas et al. haveperformed theoretical studies on charge transfer inte-grals and reorganisation energies of DLCs as a functionof molecular structure and order.[61]

2.2.1. MD investigations on DLC structureCinacchi et al. have conducted atomistic MD studies ofdiscotic HAT5 molecules was carried out to study its(i) molecular conformation, (ii) structural order and(iii) translational dynamics.[70] They used AMBERand OPLS force fields to provide the parameters forthe empirical model potential. The potential energywas described by bonded interactions (Eb) comprisingof a sum of bond-bending interactions described by itsharmonic potential and torsional energies; and non-bonded energies (Enb) which is dependent on two interacting atoms described by Coulomb and Lennard-Jonesterms. This work suggested a structure of the alkylchains with respect to the triphenylene core, formedan intermediate state between the diablo-like config-uration, with the chains in the triphenylene plane; andthe octopus-like configuration, with the chains alter-nating out of the triphenylene plane, which was sug-gested by 13C and 2H NMR, respectively.

A system containing 80 HAT5 molecules was thensimulated to enter the liquid crystalline phase. Their

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evaluation of positional and orientational correlationsuggested that (i) the initial hexagonal positional orderis retained throughout the simulation; (ii) the parallelcorrelation function gives a spacing between moleculesof 3.55 Å which is very close to the experimental valuefor intramolecular distances of 3.6 Å for adjacent co-facial molecules; and (iii) molecules within a columnhave a helicoidal arrangement, with a twist angle of 36°from between adjacent molecules, which again com-pare very well with experimental data. In brief, theoutcome of the bulk structural properties of the simu-lated system agrees well with the Dho phase of a realHAT5 system.

A picture of the translational dynamics was alsoprovided by this work, through mean square displace-ment (MSD) analysis of the molecular centre of mass.The system demonstrated liquid crystal behaviourthrough the following observations: The solid-like beha-viour observed perpendicular to the columnar axis,agreed substantially with NMR experiments that yielda diffusion coefficient, D⊥, of the order 10–14 m2 s−1.Along the columnar axis, the MSD indicates significantdiffusion which they concluded to be liquid-like slidingmotion between the columns.

Summarily, this work successfully simulates a repre-sentation of the liquid crystal order within a discoticsystem, which allows us an insight into the molecularconformation, positional and orientational order, andliquid-like flow within the columnar structure. Thisprovides an insight into the structural characteristicsof DLCs, upon which our understanding of dynamicsand charge transfer can be built up.

From a different perspective, Haverkate et al. [23] haveinvestigated the probabilistic distribution of DLC’s struc-tural parameters within a bulk DLC material: core–coreseparation (D), in-plane twist angle (θ), and lateral slidebetween the polyaromatic cores. They used MD simula-tions to predict structure and dynamics of DLCs usingforce-field methods. The force field was described by theLondon dispersion energy using Lennard-Jones function,using COMPASS in Materials Studio suite, which is ableto include cross terms in energy expression to account forbond and torsional distortions.

This work used a 72-all-atom supercell (12 × 6matrix), with 3.65 Å between molecules in a column,and 21.04-Å intercolumn spacing which agrees wellwith most other works [70] and the results were com-pared to powder NMR diffraction. The simulated aver-age equilibrium twist angle was between 36° and 38°,which correlated well with experiments. Positionalorder was correlated, and it was found that the lateraldeviation with respect to column axis was 2.5 Å orhigher, which indicated significant barrier to the

smooth charge transfer along the columnar axis. Theyalso noted that a competition between the van derWaals interactions of the cores, versus the steric repul-sion of the tails resulted larger distribution of core–core distances. For example, 35% were larger than3.7 Å and 20% were larger than 4 Å, compared to thewell established 3.6 Å intermolecular spacing. Spacingof more than 4 Å are considered as structural traps onthe picosecond time scale, and again provide a barrierto charge transfer. The effect of these variations in thevalues of the structural parameters have a direct impacton the charge transfer characteristics of the DLCs, asillustrated further in Section 2.4.2.

2.2.2. The potential energy surfaces approachEquilibrium states in liquid crystal position and orien-tation can be identified through the global energyminima of potential energy surface (PES) plots. Forexample, Chakrabarti et al. has used the PES approachto understand the relationship between orientationaland translational order in the calamitic mesophases.[71,72]

In the case of DLCs, PES was employed by Zbiriet al. through a DFT study on two stacked HAT6molecules to determine the most stable configuration.[65] The PES of two stacked molecules was describedin terms of its co-facial separation (D), twist angle (θ),and lateral slide (L) and its PES calculations werecarried out using Gaussian software. The exchange-correlation (XC) meta-hybrid functional PBE1KCISwas employed. This function includes a definedamount of the exact HF exchange combined with ahigh-level kinetic energy density. Through the PESapproach, they estimated a distinct energy minimumfor the equilibrium structure at D = 3.5 Å and θ = 30°when L = 0, which agrees well with other works.[73]

2.3. Modelling of DLC dynamics

2.3.1. Core and tail dynamicsA work by Mulder et al. combined QENS measurementswith MD simulations on the discotic molecule hexakis(n-hexyloxy)triphenylene (HAT6) in order to investigate thecore and tail dynamics of the molecule.[67] This workfocussed on the dynamics of HAT6’s polyaromatic cores,which play a key role in the charge transfer of DLCs. Amodel of a single HAT6 molecule was constructed, com-prising of a stack of four triphenylene cores each with thesix side chains of O(CH2)5CH3. The minimum energyconformations are shown in Figure 6. The use of a singleshort column eliminated the consideration of intercol-umn interaction, which was on a longer time scale. TheCOMPASS force field was used to optimise the molecular

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structure. Analysis was only carried out on one of thecentre cores, with its associated chains, for comparisonwith the QENS spectra, as this is seen to be mainlyresponsible for the charge transfer mechanism. The MDsimulation parameters were adjusted to fit to the EISFdata from QENS, as outlined in Section 1.3.1, where itwas found that a core–core spacing between 3.5 and 3.7 Åprovided the best fit in terms of the time scale comparedto the experimental time scale. The intermolecular chargetransfer was on similar time scales of the dynamics whichis dominated by van der Waals interactions. In addition,the EISF data (as shown in Figure 7) implied not only arethe dynamics of core and tails on different time scales, butthe whole molecule is moving in different dimensions ondifferent time scales.

Furthermore, the EISF data above 360 K (i.e. in theisotropic state) are shown in Figure 7, indicated thesame spectral components which are present inthe columnar phase, despite evidence that phase transi-tion had occurred. Thus, this interestingly suggests thatalthough the material has entered the isotropic phase,the positional correlations still exist on a time scalelonger than that measured by QENS. Structurallyspeaking, (i) the core–core and tail–tail van der Waalsinteractions drive the self assembly of the columns, and(ii) coupling between the tail and core motion is

instrumental to the alignment of the cores, and hencerigidity of the columns.

Comparison between MD simulations and QENSexperiments was also carried out by Haverkate et al.

Figure 6. (a, b) Illustrations of a minimum-energy orientation with the aromatic rings nearly sumperimposed. (c) and (d) wereminimised from a 45° phase difference between disks. Reprinted with permission from [67]. Copyright 2003 American ChemicalSociety.

Figure 7. Elastic structure factor at 336, 348, and 358 K (over-lapping solid lines at the top) showing Bragg peaks due toliquid crystalline ordering. The dashed lines (in the middle)without Bragg peaks at 368 and 378 K, and the dotted line(bottom) is for 433 K. Rigidity of column are shown at 336, 348,and 358 K because the peaks overlapping which indicate thestructure is rigid in that temperature range. Reprinted withpermission from [67]. Copyright 2003 American ChemicalSociety.

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to measure the temporal and spatial dynamics in theliquid crystalline phase.[23] They modelled an all-atomforce field system on hexagonal periodic supercell com-prising of 72 HAT6D molecules, which was comparedwith newton powder diffraction patterns and QENSdata. They showed that on the picosecond the tilt ofthe core was shown to be too fast to be followed by thetail. The tilt of the core shows an amplitude of 1.5°,whilst the overall tilt of the molecule remainsunchanged. In comparison, the translational motionof the core and tail are correlated, with comparableamplitudes of 0.1 and 0.15 Å. The directions of transla-tion are perpendicular and parallel to the column axis,respectively. On a 7-ps time scale, the rotationalmotion of the tail begins to follow that of the core.Correlation between the tail and core on the parallelmotion is weaker. They concluded that in-planemotion contributed most to the 0.2-ps QENS spec-trum, whilst on the 7-ps scale, both tilt and twist ofthe molecule contributed to the spectra.

2.3.2. Lattice dynamicsIn DLC systems, charge trapping arise due to the pre-sence of impurities, mostly from reactions with themetal electrode. In DLCs, structural defects are ableto heal over time. Typically, the time to heal, τd, is inthe range of 10–5–10–6 s, whilst τt, the transit time of ahole or electron across a distance d is ~10–3 s.[14] Themain scattering events involving the transit of chargecarriers in a discotic column is the oscillation of themolecule parallel and perpendicular to the director.[74]

For the DLC system in question, it is important todecide whether the system is defined as fully static orwhether there exists a significant dynamic contribu-tion. Olivier et al., through their MC modelling, haveincorporated a factor of lattice dynamics into system ofliquid crystalline phthalocyanine stacks.[75] Theynoted that even at high-driving fields, there exist situa-tions where there is negligible charge transfer, orcharge transfer against the direction of the appliedelectric field. This is thought to occur when the chargetransfer is momentarily blocked by a segment of thecolumn which acts as a defect, which will self-annealover time, as discussed earlier. In order to understandthe effect of these dynamic structural defects, latticedynamics was incorporated into the MC model fortwo different cases: (i) a frozen lattice motion and (ii)inclusion of fast thermal motions.

In the case where the lattice motion was frozen, thelifetime of the defect was considered to be infinite.Consequently, low mobility values for holes wereobtained, i.e. 3.12 × 10–3 and 2.92 × 10−3 cm2 V−1 s−1

in the rectangular and hexagonal mesophases,

respectively. These values actually corresponded quitewell to TOF measurements of similar PC molecules.On the other hand, a simulation incorporating fastthermal fluctuations averaged for each dimer over 650snapshots over a period of 65 ns. This model yielded ahole mobility about two orders of magnitude larger andcorresponds to the experimentally measured PR-TRMC technique (µ) 0.08–0.37 cm2 V−1 s−1. The dif-ference between the two models implies that there existmany dynamic structural defects along the columns.

Taking into consideration the molecular and latticedynamics described above, we are starting to build up arepresentation of how the MD of the DLC columnarsystem contributes to the charge transfer. Next, furtherconsiderations related to the electronic behaviour andcharge transfer specific to the DLC phase will bediscussed.

2.4. Modelling of DLC charge transfer

Charge transport in DLCs is either through bandedconduction or charge hopping, depending on the nat-ure of the polaron formed. Excess charge accumulationdistorts the surrounding medium and gives rise to apolaron. If electron motion that is sufficiently fasterthan the timescale of molecular vibrations, the latticedoes not have time to relax to the distorted geometrywhilst the excess charge remains on the lattice. In thiscase, the large polaron is dragged along with thecharge, causing an increase in effective mass and nar-rowing of bandwidth, i.e. the band structure is per-turbed. This band transport model has been discussedat length by Lever et al.[76] On the other hand, forslower electron motion, the lattice is able to relax to thedistorted geometry and this causes charge localisation(trapping) in the lattice. In this case, charge transfer isthrough phonon-assisted hopping. The phonon-hop-ping description suits many scenarios for DLCs andwill be the focus of discussion in the following sections.

On a final note, there a quantum tunnelling modehas also been proposed for binary mixtures of DLCs, inorder to explain intercolumnar charge transport ofbinary DLC mixtures. Given that binary mixtureshave been mentioned to stabilise the overall bulkDLC system through intercalation, a quantum tunnel-ling model has been proposed to explain the enhance-ment of charge mobility of such systems (which can bethree orders of magnitude higher than single DLCs).Wegewijs et al. have evaluated the tunnelling viabilityof binary mixtures based on three triphenylene deriva-tives and compared them against charge mobility mea-sured using TOF and PR-TRMC techniques.[74] Theyconcluded that the high-integrity columnar structure

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afforded by binary mixtures, together with long-rangealloy band structure contribute to the increased mobi-lity of the binary mixtures.

2.4.1. Thermally activated charge hoppingCharge hopping rates strongly depend on the chemicalcomposition and local molecular ordering of the liquidcrystal director, whilst the global charge carrier path-way is defined by the presence of defects and overallmorphology. Bässler et al. has written a comprehensivereview of the charge transport in DLCs modelledthrough MC simulations.[77] Charge transport is dueto a hopping mechanism, where charges jump frommolecule to molecule at a rate determined by its gov-erning parameters.

A theoretical description which relates the chargehopping in a columnar stack of DLCs, to the mobilityis described by Lemaur et al. [61] which will be dis-cussed in this section. They assumed charge hopping tobe localised and jumps from disc to disc in the stack.The charge hopping frequency is approximated to thefirst degree by semiclassical Marcus theory:

ket ¼ 4π2

h

� �t2 4πλkBTð Þ�0:5 exp � λ

4kBT

� �(3)

2.4.1.1. Charge hopping parameters. In this model,the system goes through a transition state where thetwo molecules involved in charge transfer assume iden-tical geometrical conformations in order for chargetransfer to occur.

The two main parameters which govern charge hop-ping are as follows:

(1) Reorganisation energy (λ), which is the sum of theinner reorganisation energy of the molecule (λi)and the reorganisation energy of the surroundingmedium (λs).[75] λi represents the energeticrelaxation involved with the conformationalchange of the molecule and radical ion whengoing from the neutral to ionised state. The alkylchains are generally substituted by hydrogenatoms since they have little impact on the chargehopping parameters. λs describes the change inelectronic polarisation of the surrounding mole-cules and their possible reorientations. It is gen-erally found that the packing density of the discshas a larger contribution to this parameter com-pared to the molecular structure.

(2) Intermolecular transfer integral (t) quantifiesthe electronic coupling between the molecules.

2.4.1.2. Computation methods. The reorganisationenergies were modelled at the DFT level using theUB3LYP functionals and a 6-31G(d,p) basis set.[78,79] The charge transfer integral, J, in its basicform, is calculated by the dimer model, which assumeszero spatial overlap between two adjacent molecules,and allows an approximation of the charge transferbetween the molecules given this condition. The chargetransfer integral for hole transport in such a situation isthen calculated from the energetic splitting of the twohighest occupied MOs (HOMO and HOMO-1) in asystem. These splittings are calculated using the semi-empirical intermediate neglect of differential overlap(INDO) Hamiltonian [80] based on the geometry-opti-mised conjugated cores at the DFT/B3LYP level.

However, in a columnar system, the dimer model isinaccurate, and a different approach is needed to modelthe large spatial overlap of the stacked discs. A pre-ferred way of doing so is using the fragmentedapproach through the Amsterdam DFT (ADFT) calcu-lations and the quantitative MO model. Symmetry-adapted orbitals of a stack of discotic molecules areemployed in ADFT. The charge transfer integrals andsite energies are directly obtained from the off-diagonaland diagonal matrix elements of the Kohn–ShamHamiltonian, respectively. A correction is then addedto account for the large molecular overlap of the mole-cules in a stack.

These DFT calculations have been carried out at thegeneralised gradient approximation (GGA) level usingthe newly developed asymptotically corrected exchangeand correlation functional SAOP (statistical average oforbital potentials) and an atomic basis set of Slater-typeorbitals of triple-ú quality including two sets of polar-isation functions on each atom (TZ2P basis set inAmsterdam density functional [ADF]).[81,82]

The mobility µ of the charge carriers within thestack can then written as

μ ¼ vF¼ Δx

FΔt(4)

with ν the net drift velocity of the charge carriers and Fthe amplitude of the electric field inducing the chargedrift. In an ideal columnar stack, Δx can be assumed tobe core–core distance, D; and Δt as the hopping time.

2.4.2. Examples of charge transfer modellingThe above approach has been verified by Lemaur et al.against the mobility values of a range of DLCs based ontriphenylene, hexaazatriphenylene, hexaazatrinaphthyleneand hexabenzocoronene derivatives, measured using thePR-TRMC technique.

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Similarly, Zbiri et al. has evaluated the charge trans-fer integrals in terms of separation (D), twist angle (θ)and lateral slide (L) using [65] the ADF. The GGA wasadopted, where the exchange contribution to GGA wasapproximated by the Becke gradient correction(Becke88) and the correlation part by the Perdew–Wang correction (PW91c).

Following on from their work on identifying equili-brium DLC structure parameters through the use of PESas described in Section 2.2.2, the spatial overlap integrals(S) and charge transfer integrals (J) were then evaluated asfunction ofD and θ, as shown in Figures 8 and 9. Both the

dimer and fragmented approach were used, and the out-comes compared. Evaluation of J as a function of θ differssignificantly between the fragmented approach and thedimer approach. There is significant difference betweenthe calculations from the fragmented and dimer approach,due to neglect of spatial overlap in the dimer approach.The maximum and minimum values of J from the frag-mented approach are 0.55 and 0.02 eV, whilst from thedimer approach they are 0.34 and 0.0 eV, respectively.

For variation of D, the value of J decreases exponen-tially with increased separation, D, until it reaches themonomeric zero overlap limit. In this work, amongstthe three parameters, D is seen as the limiting factor tocharge transfer. In addition, the effects of L, lateralslide on symmetry breaking and spatial overlap cansignificantly perturb the charge transfer process.

When D and θ are fixed at their equilibrium valuesof 3.5 Å and 30°, respectively, and a lateral slide isinduced in the model, it is observed that the changesin J are reflected by their local maximal and minima, asshown in Figure 10. This can be viewed in terms of theconstructive/destructive characteristics of the overlapas the molecule slides laterally. This is further sup-ported by the spatial overlap, where zero overlap willresult in zero charge transfer.

Charge transfer in phthalocyanines was studied byOlivier et al., through evaluation of the in-plane andout of plane tilt angles, β and τ, respectively.[75] Theyconcluded the following points:

(1) Tilt angle, β, between two adjacent stackedmolecules. The charge transfer integral wasshown to increase as function of β, due to the

Figure 8. Calculated CTIs (J) and their dependence on the twistangle θ obtained using the fragment approach (full circles) andthe dimer approach (open circles). The co-facial separation andthe lateral slide between two stacked HAT6 molecules are keptfixed at D = 3.5 Å and L = 0 Å, respectively. Reprinted withpermission from [65]. Copyright 2009 Springer.

Figure 9. Calculated CTIs (J) and their dependence on the co-facial separation D obtained using the fragment approach (fullcircles) and the dimer approach (open circles). The twist angleand the lateral slide between the two stacked HAT6 moleculesare kept at θ = 30° and L = 0 Å, respectively. Reprinted withpermission from [65]. Copyright 2009 Springer.

Figure 10. Calculated CTIs (J) and their dependence on thelateral slide (offset) L between the two stacked HAT6 mole-cules. The twist angle θ and the co-facial separation D are keptfixed at their equilibrium values, 30° and 3.5 Å, respectively.Reprinted with permission from [65]. Copyright 2009 Springer.

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increased proximity of the molecules upon tilt-ing, regardless of the distance created by thefurther ends of the molecules.

(2) In plane rotation angle, θ, shows a broad peak inthe charge transfer integral (CTI) between 60°and 120°, with a peak at 90°. This correspondsto an eclipsed conformation preferred by adja-cent PC molecules in order to maximise the vander Waals interactions between the saturatedchains. A marked difference was observedbetween the rectangular and hexagonal phases.A rotation in the rectangular phase was accom-panied by a lateral slide of the molecules; result-ing in a lower overall charge transfer integralcompared to the hexagonal phase. In compari-son, the hexagonal phase gives a rather isotropic2D map and nonzero probability for the cofacialconfiguration. This implies that the rectangularphase is more constrained compared to the hex-agonal phase.

Senthilkumar investigated the charge transfer integralsfor unsubstituted and methoxy- or methylthio-substi-tuted triphenylene derivatives, similar to the approachoutlined above by Lemaur et al. and Zbiri et al. Theyfound that the charge transfer integrals were highlydependent on the twist angle, θ, with a maximum ofalmost for θ =0° and a minimum of 0.1 eV, θ = 60°.The charge transfer integrals decreased with the dis-tance between the stacked molecules. The charge trans-fer integrals calculated for methylthio-substitutedtriphenylene from this work is approximately doublethat reported by Cornil et al.[83] This reasonable asCornil et al. used the dimer model to calculate theirCTI. They also suggested unsubstituted triphenyleneare most affected by lateral slide, compared to substi-tuted triphenylene, for which the effects are quite mini-mal. Their calculations also indicated that chargetransfer integrals and site energy fluctuations for meth-oxy- and methylthio-substituted triphenylenes werenot significantly different. This is in agreement withthe similar charge carrier mobilities of 0.002 and0.008 cm2 V−1, measured by PR-TRMC measurementson the Dh phase of hexyloxy- and hexylthio-substitutedtriphenylenes, respectively. In contrast, the low mobi-lity values measured by TOF measurements on alkoxy-substituted triphenylenes seem to match the results forlarge lateral slide and small charge transfer integral,which results in a low mobility of the magnitude of0.001 cm2 V−1.

Bag et al. used atomistic MD studies to evaluate thepositional and orientation characteristics, HBC corewith six pendant oligothiophene unit.[84] They also

evaluated the charge transfer characteristics of thismolecule based on the equilibrium structure, wherethe twist angle (θ) was 25°, but also that two adjacentHBC molecules in a stack are tilted by 5° with respectto each other. The HBC cores are also tilted at anaverage of 43° with respect to the column axis.

The HBC cores of the molecules formed a very well-ordered columnar structure and consequently, mobilityalong the column was high. Once the charge transferintegral was calculated, kinetic MC method was used tosimulate charge carrier dynamics and calculate mobi-lity, which was calculated to 0.23 cm2 V−1 s−1 in thisphase.

3. Modelling of electronic orbitals

So far, most of the discussion has been on the investigationof charge transfer models in DLCs, as it has a direct impacton chargemobility, and hence device application potential.Whilst valuable insight into the structure, dynamics andcharge transfermechanism have been achieved bymergingsimulation works with experimental results, there remainssome space for exploration. The information on the elec-tronic DOS, especially of π electron levels in DLCs are alsoof significant importance, especially in cases of chargeinjection from electrodes, and applications such as currentrectification and thermoelectricity.

Previously, Barlow et al. have used DFT to calculatethe frontier orbitals and reorganisation energies of theHAT derivatives which they synthesised.[85] This is aninteresting example where the investigation of molecularstructure, ionisation potential and electron affinities.Figure 11 shows the frontier orbitals for two of the struc-tures shown, and their calculations of the conformationalchanges due to oxidation and reduction of these mole-cules then led to their analysis on reorganisation energy.For these derivatives, they suggested that the ratherexothermic electron affinities, the ability for π-stackingof the orbitals and low intramolecular organisation ener-gies suggested by the DFT calculations indicated thepotential of these materials as for electron transport.

Interestingly, these calculations also indicated thatthe valence level orbital (HOMO) is spread over theoxygen atoms which bridge the core and alkyl chains.Thus, for certain conformational configurations of thecolumnar phase, oxygen atom position influences theC–C and C–O tail bond order. This also implies thatthe overlap of the HOMO over the bridging oxygenatoms confers an electronic role to the tails, in additionto stabilising the columnar phase.

Efforts to obtain an insight into the electronic con-figuration of DLCs through a combination of experi-mental and modelling works have been explored by

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Crispin et al. [86] In this work, experimental data fromangle-resolved ultraviolet photoelectron spectroscopy(ARUPS) has allowed insight into the electronic struc-ture. The photoemission process due to the ultravioletphotoelectron is much faster than the nuclear geometryrelaxation, and hence allows a direct probe into theelectronic states of the molecule. Quantum-chemicalcalculations on the isolated molecule, and in stacks of2–6 molecules are then correlated with the experimen-tal data to understand the π-electron delocalisation.The theoretical UPS spectra of the isolated moleculeand of stacks containing from two to six moleculeshave been simulated, based on the INDO semi empiri-cal HF method developed by Zerner and coworkers[87]). These calculations implied the creation of newelectron orbitals in the forbidden energy gap of theisolated conjugated core. This has been fully confirmedby the ARUPS experiments, and implies the formationof a quasi-band structure which extends over severalmolecules in the column.

4. Structural effect of DLC stacks on band gapand DOS

So far, it can be seen that there is a more establishedbody of knowledge with regards to molecular

investigations of charge transfer in DLCs, comparedto studies on the electronic orbitals. Recognising thisgap of knowledge with regards to electronic orbitals ofDLCs, and we investigate a multiscale approach toinvestigating the effect of DLC column parameters,namely spacing (D) and twist angle (θ) on the bandgapand DOS of the system.

We simulated an all-atom model of two stackedHAT6 molecules using the Materials Studio simulationpackage. The HAT6 molecule input (144 atoms) wasobtained by using benzene as basic building blocks forthe aromatic core and hexyloxy for the tails(R = OC6H13), as shown in Figure 12. The two HAT6molecules were stacked in a periodic unit, where thetwo geometry optimised molecules were superimposedso that the normal axis of the central triphenylene coreoverlap. No further geometrical optimisation applied tothe two stacked molecules. HAT6 dimer constructed isused to calculate the charge transfer in columnar DLC.Since electronic interaction only occurs at very closedistance, charge transfer in dimer is enough to repre-sent charge transferability as demonstrated earlier byZbiri et al.[65,88] The investigation of geometrical andenergetic stabilities of HAT6 were investigated usingthe density functional spin polarised calculations andPerdew–Burke–Ernzerhof (PBE) XC functional,[89–91]

Figure 11. Frontier orbitals calculated at the B3LYP/6-31G** level for molecule (a) (left) and (b) (right). Reprinted with permissionfrom [85]. Copyright 2007 Wiley-VCH.

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in which the functional provide great accuracy in widerange of system especially with well-established atoms(O, C and H).[92] The Kohn–Sham equation wasexpanded in a double numeric quality basis set (DNPver. 4.4) [93] with polarisation functions which shouldprovide accurate approximation until d orbital. TheDFT semi-core pseudo-potentials [94] were used forthe treatment of the electrons. Full details of the meth-odology are outlined in a separate publication.

Single point energy calculations were carried out toidentify the optimal core–core distances and twist ofthe stacked molecules, which were determined to be4.0 Å (for an initially untwisted stack), and a twistangle of θ = 25°. The equilibrium core–core distancesare slightly larger than those mentioned in literatures,[23,88,95] possibly due to the untwisted initial confor-mation of the system. The bandgaps of the stacks werethen calculated for a variation in core–core distance, Dand twist angle, θ. Tables 2 and 3 list the values ofbandgap as a function of D and θ, respectively.

Referring to Table 2, it can be seen that for lowercore–core distance, the bandgap is smaller, due to thelarger extent of π overlap at closer distances. However,

this is offset by the structural instabilities at these closerdistances. The trend of the DOS as a function of core–core distance is shown in Figure 13. It can be seen thatthe largest effect comes from the DOS of the p orbital,where the p-orbital electrons are the ones responsiblefor the transition into the conduction band. The con-duction band is also shifted to a higher energy level atlonger distances. The intensity of DOS at edge ofvalence band and conduction band are also strongerat larger distances. This may be explained by largerlocalisation of the electrons at larger distances, due tothe reduction of the π–π overlap. Similar trends for thed orbitals are also observed, but to a lesser extent, asthe d orbitals are considered to be virtual states forcalculation purposes. S-orbital electrons are unaffectedby distance, as they do not exist near the valence band.

Referring to Table 3, it can be seen that the band gapof the structure is smallest when the molecules did nothave any twist angle, and it has the largest gap when themolecules are at 60° which is the middle point of D3h

symmetry. This implies the band gap is directly affectedby alignment of the π overlap where it has the mostoverlap when twist angle 0°, and least overlap whentwist angle 60°. Referring to Figure 14, the change intwist does not have a significant effect on the overallDOS. However, interestingly, we found that peak ofDOS at both the valence and conduction bandincreased, which implies the electron localisation occursat both energy levels. In the s orbital, there are nocontributions towards conduction at band gap. Thevalence band is mostly occupied by states at p orbitals.We find that the more twisted the structure, the valenceand conduction band has higher peak which may implylocalised electrons at those bands. Here, we can deducethat misalignment of π overlap does not just broadenthe bandgap but also localises the electrons.

Figure 12. An all-atom model of two stacked HAT6 molecules.Variables to the stack structure are introduced in the form oftwist angle, θ, and core–core facial separation, D.

Table 2. Calculated band gap by varyingdistance at fixed twist, θ = 0°.Distance (Å) Band gap (eV)

3.0 0.0003.2 0.5033.4 1.0303.6 1.4273.8 1.7234.0 1.9354.2 2.0864.4 2.1944.6 2.2754.8 2.3325.0 2.372

Table 3. Calculated band gap by varyingtwist angle at fixed distance, D = 3.6 Å.Twist (°) Band Gap (eV)

0 1.42710 1.59720 1.87925 1.97330 2.05240 2.20150 2.26960 2.30170 2.26980 2.20190 2.05295 1.973100 1.880110 1.569120 1.427

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Through the work illustrated above, an importantunderstanding of the correlation between the struc-tural parameters of the DLC on the electronic DOSand bandgap can be understood. This, in turn, can bea starting point of investigation on tunability of theDOS for DLCs through refinement of the columnarphase packing. This is particularly important for ourinvestigations of DLCs as potential candidates forOTEs, and is projected to be useful for other scenariossuch as the orbital interaction between the DLC andelectrode material to study charge injection fromelectrodes.

5. Conclusions

In this paper, a bird’s eye view of the DLC structure,dynamics and electronics characteristics has beengiven. It gives an insight on molecular modelling as atool for understanding fundamental DLC behaviour,when treated in correlation with experimental data.Much effort has been expended to understand chargemobility in DLCs, given its potential as molecular wiresin molecular electronics applications, such as OPVs,OLEDs and OFETs. We propose that further under-standing of the electronic orbitals of DLCs may lead to

Figure 13. DOS of two stacked HAT6 at fixed twist, θ = 0° with a variation in separation distance. (a) Total DOS; (b) Partial DOS of sorbital; (c) Partial DOS of p orbital; (d) Partial DOS of d orbital.

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molecular engineering of DLC materials for diverseapplications such as thermoelectricity, organic magne-toresistance devices and current rectifiers.

Acknowledgement

Special thanks to Dr. Abhijit Chatterjee of BIOVIA for usefuldiscussion on DFT molecular approach. This work was sup-ported by the University of Malaya−Ministry of HigherEducation Grant under Grant UM.C/1/625/HIR/MOHE/ENG/29; Science Fund under Grant SF-020-2013;Fundamental Research Grant Scheme (FRGS) under Grant

FP011-2014A; and Universiti Malaya Research Grant(UMRG) under Grant RP023A-13AET.

Disclosure statement

No potential conflict of interest was reported by the authors.

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Figure 14. DOS of two stacked HAT6 at fixed distance, D = 0 Å with variation in twist angle. (a) Total DOS; (b) partial DOS of sorbital; (c) partial DOS of p orbital; (d) partial DOS of d orbital.

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