Volume 10 | Number 8 | 7 August 2008 | Pages 923–1092

HIGHLIGHTBrillante et al.Probing polymorphs of organic semiconductors by lattice phonon Raman microscopy

HOT ARTICLEZheng et al.An unusual metal–organic framework showing both rotaxane- and cantenane-like motifs

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CrystEngComm

HIGHLIGHT www.rsc.org/crystengcomm | CrystEngComm

Probing polymorphs of organic semiconductorsby lattice phonon Raman microscopyAldo Brillante,*a Ivano Bilotti,a Raffaele Guido Della Valle,a Elisabetta Venutia and Alberto Girlandob

DOI: 10.1039/b804317e

Using micro-Raman techniques to investigate crystal polymorphism is an efficient method,capable of monitoring physical modifications and phase inhomogeneities in crystal domainsat the micrometre scale. In the presence of polymorphism, phase mixing is a commonoccurrence which becomes a crucial issue in structured organic materials tailored forapplications in molecular electronics and photonics. A good phase homogeneity is, in fact,required for optimal and reproducible device performance. We tackle the problem ofpolymorphism in organic semiconductors by combining experimental and theoreticalmethods. Experimentally we have found that different crystalline polymorphs may beconveniently investigated using their Raman spectra in the region of the lattice phonons,whose frequencies probe intermolecular interactions and are very sensitive to differences inmolecular packing. We propose lattice phonon confocal micro-Raman mapping as a fast andreliable diagnostic tool for in-situ characterization of the phase purity. The theoreticalapproach aims to predict crystal structures and possible coexistence of polymorphs by rankingthem in energy and proving that the deepest calculated minima actually correspond to theexperimental X-ray diffraction structures of bulk crystals. This combined spectroscopic andtheoretical approach to the dynamical properties of a crystal lattice provides a unique body ofinformation on crystal structure recognition of molecular crystals.

Introduction

Polymorphism occurs when the same

chemical compound exhibits two or more

Aldo Brillante

Aldo Brillant

University of

D. P. Craig

appointed in

(San Jose) a

project. He w

University of

Stuttgart. He

at the Univer

many aspects

thin films and

elementary e

plasmons and

and spectros

polymorphism in organics and its applicati

electronics. He is author of 125 scientific articl

aDipartimento di Chimica Fisica e Inorganicaand INSTM-UdR Bologna, University ofBologna, Viale Risorgimento 4, Bologna,I-40136, Italy; Fax: +39-051-2093690; Tel:+39-051-2093714bDipartimento di Chimica GIAF and INSTM-UdR Parma, University of Parma, Parma,I-43100, Italy

This journal is ª The Royal Society of Chemistry

crystalline modifications1,2 and is quite

common in organic molecular materials

where molecules are held together by

non-directional, weak Van der Waals

forces. The increasing interest of material

engineering in the development of new

electronic devices based on organic semi-

conductors3–5 has raised attention to this

subject for organic materials.

Organic semiconductors, such as

acenes, oligothiophenes and rubrene have

the potential to challenge silicon based

e graduated in Industrial Chemistry at the

Bologna. Former postgraduate student of

(Australian National University), he was

the mid 70s by IBM Research Laboratories

s Postdoctoral Fellow in a surface science

as involved in many research projects at the

Dusseldorf and the Max-Planck-Institut

is presently Professor of Chemical Physics

sity of Bologna. His research activity spans

of spectroscopy of molecular crystals and

has been mostly dedicated to the study of

xcitations in solids (excitons, phonons,

polaritons) and to high pressure chemistry

copy. He is currently studying crystal

ons to molecular materials for organic

es on international journals.

2008

semiconductors with the goal of making

devices that, although not efficient as

those silicon-based, are cheap and offer

the advantage of flexibility and large area

integration.6–8 Whereas only extremely

high chemical purity is required for

silicon, also good phase homogeneity is

necessary for organics. The control of the

polymorphism has therefore become

a crucial issue in structured organic

materials tailored for applications in

molecular electronics and photonics such

as field-effect transistors, light emitting

diodes, photovoltaics, etc.3,9 Indeed, even

though the system is otherwise chemically

pure, polymorphism may easily yield

phase mixing, and thus constitute an

intrinsic source of disorder with detri-

mental effects on charge transport and

other key properties.6,10 Although less

considered than chemical contamination,

phase inhomogeneities may be wide-

spread, because the intrinsic molecular

properties of the organic semiconductors

seem to facilitate the occurrence of

different polymorphs. The ideal organic

semiconductor is, in fact, characterized by

high p conjugation and by extended

transfer integrals, which are both required

to lead from isolated molecules towards

CrystEngComm, 2008, 10, 937–946 | 937

molecular wires or planes. These

requirements favor electronic delocaliza-

tion and are encountered with quasi-

planar structures, presence of functional

groups and large molecules. Large and

flexible molecules, kept together by weak

non-directional forces, are expected to

exhibit many alternative packing

arrangements, with small differences in

structure and energy, leading to poly-

morphism. Even these small differences

may affect the narrow band structure of

organic semiconductors, as well as other

important physical properties, such as

electron–phonon coupling.

Chemical purity and phase homoge-

neity (i.e., physical purity) are then both

required for optimal and reproducible

device performance, effectively ensuring

that the performance parameters are due

to the intrinsic properties of the material.

In this paper we show how poly-

morphism can be successfully recognized

by using Raman spectroscopy in the

region of lattice phonons, which represent

the fingerprint of the individual crystal

lattice. Distinctive spectral patterns

consistent with the different X-ray

diffraction (XRD) data are readily

obtained. Furthermore, the possibility of

interfacing optical microscopy to Raman

spectroscopy permits a careful discrimi-

nation among different polymorphs of an

organic molecular crystal. This yields

important information on phase homo-

geneity in crystal domains whose size is

less than 1 mm.

Finally, an account on theoretical

polymorphs and crystal structure predic-

tion is given, showing that the deepest

calculated minima actually correspond to

the experimental XRD structures of bulk

crystals. This combined spectroscopic

and theoretical approach to the dyna-

mical properties of a crystal lattice

provides a unique body of information on

crystal structure recognition of molecular

crystals.

Raman spectroscopy and crystalstructure

It is well established that Raman

spectroscopy is a valuable tool for non

invasive, in situ recognition of molecular

identity and conformation. However,

when polymorphism occurs in molecular

crystals, the chemical identity in the

different crystal phases implies very

938 | CrystEngComm, 2008, 10, 937–946

similar or identical spectra for the intra-

molecular vibrational modes of different

polymorphs. One should then focus one’s

attention on intermolecular modes, i.e.,

collective translational or rotational

motions of the molecules in the unit cell.

These modes produce dynamical defor-

mations of the crystal lattice called lattice

vibrations or lattice phonons, whose

frequencies, involving Raman shifts in the

range �10–150 cm�1, probe the inter-

molecular interactions and are hence very

sensitive to different molecular packing.

Because each crystal structure has its own

dynamics, in organic molecular crystals

lattice phonons are the fingerprints of the

individual crystal structure.

A typical example of the application of

Raman spectroscopy to polymorphism is

reported in Fig. 1 for pentacene,11,12

tetracene,13 a-quaterthiophene (T4)14 and

a-sexithiophene (T6).15 These materials

are, among the organic semiconductors,

those showing some of the highest charge

mobilities. They all show polymorphism.

The two polymorphs of T4 and T6 are

labelled LT (low temperature) and HT

(high temperature), according to the

substrate temperature during vapour

deposition under high vacuum. To unify

the different nomenclature found in the

literature we have adopted the same

labelling also for the two phases of pen-

tacene12 and tetracene. The occurrence of

two genuine polymorphs has been

assessed by the identical spectra in the

intramolecular region (molecular

vibrations) which confirm the molecular

identity in both crystal phases.

The relationship between each lattice

phonon pattern (lattice dynamics) and its

corresponding XRD pattern (lattice

structure) makes Raman spectroscopy

a powerful tool for complementing

information on distinct crystal structures.

The case of pentacene is exemplary: for

a long time the HT structure was assumed

to be a spurious structural result, until

eventually reproduced in the laboratory.12

Earlier calculations16 and Raman

spectra11 had anticipated this finding

independently of diffraction experiments.

Both pentacene polymorphs are found

stable at ambient p,T, though, by

applying pressure, the HT phase trans-

forms irreversibly to the denser LT phase

at room temperature.17 The case of

tetracene is a classic one. Two different

phases have been obtained, depending on

This journ

sample preparation and history. The HT

polymorph is the most frequently grown

phase, stable at ambient conditions.

Application of pressure above 1 GPa

yields the LT polymorph, which is also

obtained by cooling below 140 K. Due to

the large hysteresis of the temperature-

induced phase transition, the LT poly-

morph can be maintained at ambient

conditions.13 The spectra shown in the

lower part of Fig. 1 confirm the expecta-

tions of polymorphism in oligothiophenes

with an even number of thiophene

subunits.18 As long as the vibrational

studies of T4 and T6 crystals were limited

to the detection of the intramolecular

modes, there was no hope of spectro-

scopically discriminating between poly-

morphs. A lattice phonon spectrum

would instead be a fast, reliable and non

destructive tool for probing phase

assignment. The LT polymorph is

normally assumed to be the more stable at

ambient p,T and, as a consequence, the

only one present in organic semi-

conductor devices. Therefore a possible

phase coexistence can go undetected.

Finally, from the analysis of polarized

spectra and vibrational selection rules

additional information on mode

symmetry, number of molecules per unit

cell and crystal anisotropy can be

obtained.19

Scaling down in size: confocalRaman microscopy and phasemixing

Interfacing an optical microscope to the

Raman spectrometer and making the

microscope confocal permits the scaling

down in size of the crystal region under

investigation. Raman scattering is trans-

mitted to the spectrometer only from the

restricted sampling volume determined by

the focused region of the laser beam,

enabling fine tuning of XYZ discrimina-

tion. Spatial resolution down to 1 mm and

less can be easily achieved, opening the

way to new opportunities in materials

science.20 The analysis of the molecular

homogeneity (chemical impurities) and of

the physical purity (phase homogeneity) is

mostly facilitated. The latter point is

directly related to crystal phase identifi-

cation. In fact, as an intriguing conse-

quence of the small energy difference

between different polymorphs of organic

al is ª The Royal Society of Chemistry 2008

Fig. 1 Lattice phonon Raman spectra of the two polymorphic forms of pentacene, tetracene, a-sexithiophene and a-quaterthiophene and their

corresponding crystal structures.

Fig. 2 A typical example of phase mixing in crystalline pentacene and T6. Red and blue profiles

refer to HT and LT physically pure polymorphs, respectively. Green traces show more complex

profiles of sample regions where phase mixing occurs. The dotted vertical lines help in assigning

some spectral features to either polymorph.

molecular materials, different crystal

phases can coexist as different domains in

the same crystallite, originating a phase

mixing which ultimately affects the

physical purity of the sample.21

The problem of phase mixing is well

known in thin films,22,23 and is one of the

reasons of the difficulties in obtaining

reliable structural characterization. We

aim to show that this problem is relevant

also for single crystals and a typical

example is shown in Fig. 2. Once the

spectral profiles of the single polymorphs

are identified by lattice phonon Raman

spectroscopy, they are used as reference

spectra and it is easy to monitor physical

impurities in which domains of one

polymorph are embedded inside the

other. The related examples are shown in

Fig. 2 for crystalline samples of pentacene

This journal is ª The Royal Society of Chemistry 2008 CrystEngComm, 2008, 10, 937–946 | 939

and T6, where the coexistence of phases

appears as an overlap of distinctive

phonon bands of either polymorph in the

same crystal grain (green traces), as

indicated by the vertical bars with refer-

ence to the pure polymorph spectra.

Phase mixing, or physical inhomo-

geneities, is indeed observed in most cases

where polymorphism occurs,11,13,24

demonstrating the general validity and

the sensitivity of this technique for

detecting the presence of domains of

either structure at the mm scale.

We do stress here that it would be

impossible to identify these physical

inhomogeneities without a careful

previous analysis of the spectral contours

of the pure phases. On the other hand,

phase mixing may go undetected in single

crystal diffractometric methods, which

ordinarily may be less efficient in

discriminating phase mixtures at the mm

scale, in particular when similar struc-

tures are involved.

A method to control phasehomogeneity and phase mixing:lattice phonon Raman mapping

It is of great importance to find a suitable

method for checking phase homogeneity

in each crystal domain by obtaining

a visual display of chemical and physical

Fig. 3

940 | CrystEngComm, 2008, 10, 937–946

purity. We have shown that this task can

be nicely fulfilled by confocal Raman

mapping (CRM) in the region of lattice

phonons (10–150 cm�1), outlining

a further application of confocality to

micro-spectrometry techniques. By scan-

ning the surface, typically a few tens of mm

wide, with steps as close as 1 mm, one can

obtain a series of Raman spectra which

can be collected, point by point, in a false-

colour map to be compared to the optical

image of the original sample,21,24 as

schematically shown in Fig. 3. This will

yield crucial information on the topo-

graphy of each crystal whose phase

homogeneity needs to be checked. The

spatial resolution is given by the laser spot

area and is ranging from 0.88 to 1.05 mm,

depending on the numerical aperture of

the microscope objective and on the

wavelength of the laser line.

The actual recipe of the lattice phonon

CRM technique can be summarized in

four steps:

1. Assign spectra to structures

2. Scan selected crystal regions

3. Identify phase mixing

4. Map structural homogeneity

The first step requires a careful micro-

Raman investigation of a large number of

crystalline samples grown in as many

conditions as possible, to search for all

possible polymorphs. This will yield

Sketch of a confocal Raman mapping experimen

This journ

a series of ‘‘reference spectra’’, each

corresponding to a distinct polymorph.

This also enables one to select suitable

wavenumber windows typical of each

crystal phase. The second step concerns

the choice of the specimen regions to be

investigated, planning a number of point

spectra sufficient to reconstruct spectro-

scopically the sample with a good spatial

resolution. In the following step the

identification of phase mixing is achieved

by comparing complex spectral profiles

with the reference spectra of the pure

polymorphs. The final step eventually

yields the phase Raman mapping of the

selected crystal domain, which is obtained

by monitoring the spectral windows

where either one or the other polymorph

shows phonon bands. The relative

amount of one phase with respect to the

other can therefore be quantitatively

represented by the intensity ratio of

selected bands and at once converted,

with a suitable software, in a conventional

palette of colours. For instance, when

both HT and LT forms are present, one

can represent the intensity ratio HT/LT

by adopting a blue–green colour for the

LT phase, while the red–yellow shades

correspond to an increasing amount

of a HT phase. A deconvolution of the

phonon bands with background

suppression will assure a reliable

t.

al is ª The Royal Society of Chemistry 2008

representation of the data. The spread of

colours indicates the extent of the phase

mixing between the two polymorphs

analyzed in the chosen crystal domain.

Phase purity obviously is obtained when

the overall colour remains virtually

homogeneous throughout the whole

surface scanned. Phase mixing is instead

represented by a different extent of one

phase inside the other and produces

marked differences in the colour conven-

tionally chosen as reference of either

polymorph. Examples of lattice phonon

CRM are given in Fig. 4 and 5 for

pentacene and T6, respectively. A variety

of situations is observed in pentacene

which shows a different extent of phase

mixing in three selected crystals whose

optical images are otherwise homoge-

neous. Pentacene was the very first

Fig. 4 Optical (left) and Raman (right) images o

the optical image of the crystal. In the Raman map

scale is selected each time to emphasize the phase m

GmbH & Co. KGaA.

This journal is ª The Royal Society of Chemistry

example of an organic material mapped

with this technique.21 In the case of T6 the

sample in the lowest part of the figure is an

exemplary case of phase purity, showing

a full homogeneous colour, in spite of

a large expansion of the conventional

colour scale. Phase mixing is instead

represented by a different extent of one

phase inside the other and produces

differences in the colour maps, as shown

for the other two specimens (top and

middle sets of Fig. 5).

As expected, the contours of the optical

images are nicely reproduced in the

corresponding Raman maps, yielding

direct information on which the crystal

phase is present and in what extent.

Furthermore, the comparison between

the optical images and the Raman maps

shows clearly that no relationship exists

f selected pentacene crystals. Raman mapping refe

s the colour drifts from blue (full H phase) to green/

ixing in the crystal grain. Reproduced with permiss

2008

between morphology and crystal phase:

structural information and phase mixing

can be efficiently monitored only by

Ramanmaps. It is then crucial to perform

a spectroscopic test in order to verify the

phase purity in all crystals treated, espe-

cially for those cases in which crystal

morphology cannot assist phase recogni-

tion. It is thus conclusively shown that

lattice phonon CRM is a very efficient

tool for identifying polymorphs and their

mixing in the same crystallite on the

micrometre scale.

Getting deep inside the crystal

An additional feature related to the

confocality of the micro-Raman tech-

nique concerns the possibility to probe the

phase homogeneity of crystal domains at

rs to the area XY (mm2) drawn as a box over

red (increasing amount of C phase). The colour

ion from ref. 21. Copyright Wiley-VCH Verlag

CrystEngComm, 2008, 10, 937–946 | 941

Fig. 5 Optical images (left) and Raman maps (right) of T6 crystalline samples exhibiting phase inhomogeneity. Raman mapping refers to the area XY

(mm2) drawn as a box over the optical picture of the crystal. In the Raman maps the colour drifts from blue–green (LT phase) to red–yellow (increasing

amount ofHTphase). The colour scale is selected each time to emphasize the phasemixing in each crystal grain. Reproducedwith permission from ref. 24.

Copyright Wiley-VCH Verlag GmbH & Co. KGaA.

different sample depths.21,24 This is illus-

trated in Fig. 6, where lattice phonon

Raman spectra, taken on the very same

spot in a given crystal domain, show

a variation of the relative amount of

either polymorph on penetrating inside

the bulk. This is achieved by probing the

sample surface at different penetration

depths by focusing the laser light with

microscope objectives having different

numerical apertures. Typical values of the

theoretical penetration depths vary from

7.5 mm (100�) to 25 mm (50�) up to

a depth of about 450 mm (10�).

942 | CrystEngComm, 2008, 10, 937–946

On getting into the bulk different

amount of phase mixing is found with an

increase of the fraction of the LT poly-

morph, as indicated by the vertical lines

that monitor both phases with their

reference phonon. It is then important to

remark that phase inhomogeneity is not

confined to the first layers of the crystal

surface, but it propagates into the bulk.

The possibility of a three dimensional

investigation of single crystal homo-

geneity is thus an additional appealing

feature of this technique applied to

heterogeneous solid phases.

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Polymorphism and molecularelectronics

The reliability of the CRM method

enables us to extend its application from

bulk crystals to thin films on techno-

logically relevant surfaces and,

eventually, to organic electronics

devices.24 As previously mentioned, the

problem of polymorphism here is related

to the boundaries between crystal

domains belonging to different crystal

phases. They become physical traps,

effectively decreasing the mobility of the

al is ª The Royal Society of Chemistry 2008

Fig. 6 An example of Raman phonon spectra

of T6 taken with different microscope

objectives, as labelled. The penetration depth

increases from the bottom to the top spectra (in

black) of the figure. For better reference,

HT and LT lattice phonon spectra are also

reported.

Fig. 7 Ramanmap (bottompicture) and optical image of aH4T6-based FET. The area selected for

the Raman mapping corresponds to the entire area of the device reproduced in the figure (top left).

Phase identification is readily done by assigning the patches of colours to either polymorph as

represented in the corresponding Raman spectra, also reported (top right).

semiconducting layer with detrimental

effects on device performance.6,10 For

instance, thin films are usually grown in

out-of-equilibrium conditions25 and, in

the growth by high vacuum sublimation,

the time scales of the process do not allow

molecules to reach a crystal state with

a long range order, even when molecu-

larly ordered domains are formed.26 This

often implies coexistence of different

structures, some of which correspond to

those of the bulk crystal.22,23,26 A related

example has recently been reported on the

application of Raman micro-spectro-

scopy to T6 thin films deposited on

different substrates with thickness

ranging from 5 to 40 nm. By comparison

with the reference spectra of the bulk, the

polymorph formed on each substrate

could be identified.24An important follow

up of the experiments on thin films is the

application of CRM to T6 grown on

micro-fabricated patterns as prototypes

of organic field effect transistors

(OFET’s).24

To establish a correlation between

structure and properties of thin films, the

knowledge of phases and their spatial

distribution would be useful, in order to

control the transport phenomena. The

example reported in Fig. 7 refers to CRM

of the organic semiconductor tetrahexyl-

This journal is ª The Royal Society of Chemistry

sexithiophene (H4 T6) dispersed in a self-

organized polystyrene (PS) latex bead

matrix.27 The H4 T6/PS composite has

then been used to form the transport layer

of a FET device. CRM has been applied

to FET transistors in order to establish

a relationship between crystal structure

inside the FET channel and device

behavior. The two known polymorphs of

H4 T6 (Y and R in the figure) quite

commonly coexist in different crystal

grains or thin films of deposited material.

Fig. 7 shows that their spatial distribution

can be easily monitored in selected areas

of the transistor channels. The relative

amount of the two polymorphs for

a series of devices was related to the

transistor efficiency.27 This procedure can

be widely extended as a quality test

for a number of electronic devices based

on active layers of different organic

materials.

Theoretical polymorphs: arecrystal polymorphs predictable?

The experimental investigations are

supported and, in some cases driven, by

calculations performed to identify or

predict crystalline polymorphs. To

2008

theoretically identify the possible poly-

morphs of a given compound, one starts

either from all known experimental

structures or from a large number of

generated structures and, by steepest

descent, seeks the local minima of its

many-particle potential energy hyper-

surface. These minima correspond to the

possible configurations of mechanical

equilibrium and thus constitute the

‘‘natural’’ or ‘‘inherent’’ structures that

the system can exhibit. The concept of

‘‘inherent structure’’, originally deve-

loped28 to describe liquid and glassy

states, provides a powerful theoretical

device to identify all distinct stable phases

of a crystalline compound.

In our standard computational

strategy, we start with the choice of

a potential model suitable to describe the

intermolecular interactions which char-

acterize the crystal. Then we identify the

inherent structures of all known X-ray

structures, by varying unit cell axes,

angles, and molecular positions and

orientations till a minimum of energy is

found. The comparison between the

inherent structures can now be used to

unambiguously diagnose the identity of

the corresponding crystal phases, since it

CrystEngComm, 2008, 10, 937–946 | 943

eliminates the ‘‘noise’’ due both to the

thermal expansion (so that data collected

at different temperatures can be effec-

tively compared) and to the experimental

uncertainty in the lattice parameters. In

addition, we compute lattice phonon

frequencies for the inherent structures by

lattice dynamics methods. These provide

a further powerful means of investigation,

as they can be directly related to the

experimental Raman spectra.

As mentioned in a previous section, the

first successful application of this

strategy16,29 dealt with the case of the ‘‘lost

and found’’ polymorph of pentacene.12

Inherent structure calculations16,29 clearly

showed that while all recent experimental

structures30–32 converged to the same

energy minimum, and therefore they all

belonged to the same phase (the LT

phase), the oldest structure33,34 instead

converged to a different minimum, and

necessarily had to be attributed to

another phase (the HT phase). The

unexpected theoretical support for the

stability of the two forms, along with

the prediction of significant differences

between their lattice phonons spectra, led

to extensive experimental search and

Raman experiments which finally

confirmed the existence of two distinct

phases.11,17 The published lattice para-

meters of both forms were then checked

and finally reproduced in powder17 and

single-crystal X-ray diffractions

measurements.12

Fig. 8 Structure of selected potential energy minim

approximately perpendicular to the plane of the page

site symmetry.

944 | CrystEngComm, 2008, 10, 937–946

The differences found in the experi-

mental Raman lattice phonon spectra of

distinct polymorphs can be easily repro-

duced by the calculations, as shown both

by the example of pentacene35 and by

a number of other compounds.13,15

Indeed, in some cases, the match between

experimental and calculated spectral

patterns can be successfully used for

phase identification even before being

accounted for by X-ray measurements.16

The procedure of minimizing the

energy starting from all the experimental

structures, to discover which of these

correspond to genuinely distinct poly-

morphs, yields the analysis of the local

stability of the known crystal phases.

After this step, our standard computa-

tional strategy involves a systematic

sampling of the potential energy hyper-

surface, to check for the global stability of

the observed structures and to investigate

the possible occurrence of further

polymorphs. Sampling the potential

hypersurface essentially corresponds to

a procedure of crystal structure predic-

tion, which is currently the focus of much

research activity.36,37 A good assessment

of the current approaches to this issue is

given by the blind tests conducted by the

Cambridge Crystallographic Data Centre

in 1999, 2001, 2004 and 2007.38–41 Each

test involved several research groups,

which were invited to submit predictions

for a handful of given compounds. In the

basic prediction strategy, shared by most

a for crystalline tetracene, shown with an orientatio

.Minima are labelled by their energy rank N, space g

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researchers, one starts from a given

molecular model, generates several thou-

sands of different crystalline arrange-

ments, minimizes the lattice potential

energy of each arrangement, and finally

selects the structures with the lowest

potential energy.

Exhaustive sampling of the potential

energy hypersurface has so far been

applied to three of the organic semi-

conductors discussed in this paper,

namely pentacene, tetracene and alpha-

sexithiophene. All of these display at least

two bulk crystal polymorphs and could

therefore be selected as the best suitable

candidates to check how our procedure

performed in predicting stable coexisting

phases. Remarkably, in each case the two

deepest energy minima identified by

sampling were found to correspond to

the two experimentally known poly-

morphs.42–45 This result, which clearly

indicates that crystalline polymorphs of

organic semiconductors may be predic-

table, is highly significant, especially in the

light of less satisfactory outcomes for

other types of molecules.38–41

As an example of the bewildering

variety of different possible structures

that may be found, we display in Fig. 8

a selection of the energy minima

computed for crystalline tetracene. It is

worth noticing that all deep minima of

tetracene,43,44 like those of pentacene and

sexithiophene,42,45 present close packed

herringbone structures which allow both

n in which the shortest cell axis (either a or b) is

roup, number Z ofmolecules in the unit cell and

al is ª The Royal Society of Chemistry 2008

for an optimal packing and for a signifi-

cant overlap between the p orbitals of

neighbouring molecules. This character-

istic molecular arrangement may

contribute to the excellent charge trans-

port properties of both oligoacenes and

oligothiophenes.3

The agreement between the predicted

structures and the X-ray data is excellent

for all semiconductors studied so far,

especially once the effects of temperature

T and pressure p are accounted for. This

can be achieved by minimizing the crystal

Gibbs energy G(p,T) at given p,T condi-

tions with quasi harmonic lattice

dynamics (QHLD) methods.46 Thus,

QHLDmethods are capable, in principle,

of predicting not only the relative

thermodynamic stability of the various

polymorphs but also solid–solid phase

transitions in organic molecular crystals,

providing a useful aid for the definition of

the phase diagram of the compound.

Quite interestingly, both for oligoacenes

and oligothiophenes, phase transitions

cannot be reproduced by calculations,

although distinct polymorphs are char-

acterized by very small computed Gibbs

energy differences (DG � kBT)

throughout the range of their mechanical

stability. Far from being an unsatisfac-

tory result, this confirms the finding that

polymorphs can often be obtained under

very similar experimental conditions and

may coexist at ambient conditions.

Kinetic and entropic factors, besides the

packing energy, indeed play important

roles in crystallization.

Conclusions

Polymorphism is widespread in organic

semiconductors, quite often yielding

phase mixing. The careful phase control

of polymorphic materials is of paramount

importance whenever phase purity is

a strict requirement in sample prepara-

tion, as, for instance, in organic electronic

devices whose carrier mobility, being

dependent on the purity and the method

of preparation of the material, will ulti-

mately depend strongly on their crystal

structure.47 Phase homogeneity cannot be

taken for granted, even for well formed

single crystals. Different polymorphs can

coexist down to the mm scale and physical

inhomogeneities occur at surfaces and in

the bulk. Experimentally we have found

that different crystalline polymorphs may

This journal is ª The Royal Society of Chemistry

be conveniently probed by their Raman

spectra in the region of the lattice

phonons (usually below 150 cm�1), whose

frequencies probe the intermolecular

interactions and turn out to be very

sensitive to differences in molecular

packing. The method illustrated here,

lattice phonon confocal Raman mapping,

is a powerful technique to probe the

crystal structure of organic materials,

being fast, reliable and capable tomonitor

in situ physical modifications and phase

inhomogeneities in crystal domains on the

micrometre scale. Comparison of optical

images and Raman maps conclusively

shows that no relationship exists between

morphology and crystal phase: structural

information can be drawn only from

Raman images. It is then crucial to

perform a spectroscopic test in order to

verify the phase purity in all crystals

treated, especially for those cases in which

crystal morphology cannot assist phase

recognition.

From a theoretical point of view we

have shown that successful a priori

prediction of polymorphism in organic

semiconductors may be feasible. We have

computed the possible crystal structures

of mechanical equilibrium, either by

starting from all known X-ray structures

or by generating thousands of random

structures to sample the overall distribu-

tion of potential energy minima. The

cases studied, pentacene, tetracene and

a-sexithiophene42–45 show that the deepest

minima calculated indeed correspond to

the experimental XRD structures of bulk

crystals.

In conclusion, the problem of

polymorphism in the preparation and

characterization of new materials should

benefit from this technique as a sound

method capable of controlling both

crystal structure and molecular recogni-

tion in single crystals, thin films and in

electronic devices.

Acknowledgements

This work was in part supported by EU

Integrated Project NAIMO, project No

NMP4-CT-2004–500355. The support of

INSTM is gratefully acknowledged. We

thank drMassimo Placidi, Horiba JY, for

skillful technical advice and Drs Chiara

Dionigi and Fabio Biscarini, ISMN-CNR

Bologna, for the sample represented in

Fig. 7.

2008

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