CrGrowthDesign-Palczynski-2014.pdf

Growth and Characterization of Molecular Crystals of para-Sexiphenyl by All-Atom Computer SimulationsKarol Palczynski,, Georg Heimel,, Jan Heyda, and Joachim Dzubiella*,,

Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, GermanyInstitut fur Physik, Humboldt-Universitat zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany

*S Supporting Information

ABSTRACT: We present all-atom molecular dynamicscomputer simulations of molecular crystals of the conjugatedorganic molecule para-sexiphenyl (p-6P), which constitutes apopular basic molecule for optoelectronic applications. Aftervalidating single-molecule properties with ab initio calculations,we demonstrate that gradually performed simulated temper-ature annealing leads to the spontaneous self-assembly of p-6Pmolecules from the fully isotropic state into the correct room-temperature solid crystal, with only a few percent deviationfrom the experimental unit-cell structure. A detailedinvestigation of the single crystal in anisotropic Gibbsensemble simulations yields experimentally consistent structures and solid to liquid-crystal phase behavior over a widetemperature range, providing molecular insight into nanometer-scale structural and dynamic properties of self-assembled p-6Pcrystals. This study thus paves the way for future investigations of the computational description of nucleation and growthmechanisms of novel p-polyphenylene derivatives in the bulk as well as at functional interfaces or heterojunctions.

INTRODUCTIONConjugated organic molecules (COMs) have been extensivelystudied in the last years for their optoelectronic properties andare currently employed as organic semiconductors in a widerange of applications, such as eld-eect transistors (OFETs),light-emitting diodes (OLEDs), or photovoltaic cells(OPVCs).1 Among those COMs, p-oligophenyls have attractedmuch attention due to their high thermal stability2 andquantum yield.3 In particular, the rod-like para-sexiphenyl orpara-hexaphenyl (p-6P; C36H26) is a well-characterized andwell-investigated representative of p-oligophenyls,46 whichself-assembles spontaneously into neat crystals and, due to itsblue electroluminescence emission, is useful in multicolorOLEDs or laser applications.611

A necessary prerequisite for the fabrication of electronicdevices is the deposition of a thin organic lm not only of well-dened morphology, but also with a specic molecularorientation.1214 Due to the anisotropy of the p-6P crystals,the energy-level alignment and optoelectronic properties arestrongly dependent on the detailed structure and orientation ofthe organic crystallites on a surface with great implications fordevice performances.6,11,15,16 In turn, the electronic propertiesand energy level alignment at the interfaces strongly depend onthe nature of the surface, which can be metal,1721 inorganicmaterials such as KCl22 or ZnO,23,24 or silica sheets.2527

Therefore, increasing eort is devoted recently to study theearly stages of epitaxial growth for a better understanding of theinitial nucleation events, characterized by critical clusterstructure and sizes16,2629 and diusion barriers.30 However,

atomic-level insights into the full dynamic nucleation and initialgrowth process of COMs are just beginning to be made.In principle, the appropriate tool to theoretically investigate

such dynamic nucleation and growth events is atomisticallyresolved molecular dynamics (MD) and stochastic dynamics(SD) computer simulations.3135 Much progress has beenmade here in the last years in the development and applicationof classical force elds to study, for instance, the structure oforganic solid crystals,3638 liquid crystals,3943 perylenedeposited onto self-assembled monolayers,44 pentacene growthon various surfaces,4548 oligothiophene structure on full-erenes,49 or step-edge barriers for a few small COMs includingp-6P.50 The accuracy of these kinds of simulations sensitivelydepends on the employed force eld, which nely tunes thebalance between intramolecular bond, angle, and torsionpotentials and intermolecular interactions such as van derWaals (vdW) and electrostatic potentials. The force elds aretypically benchmarked to ab initio calculations31,32,34,35,38 oroptimized empirically. In a few cases, computationallyexpensive force elds with explicit polarizability have beenemployed,38,50 although it is not fully understood for whichclass of molecules this is required for a correct structureprediction.For growth and nucleation studies, it would be highly

desirable that the force eld is good enough to provide a

Received: February 14, 2014Revised: June 11, 2014Published: July 23, 2014

Article

pubs.acs.org/crystal

2014 American Chemical Society 3791 dx.doi.org/10.1021/cg500234r | Cryst. Growth Des. 2014, 14, 37913799

spontaneously self-assembled room-temperature solid crystalfrom scratch, like in experimental reality, without anyadditional bias or assumptions in the simulated system.Apparently, this constitutes a big challenge for the currentsimulation methods due to the above-mentioned ne balancesbetween interactions required in the force elds. Another issuecould be the limited simulation time, which may not be longenough to let the strongly attractive molecules arrange intoordered positions. Only very recent contributions pushedforward by Zannoni and co-workers42,47 indicated that thisseems possibly feasible, at least for pentacene and sexithiophenemolecules: Muccioli et al.47 demonstrated that in progressivepentacene deposition on a C60 crystal the molecules self-assembled into crystal nuclei resembling the bulk crystalstructure but with deviations that might have originated fromsurface distortions or force eld imbalances. Pizzirusso et al.42

showed for the rst time by rapid cooling of an already orderedhigh temperature (liquid crystal) phase of sexithiophene thatthe latter spontaneously rearranged into an ordered solidcrystal-like structure at room temperature, consistent withexperimental densities and global orientations. Rapid coolingmeans here that the initial high temperature structure wasdirectly equilibrated at room temperature, so that cooling wasbasically instantaneous. The authors hypothesized that possiblya slower, that is, gradual cooling may likely lead to the correctroom-temperature solid crystal, but whether that is really thecase still awaits disclosure.In this work, we demonstrate that a simulated annealing

protocol of a well-balanced force eld, very similar to thatemployed previously for sexithiophene,42 is indeed capable ofproviding a spontaneously self-assembled room-temperaturesolid crystal of the archetypical conjugated organic molecules p-6P. Strikingly, we nd that such a cooling protocol works forrelatively high annealing rates, about 240 K/ns (0.24 K/ps),even if starting from the totally disordered, isotropic hightemperature gas phase. Furthermore, we give evidence that thesingle-molecule properties are consistent with quantumcalculations and that the high-temperature liquid-crystal phasesare consistent with the experimental phase behavior. Ourresults will be highly useful for future studies of growth andnucleation of p-6P on surfaces with various chemistry andtermination for a better understanding of the molecularstructure of heterojunctions in optoelectronic devices. Wealso anticipate that chemical derivatives of p-6P, for instance,those with highly polar head groups yielding interesting opticalproperties,51 can be successfully simulated for the prediction ofstructure in the early stages of deposition and growth.The equilibrium bulk crystal structure (so-called -structure)

of p-6P at room temperature is known.4,52 X-ray diractionmeasurements on single crystal thin lms at room temperature(T = 295 K) revealed that it crystallizes in the monoclinic P21/cspace group (with angles = = 90) in a herringbonestructure. For convenience of the reader, the -crystal structureis illustrated and described in Figure 1. Several polymorphs,that is crystalline mesophases, have been observed uponcooling and heating of the p-6P crystal, for example, high-temperature phase transitions occur at 713 K (crystalsmectic)and 748 K (smecticnematic).53 The molecules decompose ataround 773 K, before the anticipated nematicisotropictransition occurs at higher T.4

RESULTS AND DISCUSSIONSingle Molecule Properties. We rst briey demonstrate

that our classical force eld model reproduces variousgeometrical and energetic properties of an isolated p-6Pmolecule. For this we compare our MD results withquantum-mechanical approaches from density functional theory(DFT) calculations on the B3LYP/cc-pVTZ level as performedconsistently in this work (see Methods) and previous work.50

In Figure 2, the change of the total energy E(CC) of asingle p-6P, resolved by the torsion angle CC, is comparedwith the DFT calculations. The total energy consists of theintramolecular Coulomb and Lennard-Jones energies inaddition to the angular and dihedral potentials. All vetorsional angles in the molecule are set to the same value,though with alternating sign, using dihedral restraints.The MD result shows the correct functional behavior, that is,

a roughly parabolic E(CC) prole with a minimum energyat an intermediate angle of value 29.5 (cf. Table 1). Theoptimal (ground-state) twist angle, CC* , deviates by roughly

Figure 1. Schematic illustration of the experimental p-6P room-temperature -crystal structure: (a) view in the direction of themolecule long axis, (b) view perpendicular to the long axis, (c)illustration of the herringbone angle, H. The lattice parameters havebeen determined4,52 and are a = 0.809 nm, b = 0.557 nm, c = 2.624nm, = 98.2, and monoclinic angles = 90 and = 90 (notshown). All molecular long axes are parallel to each other. Themolecules possess a herringbone structure with a characteristic tiltangle of H = 66 between the molecular planes of two moleculesdening the base. The phenyl rings within each molecule are onaverage coplanar, though they undergo thermal torsional motion atroom temperature with respect to the single bonds between them. Thetorsional angles between two adjacent phenyl rings in the same p-6Pmolecule amount to approximately 20 in the crystalline phase at roomtemperature.4,52 The angle between the molecular long axis and thelayer normal (inclination angle) is reported to be = 18.

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67 from the DFT results, that is, approximately 20%. Theenergy dierence between planar and twisted states, Ept =E(0) E(CC* ) is also compared in Table 1 and shows adeviation of about 8 kJ/mol. Those numbers are within thetypical spread of values between results for biphenyls5457 andpolyphenyls58 from dierent quantum-mechanical approxima-tions, which are about 78 and 10 kJ/mol for the angles andenergies, respectively. Thus, our results are well within thespread of the more accurate quantum calculations. Given thecomplex interplay between the intramolecular interactions thatlead to that optimal (minimum-energy) angle,59 the MD resultcan be judged as satisfactory.In Table 1, we also compare the length of the long axis of a p-

6P molecule, in either a fully planar conguration or a twistedconguration, to results from DFT calculations on the B3LYP/cc-pVTZ level performed in this work (see Methods) andprevious work.50 The twisted conguration was chosen to bethe one corresponding to the energy minimum in the MD at atemperature of 1 K (i.e., the ground-state). Here we nd thatthe lengths calculated in the classical MD are in very goodagreement with the quantum calculations, deviating by less than0.6%.Thus, the comparison of a few structural features, that is,

length and twist angles, and the energetic behavior versustwisting, demonstrates that the single molecule properties of p-6P are suciently represented by our classical computer model.

The accuracy of the molecules structural features is anecessary prerequisite for the description of the detailedmolecular nucleation properties of p-6P crystals. We will showin the next sections that the p-6P intramolecular properties arewell enough suited for reproducing the room temperaturecrystal structure as well as the right high-temperature phases inthe right sequential order.Annealing and Crystal Growth from Scratch. We

now demonstrate the ability of the force eld to reproduce thenatural self-assembly of p-6P molecules from scratch, that is, welet them self-associate by temperature-annealing from the hot,isotropic gas phase to room-temperature conditions. Inparticular, a system of N = 200 isotropically distributed p-6Pmolecules (cf. Figure 3) is cooled from 1500 to 300 K in thecanonical (NVT) ensemble at a linear rate of 0.24 K/ps (seeMethods). These runs are repeated 10 times to gather sucientstatistical data. While the system temperature decreases, themolecules start to nucleate forming many small clusters. Overtime, the clusters assemble into one big cluster very similar to aself-assembled monolayer with a strong tendency for forming aregular crystal with herringbone structure. A snapshot of a nitecrystal cluster at T = 300 K is shown in Figure 3. Panel edemonstrates the nucleation process through snapshots of thesystem taken at several temperatures. Nucleation occurs whendensity uctuations in the molecule gas (T = 850 K) lead to thecreation of a few nuclei of critical size where other moleculesattach to due to oversaturation (T = 800 K). Further coolingresults in ordered, crystal-like structures, which merge andgrow.In order to investigate the structural order on a more

quantitative level, we make use of two order parameters, theusual nematic order parameter, S(T), to probe for orientationalorder of the long axes,60 as well as a herringbone orderparameter, (T), introduced earlier.61 For convenience of thereader, both parameters are briey discussed in the SupportingInformation. The T-dependent ensemble-averaged orderparameters are presented in Figure 3. During cooling, thenematic order starts a steep ascent at T = 750 K, apparentlycorresponding to an isotropicnematic phase transition, until itsaturates below 580 K with an average value of 0.8. Belowapproximately 650 K, a herringbone structure slowly emanatesfrom the lateral molecular interactions and increases con-tinuously up to 0.4. Higher values of this order parameter donot occur due to thermal uctuations and surface eects. As canbe seen in the snapshots in Figure 3, due to those surfaceeects, the crystalline alignment at the outer rims of the clusteris bent and distorted. The molecules in the centers of the

Figure 2. Change of the total energy of a single p-6p as a function ofthe torsion angle CC between the neighboring phenylene rings at theground state. The plot compares MD using GAFF with DFTcalculations for p-6P on the B3LYP/cc-pVTZ level. All ve torsionalangles were constrained to the same value with alternating sign.

Table 1. Comparison of Structural and Energetic Properties of an Isolated p-6P Molecule between Planar Structure and aTwisted Conformation with a Minimum-Energy Anglea

model Lplanar [nm] Ltwisted [nm] Ept [kJ/mol] CC [deg]

PBEPBE/6-31G(d,p) (DFT)50 2.472 2.453 31.9 35.7B3LYP/cc-pVTZ (DFT) 2.457 2.438 32.7 36.8GAFF (MD) 2.472 2.455 26.3 29.5

aL is the distance between terminal carbon atoms, Ept is the internal energy dierence between a planar and a twisted p-6P, and CC is the twistangle at which the internal energy is minimal. Compared are two DFT methods to a MD minimization at 1 K. For the MD and B3LYP/cc-pVTZcalculations, all ve torsional angles in the molecule were constrained to the same value, though with alternating sign. The values from previouswork50 are averaged over slightly diering angles.

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grown crystallite are least aected by the surface and alignthemselves in a well-dened herringbone structure. Thus,remarkably, the classical force eld captures the right balancebetween vdW and electrostatic interactions, leading to well-equilibrated herringbone structures at room temperature, asobserved in experiments. Apparently careful annealing isimportant to allow for the necessary rearrangement times tond the lowest free energy conguration, in contrast to an

instantaneous cooling.42 In the next section, we will investigatethe single crystal without surface eects in more detail.The Single-Crystal: Structure, Unit Cell, and Phase

Transitions. In order to properly characterize the structure ofthe grown crystal from the canonical (NVT) annealingsimulations, we cut a representative nanocrystal subset (seeMethods) composed of 4 6 1 = 24 molecules out of thecenter of the grown crystallite. The molecules in thisnanocrystal have an inclination angle = 30 and distancesin a and b direction of 0.866 and 0.563 nm, respectively. Fromthe nanocrystal, we create a periodic crystal by replicating thisstructure 4 4 4 times in all three directions. Thesehomogeneous single crystals are then used in Gibbs ensemble(NPT) simulations with N = 1536 molecules (or na = 12 nb =16 nc = 4 unit cells).The nal unit-cell parameters such as lattice lengths, angles,

and the mass density at room temperature are calculated as anensemble average over the equilibration period at T = 300 K.The results and their respective standard deviations (comingfrom the temperature and pressure uctuations) are summar-ized in Table 2 and are compared with the experimentalvalues.4 There we see that the density is very well described bythese calculations. The angles and vary by 6% and 4% fromthe 90 angles typical for monoclinic cells making the structurepossibly triclinic; the standard deviations of and , though,justify a monoclinic assignment. The monoclinic angle is onaverage 3.2 higher than in the experiments, and the inclinationangle diers by only 0.3. The a-, b-, and c-axis results deviateby 1.9%, 2.4%, and 1.1% respectively. The herringbone angle His 4.3 lower than in the experimental crystal, and the averagedtorsional angle CC in the crystal is lower by 4.3 than what isknown from literature,4 which in itself is only an approximation.The deviations are smaller than previous unit-cell predictionsby classical force elds of biphenyl62 and p-terphenyl63,64 andcomparable to the best results for oligothiophenes,36,37,42 eventhough the latter calculations started already from theexperimental crystal structure and not from self-assembledcrystals. Our deviations are also comparable to the best resultsin the latest crystal structure prediction blind test38 of organicmolecules. Thus, our results for the unit-cell structures areindeed satisfying.The thermal uctuations of the lattice parameters at room

temperature are relatively small, typically less than 2%, asindicated by their standard deviation also given in Table 2.Only the thermal uctuations of the herringbone angle, H,exceed values of about 20%, which originate from the torsionallibrations of the single molecules as detailed below when wediscuss the T-dependence of the crystal structures.We have further performed discrete temperature simulations

at elevated temperatures to characterize structural phasetransitions of the periodic p-6P bulk crystal. The studiedtemperatures range from 520 to 860 K roughly in 10 K intervalsfor 1020 ns each, depending of their state of equilibration. Anappropriate and sensitive measure for phase transitions is theisothermal heat capacity, which is the change of the enthalpywith temperature Cp(T) = H/T = U + pV/T.Corresponding to dierential scanning calorimetry data of p-6P herringbone systems,4,65 various peaks in the heat capacityindicate transitions where the overall structure undergoes aconsiderable change. The results are presented in Figure 4a:The initial room-temperature phase does not change muchupon heating until T = 587 K is reached. Between T = 587 Kand T = 596 K, a signicant characteristic change in the density

Figure 3. Nematic order parameter S(T) and herringbone orderparameter (T) as a function of the system temperature T averagedover 10 annealing runs. Errors are estimated from a standard deviationover the 10 independent simulation runs at xed T. Insets: (a)Snapshot of crystalline clusters at T = 300 K with N = 200 moleculesafter annealing. (b) Snapshot of the starting conguration for theannealing simulations. (c, d) In the crystalline clusters after annealing,adjacent molecules are usually shifted along their long axis in analternating fashion (c) or continuously (d). Sometimes bothconformations appear in the same molecular cluster. Since structured has lower potential energy per molecule, has a higher rate ofoccurrence, and is in accordance with the -phase from ref 4, it is usedas initial conguration for the NPT simulations. (e) Snapshots of thenucleation process with respect to T.

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distribution along the nematic director (cf. Figure 4c) pairedwith a very subtle change of the nematic order (cf. Figure 4b),are indicative of a phase transition from a smectic-C

conformation to a smectic-B (smCsmB) structure. This isclearly conrmed by the trajectory snapshots in Figure 4e,which primarily show that the average inclination angle

Table 2. Crystallographic Data of P-6p Calculated in the Room-Temperature Herringbone Phase from Npt EquilibrationSimulations at T = 300 K. The Error Of These Values From Block Averaging Is Less Than 1%. The Middle Row Denotes TheStandard Deviation of These Values Due to Thermal Fluctuations. The Bottom Row Shows the Experimental Results for the -Phase.4

a [nm] b [nm] c [nm] [deg] [deg] [deg] [deg] H [deg] [g/cm3] CC [deg]

simulation 0.827 0.548 2.668 90.1 101.4 89.8 17.7 61.7 1.295 15.7standard deviation 0.016 0.013 0.03 5.5 6.0 3.3 6.0 13.7 0.02 7.9experiment 0.809 0.557 2.624 90 98.2 90 18 66 1.3 20

Figure 4. Characterization of the p-6P single crystal in the NPT ensemble simulations. (a) Heat capacity as a function of temperature. Transitions aresmectic-C smectic-B (smCsmB), smectic-B smectic-A (smBsmA), where the two-dimensional herringbone vanishes, and smectic-A nematic (smAnem). Transitions from experiments are indicated using the relative positions of the corresponding peaks.4,53 (b) Nematic orderparameter, S(T), and herringbone order parameter, (T), as a function of the system temperature T. Insets: Snapshots showing the herringbonestructure at room temperature (left) and in the smA phase (right). (c) Density distribution along the nematic direction. The 18 tilt angle is thecause for the low amplitude in the density wave of the smC phase (solid red line). As the tilt angle decreases, the amplitude becomes higher and thewaveform becomes sinusoidal. When the smectic plane becomes increasingly blurry due to stronger temperature uctuations the amplitude decreaseswhile keeping its sinusoidal waveform. (d) Average torsional angle av = of an exemplary p-6P molecule from inside the crystal versustemperature. The light-blue shaded area depicts the corresponding average uctuations av2 = 2 2. (e) Simulation snapshots of the crystallinephases of p-6P.

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between the layer normal and the long molecular axis decreasesfrom its -phase value (18) to an average of 0. Between T =665 K and T = 677 K, a quasi-rst-order structural transitionoccurs with a clear discontinuity in the herringbone order(Figure 4b). Naturally, a slight decrease of the nematic orderparameter at this point coincides with the newly gainedrotational freedom of the individual benzene rings. The smecticplanes, even though becoming progressively blurry, still remaindistinguishable. To sum up, the system undergoes a transitionfrom a smectic-B to a smectic-A state (smBsmA). From T 730 K upward, the system becomes purely nematic (smAnem). The smectic planes become indistinguishable as can beseen in the density distribution along the nematic director aspresented in the bottom of Figure 4c.As shown in Figure 4a, the sequence of the phase transitions

is consistent with available experimental data.4,53 The calculatedtransition temperatures are within tens of kelvins of theexperimental reality. One should keep in mind, however, thatthe nite-size simulations are not properly sampling thethermodynamic limit (N ) and employ cut-os for thelong-ranged dispersion attraction, so that the optimization ofexact phase transition temperatures is in general system-sizeand methods dependent. Such a sensitive behavior is knownalready for simple Lennard-Jones systems,66,67 where thoseeects can easily lead to deviations in the tens of kelvins, andhas been also observed for the organic molecule sexithio-phene.42 Furthermore, deciencies in the intramolecularpotential of the single molecule and lack of electronicpolarizability also translate in the phase transition temperaturesbeing incorrect. Hence, given the sensitivity of the exactlocation of phase transitions to the underlying interactions andmethods, the transition temperatures in the simulation, whichdeviate by less than 70 K from experiments (less than 12%), aresatisfactorily described for the focus of this study but still leavesome room for improvement. With our results as a reference,further superne-tuning of the standard force eld employedhere may allow optimization also of the exact transitiontemperatures. The remarkable fact remains that the crystalstructure and phase order are correctly reproduced by thisclassical approach.Due to the structural changes, the average torsion angle of

the p-6P molecules in the crystal and its uctuationsconsiderably change with varying temperature as shown inFigure 4d. At room temperature, the molecules are squeezedtogether and the angle is about 20 5, in agreement withexperimental measurements.4 For higher T, the average valueand its uctuations increase up to 38 18. In a single-angletrajectory, 180 ips of phenyl groups are observed in thesmectic-A and nematic phases (not shown) in accord withexperiments.4 The ips express themselves in increaseductuations of the angle as shown by the light-blue shadedarea in Figure 4d. This analysis is an example for the detailedatomic-level structural insight into the (liquid) crystal structureof COMs provided by SD computer simulations.As previously shown,42 MD and SD simulations also allow

the investigation of dynamic details, important to study andunderstand the diusion-controlled growth kinetics of crystals.The structural change of the crystal at high temperatures, forinstance, has consequences on the (anisotropic) diusionbehavior of the molecules. Results for the long-time self-diusion constants perpendicular and parallel to the nematicdirector, D = (Dyy + Dzz) and D = Dxx, respectively, calculatedfrom the Einstein relation

=

Dt

r t rlim12

dd

( ( ) (0))iit

i i2

(1)

for the Cartesian coordinates i = x, y, z are presented in Figure5. At low temperatures (below 670 K), the diusion is very

slow. However, the diusion coecients start to rise in the smAregime, due to the increase in degrees of freedom. Collisionsbetween more freely rotating rings of neighboring moleculesapparently lead to a slight domination of the diusioncoecient perpendicular to the nematic director, D, over itsparallel counterpart, D = Dxx, in the region 670 T 700 K.This turns around at T 700 K, where the then faster paralleldiusion D is consistent with the more nematic nature of thesystem at temperatures above 700 K. The typical time scale fora p-6P molecule to diuse over its length ( 2.5 nm) is on the10 ns scale in the smectic-A phase and on the 1 ns scale in thenematic phase.

CONCLUDING REMARKS AND OUTLOOKIn summary, we have demonstrated that classical atomisticcomputer simulations using a well-balanced nonpolarizableforce eld and a careful simulated cooling protocol can beemployed to grow molecular crystals of p-6P molecules withthe experimentally observed structure and morphology for awide range of temperatures. The success of this method relieson amplifying the structural signal of the NVT coolingsimulations by performing NPT simulations for periodicstructures built by replicating suitably chosen noncrystallineseeds. The good performance of the method may come fromthe fact that in nanocrystals internal defects anneal out veryquickly.Those simulations provide a detailed microscopic insight into

molecular structure and dynamics of nuclei and crystals ofCOMs. Thus, our present work constitutes a necessaryprerequisite for the future study of nucleation and growth byMD and SD simulations of poly(p-phenylene) oligomers onvarious surfaces, for example, metal, organic, or inorganicmaterials, which is currently still unfeasible with computation-ally more expensive quantum-mechanical methods. Thecontrolled growth of functionalized derivatives of poly(p-phenylene) oligomers on inorganic materials is particularlyinteresting for tailoring novel optoelectronic properties ofhybrid inorganicorganic interfaces by morphology changes.24Functionalization could include, for instance, the addition of a

Figure 5. Long-time self-diusion coecients calculated using theEinstein relation, eq 1. While Diso = (Dxx + Dyy + Dzz) is the usualisotropic diusion constant, D and D are the ones perpendicular andparallel to the nematic director.

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dipole moment to couple to local electrostatic surface elds.23

It is not safe to assume, though, that the annealing/coolingstrategy introduced in the present study should generally workwith functionalized molecules. It is generally expected thatmolecules that are not rigid would be dicult to crystallizebecause of their entropic contributions to the eectiveinteraction potentials. p-Sexiphenyl is a molecule with vibra-tional and rotational degrees of freedom, composed of exiblybound benzene rings. The entropic contributions are still muchlower than in molecules with functional groups, side chains, andthe like. Under those circumstances annealing and conse-quently modeling of crystallization might be signicantly morechallenging, and more advanced techniques (compared withannealing) might be required.A type of such a functionalized p-6P-based COM could be

created by the exchange of two meta-hydrogens of one phenylheadgroup in a p-6P with uorine to a diuorinated p-6P (p-6P-2F). Such a relatively simple mutation creates a strong dipolemoment along the long p-6P axis with an anticipated signicantimpact on self-assembly and optoelectronic properties. Ourpreliminary simulations indicate that the room-temperaturecrystal is also a herringbone as shown in Figure 6. However, we

observe that the unit cells are substantially deformed (morethan 10% in the cell length c) and also 2D dipolar domains witha small correlation length can be found. Details on theseinteresting insights into the new properties of solid crystalsfrom polar COMs will be presented in future work.

METHODSMolecular Dynamics Computer Simulations. Our systems are

simulated on an all-atom level using the Gromacs simulation package68

(version 4.5.5) in combination with the generalized Amber force eld(GAFF) for organic molecules.35 Details about the Hamiltonian of thisforce eld applied to p-6P can be found in the Supporting Information.The partial charges are calculated using the Gaussian 09 software69 byemploying the B3LYP functional with the cc-PVTZ basis set using theelectrostatic potential tting method (ESP).70 They are explicitly listedin the Supporting Information. We wish to stress that the GAFFparameters are used without any alterations or adjustments. Thepartial charges were rounded to two digits only for convenience. Theexact, Gaussian-calculated partial charge values and the values used inthe simulations are provided in the Supporting Information.

The simulations are performed either in the canonical (NVT) or inthe Gibbs ensemble (NPT) with a constant number of molecules N,

constant temperature T, and either constant volume V or constantpressure P, respectively. The temperature is held constant by amodied Berendsen thermostat with stochastic velocity rescaling71 anda relaxation time of 10 ps. In the NPT runs the pressure is set to 1 barusing either a ParrinelloRahman or a Berendsen barostat with acoupling time constant of 10 ps and anisotropic pressure scaling andtilting (see Supporting Information for details) to allow for conformityof the periodic crystal. To avoid the ying ice cube problem, thetranslational and angular motion of the systems with respect to theircenters of mass is being removed in every step.72 The moleculartrajectories are integrated using the leapfrog algorithm with astochastic integrator for a smoother phase-space sampling (seeSupporting Information). A time step of 1 fs is used in the NVTsimulations and 2 fs in the longer and more time-consuming NPTruns. Particle Mesh Ewald is used to calculate long-range electrostaticinteractions. The cuto lengths of van der Waals and real-spaceelectrostatic interactions are set to 2.0 nm in the NVT ensemble and1.0 nm in the NPT simulations. The number of simulated moleculesranges from N = 1 for single-molecule characterization to N = 200 forthe NVT nucleation and up to N = 1536 for the NPT bulk-crystalmelting.

The NVT simulations are performed in a cubic box with a sidelength of 15 nm each using periodic boundary conditions. The initialisotropic structure consists of a set of N = 200 randomly distributed p-6P molecules with a Maxwell velocity distribution. The system is rstenergy-minimized using a steepest descent algorithm. The crystal-lization process is explored by using temperature annealing and anequilibrium simulation for a total period of 6 ns: the runs always startwith a temperature of 1500 K and are then cooled using the standardGromacs simulated-annealing protocol to a nal temperature T = 300K within a time span of 5 ns. Finally, 1 ns serves as additionalsimulation time to gather desired statistical data at 300 K.

After that, NPT simulations of well-dened periodic crystalstructures with unit cells extracted from the previous NVT simulationsare performed. The representative molecules taken from the NVTsimulations can be chosen either by number, that is, the most oftenoccurring unit cells (indicating a lower free energy during annealing),or by the potential energy values of their respective molecules. In oursimulations, most neighboring molecules are shifted by half a benzenering along their long molecular axes in a continuous fashion resultingin a nonzero inclination angle between the long axis and the layernormal (see Figure 3c,d). Only in a few cases adjacent molecules areshifted in an alternating fashion with an average inclination of zero. Atthe same time, the potential energy per molecule is slightly lower inthe nonzero inclination structure than in the other one. Given thesecircumstances we decide to use the nonzero inclination structure asstarting point for the NPT simulations. It is worth noting that thesubset taken from the NVT results only consists of one single layer inthe direction of the long molecular axis. In order to avoid biasing the cparameter of the unit cells in the forthcoming NPT runs, we leave 0.5nm space between each of the replicas along their long axis thusassuring that the molecules are given the chance to move into theirpreferred minimum energy conguration. An energy minimization ofthe initial periodic structures followed by an NPT equilibration at T =300 K at 1 bar using a ParrinelloRahman barostat returns theequilibrated room-temperature unit-cell structure. (A comparison of aParrinelloRahman barostat to a Berendsen barostat returned thesame structure with very similar values, see the SupportingInformation.) To study the phase behavior of the p-6P bulk crystal,we equilibrate the periodic bulk crystal at various discrete temperaturesranging from 520 to 860 K roughly in 10 K intervals for 1020 nseach, depending on the state of equilibration. The pressure is set to 1bar and is controlled using a Berendsen barostat. When we attemptedto run the simulations with a ParrinelloRahman barostat, stronganisotropic pressure uctuations at temperatures above 600 K(possibly due to the nite system size) caused the simulation box totilt so strongly that the shortest box length became shorter than theinteraction cuto length. In addition, the box became incommensu-rable with the structure of its contents. Such instabilities at hightemperatures do not occur with the Berendsen barostat.

Figure 6. Snapshot of a self-assembled equilibrated crystalline clustercomposed of diuorinated p-6P (p-6P-2F) molecules after annealing toroom temperature. The pink atoms depict the uorine.

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Single Molecule Potential Energy. The internal potential energyE of a p-6P molecule equals the sum of (i) bond, (ii) dihedral, (iii)angular, (iv) Lennard-Jones (van der Waals), and (v) Coulombpotential, via

= + + + +E E E E E Ebond dihed ang LJ Coul (2)The potentials i and ii represent the tendency of a -system to

achieve the highest possible conjugation, whereas iii and iv reproducethe mutual repulsion of the ortho-hydrogens.59 These interactionshave direct consequences on the internal structure of the molecule:they determine the twist angles between the planes of adjacentphenylene rings as well as the lengths of the bonds between the ringsand thus the length of the molecule as a whole. These quantities havebeen thoroughly analyzed previously50 using a wide variety of DFTand MD methods.

The total internal energy given in eq 2 and the spatial length of thelongest axis of the molecule are calculated using the GAFF force eldsfor several torsional angles by energy minimization at 1 K (groundstate). For this, the torsional angles CC are constrained using aharmonic dihedral potential. The length of the molecule is directlytaken from the nal conguration. The corresponding internal energy,E(CC), is calculated as in eq 2. For comparison to more accurateDFT calculations, this energy is also calculated using the Gaussian 09software69 by employing the same B3LYP functional with the cc-PVTZ basis set as for the partial charge calculations above.

ASSOCIATED CONTENT*S Supporting InformationTechnical details about the simulations methods, force elds,and order parameters. This material is available free of chargevia the Internet at http://pubs.acs.org.

AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing nancial interest.

ACKNOWLEDGMENTSWe gratefully acknowledge nancial support from the DeutscheForschungsgemeinschaft (DFG) within the CollaborativeResearch Center (CRC) 951 Hybrid InorganicOrganicSystems (HIOS). J. Heyda and J. Dzubiella thank theAlexander-von-Humboldt (AvH) Stiftung, Germany, fornancial support. We are grateful to Sabine Klapp, FritzHenneberger, Norbert Koch, and Stefan Kowarik for inspiringdiscussions, and we wish to particularly express our thanks toNicola Kleppmann and Thomas Heinemann for helpfulcomments.

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