This journal is c The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2013 New J. Chem., 2013, 37, 2229--2235 2229

Cite this: NewJ.Chem.,2013,37, 2229

A stochastic principle behind polar properties ofcondensed molecular matter

Jurg Hulliger,* Thomas Wust, Khadidja Brahimi, Matthias Burgener andHanane Aboulfadl

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree

of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring

zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only

exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single

component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals,

biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive

second harmonic generation microscopy all showed domains of opposite polarities in their final grown

state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one

direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically

controlled mono-domain state. In this review we summarize theoretical and experimental findings

leading to far reaching conclusions on the polar state of solid molecular matter. ‘‘. . . no stationary

state . . . of a system has an electrical dipole moment.’’ P. W. Anderson, Science, 1972, 177, 393.

Introduction and basic findings

Investigations of polar properties of molecular solids (crystals,polymers, tissues), in most cases, start off with the idea of thedilute gas model.2 This means, measured polar properties(pyroelectricity, piezoelectricity, nonlinear optical properties, etc.)are assumed to emerge from molecular entities featuring an

asymmetrical charge distribution. Therefore, the observation ofmacroscopic polar properties essentially depends on the pointgroup and the linear, nonlinear polarizabilities of the buildingblocks as well as on their packing geometry in the solid state.3

For a pictorial description of the effects of polarity it is useful toreduce asymmetrical (not necessarily chiral) molecules to theirpolar vector property, called dipole moment. However, this kindof a reductionism does not imply that any of the mentionedproperties would simply follow from the dipolar strength or thedipole–dipole interaction in the solid state.

Department of Chemistry, University of Berne, Freiestrasse. 3, 3012 Berne,

Switzerland. E-mail: juerg.hulliger@iac.unibe.ch

Jurg Hulliger

Jurg Hulliger studied physicalchemistry at ETH Zurich andreceived a PhD from theUniversity of Zurich. Later hemoved to the Department ofPhysics at ETH Zurich to performwork on materials and crystalgrowth. Since 1993 he has been aProfessor at the University ofBerne. His research interests covermaterials synthesis, physical proper-ties and theory of condensed matter.Since 2004 he has been a fellow ofthe Royal Society of Chemistry.

Thomas Wust

Thomas Wust studied physics atETH Zurich. During his PhD(supervision J. Hulliger) hedeveloped a model for growth-induced polarity formation insolid solutions of molecularbuilding blocks. Wust’s researchfocuses on the development ofMonte Carlo methods in scientificcomputing and their application tosimple, reductionist models suitableto address particular questions ofstochastic nature in condensedmatter or biophysics.

Received (in Montpellier, France)16th October 2012,Accepted 11th March 2013

DOI: 10.1039/c3nj40935j

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In this focus article we introduce a statistical mechanicsview to understand the polarity in molecular solids. By doingthis, we shall assume that polar molecules are the base ofmacroscopic polarity. Statistical arguments will be applied toestimate thermal expectation values for the degree of alignmentof polar entities, being proportional to hPi, which representsthe thermal average polarization of the bulk.

Because of polar blocks exposed to thermal averaging, asingle degree of freedom of dipole reversal is sufficient tocancel hPbulki in the condensed state. An evident example is awater droplet, featuring no net dipole moment, even thoughindividual water molecules do. Nevertheless, water dropletsshow a negative surface charge,4 a phenomenon which resultsfrom the fact that molecules at the surface feature differentaverage properties than those in the bulk.

In the case of a crystal in the state of (i) nucleation, (ii) growthor (iii) post growth annealing close to melting providing a degreeof freedom for a reversal (more generally speaking orientationaldisorder) of asymmetrical building blocks, recent theoreticalwork predicts5,6 that an inhomogeneous spatial distribution ofhPi is to be expected leading to hPbulki equal to zero.

The key message of this focus article is to highlight that a seed,a growing crystal and an annealed state are expected to end up in aso called bi-polar state (classification according to Shubnikovet al.,7 see Fig. 1) providing hPbulki equal to zero. We will explainin the following that this message is indeed original.

A theoretical statement cited by P. W. Anderson in hisfamous article ‘‘More is Different’’1 says, ‘‘. . . that no stationarystate . . . of a system has an electric dipole moment.’’ Stationarymeans here that a thermal equilibrium for the orientations ofpolar molecules in the solid state is provided. What is new hereis the awareness of the problem in the field of molecular solidsand a unified theoretical frame for understanding experimen-tally observed phenomena by statistical means.5,6

Over the last 15 years we have been developing a stochastictheory accounting for orientational disorder in molecularsolids.8,9 To make analytical calculations and numerical simu-lations feasible, polar molecules were described by a partrepresenting acceptor properties (A) and a part representingdonor properties (D), a straightforward decomposition of mole-cules exhibiting an asymmetrical charge distribution. For acalculation of polarity formation in the solid state we haveformally decomposed the generally complex interactionscheme of lattice sums into (i) longitudinal (DEA, DED) and(ii) transversal (DE>) nearest neighbour interaction parameters(for more details, see ref. 5 and 8).

Applied to the polar state of a nano-sized 3D object, thisapproach leads us to results as shown in Fig. 2:6 Monte Carlosimulations performed for a seed of the size 10 � 10 �50 molecules reveal an equilibrium state featuring averagepolarization hP(z)i along the z-axis being different in the signswith respect to the right and the left part of the figure. The totalpolarization hPbulki is zero. Why does this system develop into abi-polar state?

In the transversal directions periodic boundaries were appliedin simulations. Along the z-axis, there are open boundaries.Setting up an Ising Hamiltonian H10 for this system, one candemonstrate that two contributions are linear in Sz (Sz: effectiveparticle operator11) but opposite signs appear, representingelectrical field terms. Although there is no external field applied,these field terms are responsible for building up a bi-polarstate.6,10 Equilibrium bulk polarity found for a nano-sized seedis therefore due to (i) the symmetry breaking effect at the openboundaries, and (ii) the inequality of DEA and DED energyparameters. In contrast, a system coupled only by dipole–dipoleinteractions (d) would not show a bi-polar behaviour, becauseinteractions Ed(-� � �’) and Ed(’� � �-) are identical.

Now, moving on to the growth of a seed, we encounter asimilar situation: for simplicity we discuss at first a systemwhere DE> is zero, i.e. no transversal coupling is present. In1997 it was a real discovery to notice that such a system can bedescribed by a homogeneous Markov chain.12,13 The final stateis bi-polar showing hPbulki equal to zero.

When admitting transversal coupling supporting a centricalignment (DE> 4 0) of polar entities, growth upon a centricseed can lead to polarity formation in symmetry related sectors.A symmetry analysis has been worked out in which (hkl) faces ofa seed can lead to polar sectors.14 However, the symmetry of the

Fig. 1 A schematic representation of bi-polar states:7 the object is built up bytwo domains of opposite average polarities, yielding zero in total. N/Nm:symbol of the corresponding continuous group.

Khadidja Brahimi studied theoretical physics at the University ofOran. Currently she is a PhD student of J. Hulliger, working onforce field calculations for growth-induced polarity formation.

Matthias Burgener studied chemistry at the University of Berne.Currently he is a PhD student of J. Hulliger, working on scanningpyroelectric microscopy.

Hanane Aboulfadl studied molecular chemistry at the University ofRennes. She received her PhD from the University of Fribourg.Presently she is a post doc in the group of J. Hulliger working onphase sensitive second harmonic microscopy.

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entire crystal will still be that of the seed. Consequently, thenet polarization is zero and the object is described as abi-polar state.

When exposing such a crystal to an annealing procedure at atemperature significantly higher than the growth temperature,polarity may vanish or is predicted to be found very close tocrystal faces. This is due to a former growth effect related tothe surface which is undergoing a change into an equilibriumprocess in the bulk.

A special situation is found, when growth starts from a polarseed: here, Monte Carlo simulations and an analytical treat-ment predict a growth-induced transition from a mono-domainpolar state into a bi-polar state.5 In simulations, only onegrowth orientation along the polar axis undergoes a globalreversal of dipoles, which can start from a single orientationaldefect. As a result a bi-polar state is obtained and bulk polarityis cancelled also in this case.

Following our review, all systems addressed above can endup in an experimentally detectable bi-polar state, featuringhPbulki equal to zero. Both theoretical predictions as mentionedabove (bi-polarity; hPbulki = 0) are experimentally well demon-strated for a number of different materials involving (i) channel-type inclusion compounds, (ii) single component molecular crystalsand solid solutions thereof, (iii) inorganic salts containingpolar anions, (iv) optically anomalous crystals and even (v)biomimetic materials including (vi) natural tissues (for details,see the next chapter).

As mentioned above, materials can thus build up a certaindegree of polarity during growth upon a centric seeding state.However, the CSD15 reports crystals expressing a polar structure(less than about 17%). A few available studies on the growthbehaviour of polar molecular crystals have reported a pronouncedgrowth anisotropy when comparing the growth speed along the

two orientations of the polar axis (see references and table ofmaterials given in ref. 5). The presently accepted model is thate.g. solvent molecules interfere differently at (hkl) and ( %h%k%l)faces, allowing thus for an anisotropy in the growth speed. In arecent paper5 we have proposed a different mechanism basedon the stochastic theory addressed above: in case one side of thepolar axis is subjected to undergo reversal, an increasing numberof defects lead to a twinning, involving random boundaries whichcould give rise to kinetic hindrance for the growth along thisorientation. The new explanation for well-known mono-domainpolar crystals15 we have proposed5 is that stochastic orientationaldisorder of building blocks is at its origin.

Special cases of polar materials are given by ferroelectricpolymers,16 liquid crystals17 and molecular crystals.18 Changingthe temperature from high to low values, typically ferroelectricmaterials undergo a phase transition from a centric hightemperature structure into a polar phase. In the absence ofexternal fields (electrical, mechanical), a poly-domain statefeaturing hPvoli = 0 is allowed by the symmetry of the hightemperature non-ferroelectric phase. This means that thetransition from a centric mother phase into a ferroelectric statefollows a statistical process leading to a multi-domain statewhich on average shows hPbulki = 0. Mono-domain crystals canbe obtained when cooling from the high temperature phaseinto the ferroelectric one is taking place in a temperaturegradient or under the influence of an electrical field.

Materials characterized by scanningpyroelectric and phase sensitive secondharmonic microscopy

Present knowledge gained by statistical means needs a demon-stration by representative materials including advanced experi-mental techniques for a characterization of polar properties.

Scanning pyroelectric microscopy (SPEM)19 and phase sensitivesecond harmonic (PS-SHM)20 microscopy are both techniques toinvestigate the spatial inhomogeneity of polar materials. SPEM isused as a non-destructive surface analysis providing a lateralresolution of a few micrometers, averaging over a thickness ofseveral micrometers as well. PS-SHM is applied in transmissionmode yielding a lateral resolution of the ground wave’s wave-length order (about 1 mm), here by averaging over the transmis-sion length. Both techniques essentially proved to be suited todistinguish the mono-domain from bi-polar states. Applicationof the most advanced technique in this field, the scanningpiezoelectric microscopy, allows extending the resolution intothe 5–10 nm range (Fig. 3).21

Channel-type inclusion compounds

This class of host–guest crystals can provide ideal modelsystems to demonstrate growth into a bi-polar state (seeFig. 4, left), driven by a Markov chain process.12,13 Because ofa linear geometry of channels, guest molecules can undergoorientational selectivity (up vs. down) through (i) functionalgroup guest to guest interactions (A� � �D, A� � �A and D� � �D) at

Fig. 2 Monte Carlo simulations6 for a nano-sized seed crystal (3D: 10 � 10 � 50particles; z = 0, . . ., 49) showing fractional polar alignment (hP(z)i: averagepolarization) of asymmetrical A–D molecules along the z-axis. Starting from astate of random orientations, thermalization is leading to a bi-polar statefeaturing hPvoli = 0. This means that the polarizations in the left and the rightpart of the figure (for each curve) are equal but of opposite signs. Insets: snapshots of the state of alignment along the axis (above) and perpendicular to it(below). Blue and red colours symbolize dipole orientations, i.e. ‘‘up’’ or ‘‘down’’.

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the growing surface and/or (ii) guest to host (H) interactions(A� � �H, D� � �H). As growth proceeds in both directions of thechannel axis c, consequently, a bi-polar state is obtained (seeFig. 1). This means: both the upper and the lower growthsectors involving the c-axis develop the same average polarityhPsectori, but with opposite signs (hP+sectori + hP�sectori = hPbulki =0). For a pictorial representation of a cone shaped bi-polardevelopment of Markov chain polarity formation made visibleby SPEM, see ref. 19.

Single component molecular crystals

Most frequently molecular crystals belong to the space groupP21/c. In this case the point group 2/m is ideally suited for ademonstration8 of growth-induced polarity formation by orien-tational disorder at growing faces (hkl) involving the twofoldaxis (k a 0). Growth of a seed of symmetry 2/m in bothorientations of the b-axis can produce symmetry related (m)growth sectors (see Fig. 4, right) featuring the same averagepolarity hPsectori, but opposite in signs. SPEM and PS-SHManalyses of an increasing number of examples allow us toconclude that there is a high probability to find polar sectorsin crystal structures of asymmetrical compounds for which acentric average structure was reported. For an advanced X-rayanalysis involving a particular case, see ref. 22.

Solid solutions of molecular crystals

Solid solutions are of particular interest to our report, for anumber of paradoxical effects. One of these concerns theincrease of grown-in polarity by admixing symmetrical, i.e.centric molecules (A–A or D–D) to the crystallization mediumof a dipolar compound showing some grown-in polarityformation on its own. In a solid solution H1�xNx (H: dipolarhost; N: centric), the presence of e.g. a non-polar componentA–A can enhance hPsectori of a bi-polar state. For a theoreticalelaboration on these counter-intuitive phenomena, see ref. 23.

Optically anomalous crystals24

Here we have a typical case of how functional groups of dyemolecules can interact with a non-polar crystal lattice to entersymmetry related parts of a host producing opposite polaritiesin corresponding growth sectors. In the case of amaranthstained KH2PO4, PS-SHM and SPEM have revealed a bi-polar

state for sectors developing along the c-axis of a tetragonalinorganic host lattice (see Fig. 5).25

Inorganic ionic crystals

A first example showing that theoretical views presented abovealso apply to ionic crystals built from polar anions is NaClO3

(point group 23, cubic), featuring sector-wise a bi-polarstate. Due to cubic symmetry antiparallel average polarity is

Fig. 3 Scanning piezoelectric microscopy of a dentin sample.21 (a) Topographicview showing elongated collagen fibrils being aligned in somehow parallelfashion. (b) Amplitude of the piezoelectric signal, telling that there is somepolarization. (c) Phase information (grey vs. black) showing that the averagepolarization of bundles or single fibrils can have a different absolute orientationrelative to each other.

Fig. 4 Schematic view of the alignment of the dipolar orientation of polarmolecules in growing crystals. Left: the case of a channel inclusioncompound, where a Markov chain mechanism12,13 takes place in both orienta-tions of the channel c-axis. In sectors side wise to the c-axis the up–downdisorder is most pronounced. Right: polarity formation in a structure of a singlecomponent crystal, where polar entities preferably pack in a centric arrangement.Due to orientational disorder at the growing surface, polar order can, however,build up. In the most frequently found space group P21/c (point group 2/m)the process of orientational disorder lowers the symmetry to 2 (in each sector).In this case, polar effects are found only in sectors featuring blue colour.Grown-in polarity in both types of materials was experimentally confirmedby scanning pyroelectric microscopy19 and phase sensitive second harmonicmicroscopy.20

Fig. 5 Example of an acentric but nonpolar inorganic host (KH2PO4)undergoing growth-induced polar alignment of dipolar dye molecules(amaranth) in {101} sectors. (a) Optical picture showing stained sectors. Thepolarization (arrow) is parallel to the tetragonal c-axis of KH2PO4. (b) Secondharmonic response (green) for a polarization of a lo wave (1064 nm) parallelto the c-axis. (c) and (d) reveal the bi-polar state by a phase sensitive SHGexperiment.25

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observed by SPEM in all sectors built up by {100}, {111}, {011}etc. faces.14 Obviously, the asymmetrical ClO3

� unit undergoes1801 orientational disorder at growing faces. For a first demon-stration of growth-induced polarity in ionic crystals, see Fig. 6.When annealing NaClO3 crystals, by heating close to themelting temperature, grown-in effects of polarity disappear inthose sectors where SPEM had detected a pyrolectric effect forcrystals grown at room temperature.

Biomimetic crystals

Gelatine grown fluoro-apatite includes about 2% of peptidechains into the composite material. Upon the early state ofgrowth these macromolecules are aligned along the c-axis of thehexagonal modification of apatite. Such systems are discussedin the context of bone/tooth repair and formation. As naturaltissue is polar, we are investigating the polar properties of thisbiomimetic material. Literature work26 distinguishes smallseeds from later aggregates developing into a dumb-bell shapewhere peptide molecules exceed a bending of chains away fromthe initial axial alignment.27 Although polar effects are veryfaint, SPEM was able to reveal a bi-polar state (Fig. 7, left) forlate aggregates and a mono-domain state (Fig. 7, right) for earlyseeds. SHG confirmed polarity formation along the c-axis. Here,the origin of the mono-domain state upon nucleation and earlygrowth is still a question of debate. A possible answer mayemerge from knowledge of the gel state investigated at thenanometer range.

Biological tissues

Natural tissues of vertebrates represent materials providingelectrical signals for the central nerve system upon externalstimuli.28 Here, a Markov chain analysis using biochemicaldata on fibril elongation has for the first time provided amechanistic explanation for the occurrence of polar tissues innature.29 The theoretical model also explains why tissues

extending in opposite orientations end up showing the char-acteristics of a bi-polar state. In this field, the application ofscanning piezoelectric microscopy has revealed even thepolar nature of single collagen fibrils (Fig. 3).21 For pioneeringwork on the bi-polar state of natural tissues, see papers byH. Athenstaedt.30

Water droplets

We have started our discussion with the example of a waterdroplet. The unravelling of the structure of liquid water isconsidered as one of the most prominent scientific issues.31

Similarly, a contradictory debate on the surface charge of wateris found in the literature. A most recent review4 concluded thatwater is showing a negative surface charge. To explain this,6 letus project individual dipole moments onto an axis runningthrough the centre of a droplet. Thermal energy in the bulk isaveraging out vector components of hPbulki. However, near thewater to gas boundary, the symmetry of the averaging process isdeviating from spherical and thus we can apply arguments aspresented above.5,8 Water molecules are asymmetrical and sowe can anticipate that the interaction O� � �O (O: acceptor part) isdifferent from those involving only hydrogen atoms (2H� � �H2;H: donor part). It is reasonable to assume that the oxygen–oxygen repulsion is more effective than that of the hydrogenatoms. Consequently, simulations similar to those shownin Fig. 1 allow us to conclude that the surface charge of watershould be negative.

Conclusions and perspectives

The discovery of SHG effects in channel-type inclusioncompounds by D. F. Eaton et al. in the late 80’s33 has initiateda fascinating research field leading us now to raise funda-mental questions on the existence of a mono-polar state fornucleated, as grown or post growth annealed molecular crystalsin general.

The breakthrough in understanding bulk effects ofpolarity in molecular crystals is due to a unified theoreticalframe given by the application of statistical mechanics

Fig. 7 Polarity formation in biomimetic materials. Left: the bi-polar state of alater growth form (dumb-bell shape).32 Red and blue indicate plus and minussignals. Right: the mono-domain polar state of an early seed of a fluoro-apatitegelatine composite crystal. Effects here are very weak. For both samples SHGconfirmed an acentric state featuring maximum intensity along the main growthdirection. We acknowledge here collaboration for sample preparation with Prof.R. Kniep, MPI Dresden.

Fig. 6 Scanning pyroelectric microscopy showing the multi-polar as a grownstate of sodium chlorate. Electrodes are parallel {100} planes. Multi-polar meanshere that along each of the cubic axis h100i polar sectors develop. For simplicity arather thin plate was investigated. Because of one pair of electrodes used here,we can see only one pair of sectors featuring opposite polarity. This is a firstexample demonstrating stochastic polarity formation for ionic crystals built frompolar entities (ClO3

�).

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and numerical simulations: a single degree of freedom,i.e. orientational disorder for asymmetrical building blocks inthe condensed state is sufficient to obey the general rule that nostationary state of a system can feature a net bulk polarization.Applied to natural tissues this allowed us to explain for thefirst time why tissue is domain wise polar and is growing into abi-polar state.29

A most instructive example for systems following up asingle degree of freedom of reversal are channel-type inclusioncompounds. Here, steric hindrance for 1801 orientational dis-order of asymmetrical guest molecules is not an issue duringattachments. In the general case of crystal structures, however,1801 reversal of entities is encountering steric restrictionswhich may preserve structures from gaining free energythrough this entropically favoured process during the attach-ment of entities. Nevertheless, examples described aboveclearly document that the more we look at such phenomena,the more we will find interesting cases.8,22 Presented theore-tical results are applicable to nucleation as well, because theflexibility of nanometer sized aggregates is considerably largerthan that of surfaces of molecular crystals given a temperaturefar below melting. For objects of the typical size of crystal seedsset to simulation conditions representing thermal equilibrium,a bi-polar state is obtained. As nucleation is taking place undernon-equilibrium conditions, (i) kinetic control may generatea mono-domain polar seed subject to undergo reversalupon growth, or (ii) a close to equilibrium process may leadto a bi-polar seed growing into a classical 1801 twin. What isstill to be done here?

In numerical theory, Monte Carlo simulations involvinglattice sums over force-field type interactions between realmolecules will have to confirm features found using a topolo-gical set (longitudinal, transversal) of just nearest neighbourinteractions. These calculations will be necessary for systemsunder conditions of growth and for small seeds exposed tothermal equilibrium with respect to reversal.

Experimentally, polarity formation in tissues is a key issue asit plays an important role in tissue formation, function andrepair.28 Here, nondestructive methods revealing spatial polar-ity distributions at different levels of resolution are needed.SPEM and PS-SGM can reveal polar tissue structures down to afew micrometers in lateral resolution. Further insight is pro-vided by application of scanning piezoelectric microscopyexploring a resolution down to nanometers (Fig. 3). For avalidation of theoretical models explaining polarity formationin natural tissues,29 these analytical methods will have toprovide the absolute sign of local polarity in relation to the growthorientation, i.e. the fibril elongation process. There is evidencethat failure in proper absolute polarity of tissues can be thecause for diseases.34

Acknowledgements

Let me thank all my collaborators and colleagues who havecontributed over the years to this topic. Part of this project wassupported by the Swiss SNF, no. 200021_129472/1.

Notes and references

1 P. W. Anderson, Science, 1972, 177, 393.2 Nonlinear Optical Properties of Organic Molecules and Crys-

tals, ed. D. S. Chemla and J. Zyss, Academic Press, New York,1987, vol. 1,2.

3 J. F. Nye, Physical Properties of Crystals, Clarendon Press,Oxford, 1985.

4 M. Chaplin, Water, 2009, 1, 1.5 J. Hulliger, T. Wust, K. Brahimi and J. C. Martinez Garcia,

Cryst. Growth Des., 2012, 12, 5211.6 J. Hulliger, T. Wust and M. Rech, Angew. Chem., Int. Ed,

2013, submitted.7 A. V. Shubnikov, I. S. Zheludev, V. P. Konstantinova and

I. M. Silvestrova, Investigations of Piezoelectric Textures, Sov.Acad. Sci. Press, Moscow, 1955.

8 J. Hulliger, H. Bebie, S. Kluge and A. Quintel, Chem. Mater.,2002, 14, 1523.

9 H. Bebie, J. Hulliger, J. Eugster and A. Bogdanovic, Phys. Rev.E: Stat., Nonlinear, Soft Matter Phys., 2002, 66, 021605.

10 H. Bebie and J. Hulliger, Physica A, 2000, 278, 327.11 M. Plischke and B. Bergensen, Equilibrium Statistical

Physics, World Scientific, Singapore, 1994.12 K. D. M. Harris and P. E. Jupp, Proc. R. Soc. London, Ser. A,

1997, 453, 333; K. D. M. Harris and P. E. Jupp, Chem. Phys.Lett., 1997, 274, 525.

13 O. Konig, H.-B. Burgi, T. Armbruster, J. Hulliger andT. Weber, J. Am. Chem. Soc., 1997, 119, 10632; J. Hulliger,P. Rogin, A. Quintel, P. Rechsteiner, O. Konig andM. Wubbenhorst, Adv. Mater., 1997, 9, 677.

14 C. Gervais and J. Hulliger, Cryst. Growth Des., 2007,7, 1925.

15 F. H. Allen, Acta Crystallogr., Sect. B: Struct. Sci., 2002,58, 380. Comment: only organics, no protein and polymeric.

16 Ferroelectric Polymers: Chemistry, Physics, and Applications,ed. H. S. Nalwa, Taylor & Francis, 1995.

17 Ferroelectric Liquid Crystals: Principles, Properties and Applica-tions, ed. J. W. Goodby, Taylor & Francis, 1991.

18 J. Fousek, Ferroelectrics, 1991, 113, 3; R. Blinc, AdvancedFerroelectricity, Oxford Pub., 2011.

19 A. Batagiannis, M. Wubbenhorst and J. Hulliger, Curr. Opin.Solid State Mater. Sci., 2010, 14, 107.

20 P. Rechsteiner, J. Hulliger and M. Florsheimer, Chem.Mater., 2000, 12, 3296.

21 A. Gruverman, D. Wu, B. J. Rodriguez, S. V. Kalinin andS. Habelitz, Biochem. Biophys. Res. Commun., 2007, 352, 142.

22 N.-R. Behrnd, G. Labat, P. Venugopalan, J. Hulliger andH.-B. Burgi, Cryst. Growth Des., 2010, 10, 52.

23 T. Wust, C. Gervais and J. Hulliger, Cryst. Growth Des., 2005,5, 93.

24 A. Shtukenberg and Y. Punin, Optically Anomalous Crystals,ed. B. Kahr, Springer, Dordrecht, 2007.

25 H. Aboulfadl, M. Burgener, J. Benedict, B. Kahr andJ. Hulliger, CrystEngComm, 2012, 14, 4391.

26 P. Simon, E. Rosseeva, J. Buder, W. Carrillo-Cabrera andR. Kniep, Adv. Funct. Mater., 2009, 19, 3596.

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27 S. Busch, H. Dolhaine, A. DuChesne, S. Heinz, O. Hochrein,F. Laeri, O. Podebrad, U. Vietze, T. Weiland and R. Kniep,Eur. J. Inorg. Chem., 1999, 1643.

28 A. Caceres, B. Ye and C. G. Dotti, Curr. Opin. Cell Biol., 2012,24, 547; W. En-tong and Z. Min, Chin. J. Traumatol., 2010, 13, 55;A. C. Ahn and A. J. Grodzinsky, Med. Eng. Phys., 2009, 31, 733.

29 J. Hulliger, Biophys. J., 2003, 84, 3501.30 H. Athenstaedt, Nature, 1970, 228, 830; H. Athenstaedt, Cell

Tissue Res., 1968, 92, 428.

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