Soft materials for linear electromechanical energy conversion Antal Ja´kli
1and Na´ndor E´ber
2Webrieflyreviewtheliteratureoflinearelectromechanical effectsofsoftmaterials,especiallyinsyntheticandbiological polymersandliquidcrystals(LCs).Firstwedescriberesultson directandconversepiezoelectricity,andthenwediscussa linearcouplingbetweenbendingandelectricpolarization, whichmaybecalledbendingpiezoelectricity,orflexoelectricity.
Addresses
1LiquidCrystalInstituteandChemicalPhysicsInterdisciplinary Program,KentStateUniversity,Kent,OH44242,USA
2InstituteforSolidStatePhysicsandOptics,WignerResearchCentre forPhysics,HungarianAcademyofSciences,H-1525Budapest,P.O.
Box49,Hungary
Correspondingauthor:Ja´kli,Antal(jakli@lci.kent.edu,ajakli@kent.edu)
CurrentOpinioninChemicalEngineering2013,2:120–124 ThisreviewcomesfromathemedissueonMaterialsengineering EditedbyTheinKyu
ForacompleteoverviewseetheIssueandtheEditorial Availableonline10thNovember2012
2211-3398/$–seefrontmatter,#2012ElsevierLtd.Allrights reserved.
http://dx.doi.org/10.1016/j.coche.2012.10.007
Piezoelectricity
Piezoelectricityisalinearcouplingbetweenelectricand mechanical properties in special non-centrosymmetric materials. Ithasbeen knownin crystals sincethe work of Pierre and Jacques Curie in 1880 [1]. Piezoelectric propertieswerealsofoundinamorphousandpolycrystal- linematerials, such asferroelectric ceramics[2–4].The existence of piezoelectricity in certain synthetic and biological polymers [5], such as bone and tendon has been extensively studied [6,7]. Piezoelectric effects in polymersaregenerallysmall,butcanbeincreasedwhen theyaresubjectedtoastrongDCelectricfieldatelevated temperatures [8]. Owing to their flexibility and the possibilitytopreparefilmsoflargearea,thesematerials (especially polyvynilidene fluoride, PVDF) have been utilizedas theactiveelement inmanyapplicationsran- ging from infrared detectors to loudspeakers. Certain cellularpolymersinternallychargedbycoronadischarge (ferroelectrets) have been found to behave like soft sensitive piezoelectrics [9–11]. Similarly large and soft piezoelectricity was found in fiber mats composed of ferroelectricbariumtitanate(BT)nanoparticlesdispersed inpolylacticacid(PLA)[12].
As the type of materials with experimentally observed piezoelectriccoupling,sothedefinitionofpiezoelectricity
extended considerably in time. Originally it was used only for crystals in connection with compressions, but laterit was generalized to polymersand othermaterials for any strains and stresses, including shear. The direct piezoelectriceffect(whenelectricpolarizationisproducedby mechanicalstress)mathematicallycanbeexpressedbythe equation:
Pi¼X
jk
di;jkTjk; (1)
wherePiistheithcomponentofthepolarizationinduced bythestresstensorTjk.Thethirdranktensorcoefficients di,jkarecalledpiezoelectriccoefficients.
Inthe converse (or ‘inverse’) effectthe materialbecomes strained when electric field is applied. Mathematically thisisexpressedas
Sjk¼X
i
di;jkEi: (2)
Here Sjk=@sj/@xk is thestrain tensor (sj is thedisplace- mentofavolumeelementfromitsequilibriumposition), andEiistheexternalelectricfield.
Bysymmetrynotonlysolids,butalsoliquidcrystals(LC) canlackinversionsymmetryowingtothechiralityofrod- shape molecules containing carbon stereo-centers, or owingto asymmetric packingof molecules with special (bent, banana) shapes [13]. The chiral liquid crystal phases are the cholesteric (N*), chiral smectic (e.g.
SmC*ofrod-shapemolecules[14],orSmCPofbent-core molecules[15])andthechiralcolumnarphases.
Table 1 lists the LC phases that have no inversion symmetry,that is, which can have linear couplingsbe- tweenelectric field and mechanicalstrain.We seethat several of them (SmC* of chiral rod-shape, the tilted columnar phase of chiral disc shape and the SmCP of achiralbent-coreortiltedbowl-shapemolecules)haveC2
symmetry, which allows 8 independent piezoelectric coefficients.
IntheSmA*andN*phasesashearinducesatilt,which, combined with the lack of mirror plane owing to the molecularchirality,allowstheexistenceofapolarvector normaltotheshearplane.Thisisillustratedintheupper partofFigure1.
The inverse effect, when an electric field is applied perpendicular to the director, results in a shear strain, whichwouldalsoleadtoatiltofthedirector.Theoptical consequenceofthiseffect,rotationoftheopticaxis(the
director) proportional to the electric field, is known as electro-cliniceffect[16–18].
The direct piezoelectric (or linear mechano-electrical) effect inSmC* materialsisowing to theshear-induced polarization [19,20],andisarisingfromthedistortionof thehelix.Inthegroundstate(no-shear)thepolarization averages out in bulk, but shear unwinds the helix and leads toapolarizationnormalto theshearplane.Direct piezoelectric effects were also observed in various bio- logicalmembranes[21]andinaqueouslyotropics,where thehighlyconductivewaterisoftenreplacedbyethylene
glycol [22–24]. Linear mechano-electrical effects were also found on non-aqueous lyotropic phases [21,25]
Recentlyneatphospholipidswerealsoshowntobepiezo- electric[26,27].
The converse piezoelectric (linear electro mechanical) effect in SmC*materials[28–30] mayresultin audible acoustic effects implying their possible use in electro- mechanicaltransducers [31,32].Asystematicstudy [33]
withaccurate controlofthealignmentrevealedthatthe vibrations parallel to the smectic layers and the film surfacearegenerallythestrongest,especiallyifthepolar- ization isalsoparalleltotheplates.
Linear electro-mechanicaleffects offree-standingferro- electricSmC*filmswerestudiedbylightscatteringwhile applyingACelectricfieldsalongthefilmsurface[34–37].
In addition, they were alsoinvestigated in ferroelectric columnarLCs[38],SmC*elastomers[39,40]andglasses [41],invariousbiologicalsystems[42],lyotropicLCsand in membranes [21]. Converse piezoelectricity was also invoked [43] to explain the swelling of membranes in responsetovoltagechanges[44].Conversepiezoelectric measurementsinferroelectricSmCPbent-coreLCs[45]
andasummaryofexperimentalstudiesinSmC*elasto- mers[46]havebeenpublishedonlyrecently.Anelectro- clinic effectrelatedfield-inducedtwist,whosedirection changes sign with that of the electric field, was also reportedonSmA*elastomers[47,48].
Flexoelectricity
Another linear electromechanical phenomenon, flexoe- lectricity,connectsbendingandelectricity.Initiallyitwas regardedasbendingpiezoelectricity[49,50],however,in contrast to piezoelectricity, flexoelectricity does not requirethelackofinversionsymmetryandthecoupling constantseijkl aregivenbyafourthranktensor:
Piflexo¼eijkl@Sjk
@xl ; A@Tij
@xk ¼eijklEl; (3) corresponding to direct and converse flexoelectricity, respectively.Sjk(Tij)aretheelementsofthestrain(stress) tensor,andAistheareaofthesample.Incrystalsthefirst experiments[51]in1988gavee1011to1010C/m.In perovskite-type[52] andrelaxor ferroelectricceramics [53–55] and in polyvinylidene fluoride (PVDF) film [56,57] the flexoelectric coefficients are 4 orders of magnitudelargerthanindielectriccrystals,andthelarge polarizationinducedbyflexingisevidentlyofferroelec- tricorigin.
In fluid LCs stresses and strains are related mostly to orientational elasticity. R.B. Meyerpredictedflexoelec- tricity [50] for nematic LCs composed of dipolar mol- ecules with asymmetric shapes, such as pear-shape or bent-core.Intheabsenceofelectricfieldsthemolecular dipoles average out and the net polarization is zero.
Table1
Listofthemostimportant liquidcrystallinephases withtheir symmetryandnon-vanishingpiezoelectriccouplingconstants Phase Molecular
shape
Symmetry Non-zeroPiezoconstants N*,SmA* Chiralrod D1 d1,23=d2,13
SmAP Bentshape C2n d3,11;d3,22;d3,33,d1,13; d2,23
SmC* Chiralrod C2 d3,11;d3,22;d3,33,d1,13; d2,23;d1,23;d2,13;d3,12 SmCP Bentshape C2 d3,11;d3,22;d3,33,d1,13;
d2,23;d1,23;d2,13;d3,12 SmCG Bentshape C1 All18di,jk
Col*tilt Chiraldisc C2 d3,11;d3,22;d3,33,d1,13; d2,23;d1,23;d2,13;d3,12 Ph Bowlshape C1n d3,33;d3,11=d3,22 P*h Chiralbowl C1 d3,33;d3,11;d3,22 Ptilt Tiltedbowl C2 d3,11;d3,22;d3,33,d1,13;
d2,23;d1,23;d2,13;d3,12
Figure1
Flexoelectricity of bent-core nematic LC Piezoelectricity of SmA*
Current Opinion in Chemical Engineering
Illustrationofthemainphysicalmechanismofpiezoelectricityand flexoelectricityinLCs.
However,whenthedirectorissubjectedtosplayorbend deformations,respectively, thematerialbecome macro- scopicallypolar:
Pflexo¼e1nðdivnÞe2nðcurlnÞ (4)
Thiseffectisillustratedin thelowerrowofFigure 1.
Molecularstatisticaltheoriesbasedonmolecularpacking considerations[58–60]predictedforthesplay andbend flexo-coefficientse1ande3tobeabout1pC/mfornearly rod-shape molecules, and about an order of magnitude larger e3 values for banana shape molecules. Actual measurements onrod-shape LCs [61–69]typically give about e1e310pC/m, owing to a contribution of a quadrupolar mechanism [70]. These values are similar to those measured on elastomers subjected to a defor- mationgradient[51].
A‘peculiarkindofpiezoelectriceffect’wasmeasuredon blacklipidmembranes(BLM)[71–73]andfoundthatthe molecularbasisoftheflexoelectricityoflipidbilayersis anasymmetricredistributionofcharges,dipolesandthe splayed uniaxial orientation of their quadrupolar moments[74].Converse flexoelectric measurementson BLM[75]andvesicles[76]founde1100pC/m,whichis an order of magnitude larger than typical for calamitic
thermotropicLCs.Thesensorymechanismofouterhair cellcompositemembranes[77,78]canbeunderstoodby theflexoelectricpropertiesofthelipidbilayer[79].The converseofthis effect,that is,voltage-generatedcurva- turehasalsobeen observed[80].
The bend flexoelectric coefficient determined from mechanical bending induced electric current measure- mentsinbent-coreLCs[81,82]show3ordersofmagni- tudes larger values than in normal dielectric LCs. An example on 4-chloro-1,3-phenylene bis4-[40-(9-decenyl- oxy)benzoyloxy] benzoate(ClPbis10BB) in comparison withatypicalrod-shapeliquidcrystalpentylcyanobiphe- nyl(5CB)isshownin Figure2.
Thisincrease is similarto that of ferroelectricceramics [55]and indicates the presence of ferroelectric smectic clusters[83–85,86]inbent-corenematics.
Conclusion
Thephysicaleffectsreviewedaboverepresentcouplings between electrical and mechanical phenomena, which mightallowenergy conversion.
Theseconceptsturned out to beuseful in interpreting some functions of living organisms, successfully devel- opedduringevolution.Theseeffectsarealreadyutilized in state-of-the-artsensorand actuatortechnologies,and might have potential for further practical applications.
Thelatterhopefullypromptdesigningandsynthesizing moreappropriatefunctionalmaterials(presumablypoly- mersorelastomers)withlargercouplingcoefficientsand easierprocessability.
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Figure2
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