Photoferroelectric solar to electrical conversion

0.17 MB·English

by  Milos Knezevic

Photoferroelectric solar to electrical conversion
Miloˇs Kneˇzevi´c and Mark Warnera)
Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE,
United Kingdom
(Dated: 31 January 2013)
We propose a charge pump which converts solar energy into DC electricity. It is based on cyclic changes in
the spontaneous electric polarization of a photoferroelectric material, which allows a transfer of charge from
a low to a high voltage. To estimate the power efficiency we use a photoferroelectric liquid crystal as the
working substance. For a specific choice of material, an efficiency of 2% is obtained.
3
PACS numbers: 61.30.Gd, 77.84.Nh, 77.80.B-, 84.60.Jt,85.50.-n, 88.40.H-
1
0
2
-s
Photoferroelectrics are materials in which their ferro- f
n electricity can be affected by exposure to light. We pro- b - - - - - - - - - - - -
a +s + + + + + + + + + + + +
pose a device that works as a charge pump based on the
J pol
0 photoferroelectric effect. Varying light intensity cycles a x -+-+-+-+-+-+-+-+-+-+-+- ES0
photoferroelectricworkingmaterialthroughvariouselec-
3
- - - - - - - - - - - P0
tric polarization states and the associated charge in the V L + + + + + + + + + + + + S
] external circuit is pumped from low to high potential. 1
ft A body with a uniform (ferroelectric) polarization P0 -+-+-+-+-+-+-+-+-+-+-+-
o s
has zero polarization charge density in the bulk, ρ =
t.s −∇·Ps0 =0,while the surfacechargedensity assocpiaolted -spol +-+-+-+-+-+-+-+-+-+-+-+ Ef
a with the changeof polarizationfromits finite bulk value - - - - - - - - - - - -
m to zero on traversing the surface cutting Ps0 is given by + + + + + + + + + + + + +s
σ =P0. Figure1showsthisσ associatedwithtrun- f
- pol s pol
d catingP0. Suchalayerofchargeσ createsaninternal
s pol
n electric field E0 = −P0/ε ε in the material in this slab FIG. 1. A slab of ferroelectric of thickness L with two in-
o s s 0 sulating layers of thickness b under the bounding electrodes.
geometry, where ε is the relative dielectric constant of
c Apolarization surfacechargelayerσ associated withtrun-
[ the material. In the presence of the electrodes on the catingthespontaneouspolarization Ppo0l generatesaninternal
surfaces of the slab that are shorted together (V1 =0 in fieldE0. Afreesurfacecounterchargeslayerσ partiallyneu-
1 s f
Fig.1),andtheabsenceoftheinsulatinglayers,external tralizes the polarization charges to give a resultant electric
v
1 freechargesofsurfacedensityσf =−σpol flowtoneutral- field commensurate with an applied voltage V1. The electric
1 ize σpol. These free charges vitiate the field Es0 between field Ef of charges σf is also indicated.
1 theplatesbycreatinganoppositefield,Ef,thatisinthe
7 directionof Ps0. See Fig. 1 for counter chargelayers±σf
1. on the bounding electrodes. In fact, they have been fur- charges, if they cannot dissipate, generates an increased
0 ther adjusted from ∓σpol in order to increase Ef so that potential Von > V1 between the electrodes. This in-
3 the net field matches the actualapplied potential V1 6=0 creased potential Von allows charge pumping.
1 instead. It is such free, external balancing charges we
The spontaneous polarization of a photoferroelectric
: aim to optically pump.
v usually decreases1–3 under light irradiation as photons
i Considering the two electric fields, the voltage V1 can areabsorbedandmodifythepolarordering. Sincelightis
X
be expressed in the form
absorbedthe beamis necessarilyattenuated andthe po-
r
a 2b L P0L larizationprofile can no longer be uniform (except when
V = dx E −E0 =σ + − s , (1) light is powerful enough that P (x)=0 at all depths x).
1 Z (cid:0) f s(cid:1) f(cid:18)ε0ε1 ε0ε(cid:19) ε0ε Then ∇·Ps is non-zero also ins the bulk, and polariza-
tion charges will emerge inside the sample as well as at
where L is the thickness of the photoferroelectric sam-
the surface. Consequently a non-uniform electric field
ple itself, b is the thickness of insulating layers inserted
E (x,t) = −P (x,t)/ε ε appears in the sample, where
betweenthe sample andthe electrodesto preventcharge s s 0
P (x,t) is the electric polarization at the point x and
flow, and ε is the layers’ relative dielectric constant. If s
P0 were no1w diminished, then the internally-generated the illumination time t; note that Es(x,t) ≤ Es0. As the
s
field E0 would also be diminished. Now the field as- diode preventsbackflowofthe chargeto the battery(see
s
Fig. 1), the resulting voltage V (t) between the elec-
sociated with the free, formerly partially neutralizing on
trodes will be greater than V :
1
2b L 1 L/2
V (t)=σ + − P (x,t)dx, (2)
a)Electronicmail: [email protected] on f(cid:18)ε0ε1 ε0ε(cid:19) ε0εZ−L/2 s
2
ε∼ε , one gets a simple expression C =ε εA/L.
1 0
Upon switching off the light, the spontaneous polar-
izationwillevolvetoanewstate. Here,weshallsuppose
that it recovers its initial dark state value; this, in par-
ticular,holds fora largeclass ofphotoferroelectricliquid
crystals. As the polarizationincreasesintime, for acon-
FIG. 2. Charge pump diagram with S being the photofer- stant value of the charge on the electrodes, the voltage
roelectric sample. Charge is pumped from the battery V1 to across the sample starts to decrease from its value V2.
higher voltage V2. When the voltage drops to V , new charges will start
1
to flow from the left battery to maintain the voltage V
1
across the electrodes. Finally, the charge on the elec-
where the distance x is measured from the center of the
trodes recovers its value at the beginning of the cycle.
L/2
sample (Fig. 1). Writing P (t) = P (x,t)dx/L for
s −L/2 s Thiscycleisreminiscentofanopticalchargepumpbased
the spatial average of the polarizaRtion profile after time onacapacitancethatisopticallyvariable.4Inpractice,a
t, and replacing σf with the aid of Eqn. (1), we get self-priming circuit5 would avoid exhausting battery V1.
The same total charge ∆q pumped into the battery
L
Von(t)=V1+ ε0ε(cid:0)Ps0−Ps(t)(cid:1). (3) Vpr2ocisesssu.pTplhiueds,bthyeVw1otrok othuetpeultecWtroodfesthdisurcihnagrgreecpouvmerpy
is W =∆q(V −V )=∆q∆V, which gives
The described mechanism can be exploited to pump 2 1
chargefromalowtohighvoltagebattery. Manydifferent
A L
materials exhibit photoferroelectric behavior, and might W =ε0εL∆V (cid:20)ε ε Ps0−Ps(ton) −∆V(cid:21). (4)
be potential candidates for use in our device. We there- 0 (cid:0) (cid:1)
foreexplorethesuitabilityofthesematerialsforacharge
Wecanmaximizethisoutputwithrespecttothevoltage
pump, optimize their performance by specifying an ap-
difference ∆V. Using the condition dW/d∆V = 0, we
propriate electric circuit, and calculate the efficiency of
get the optimal choice of voltage difference
such pumps. Our general analysis is applicable to all
photoferroelectric materials. Only our final estimate of L V −V
(V −V )opt = P0−P (t ) = on 1. (5)
the efficiency of the pump will be demonstrated for par- 2 1 2ε ε s s on 2
ticular substances, photoferroelectric liquid crystals. 0 (cid:0) (cid:1)
The circuit diagram of the charge pump is shown in Since to pump charge we require the open circuit devel-
Fig.2. Thecentralcomponentofthiscircuitisthephoto- oped voltage to exceed that of the upper battery, that is
ferroelectric sample S placed between transparent con- V2 <Von, orequivalentlyV2−V1 <Von−V1, weseethat
ducting electrodes. The arrangement of diodes is such the above choice of voltage difference is allowed. Thus,
that the charge can flow from the voltage V1 to a higher for given voltages V1 and Von, the optimal V2 is
voltage V only. We shall describe how the electric po-
2
V +V
larization varies during a cycle. Vopt = 1 on. (6)
The photoferroelectric sample S in the dark state is 2 2
connected to the voltage V . When light is shone on
1 The maximum output W is then
m
the sample, the electric polarization decreases and the
voltageacrosstheelectrodesisincreasedabovethe value W = AL P0−P (t ) 2. (7)
V1, with charge on the electrodes being fixed (the left m 4ε ε s s on
diode prevents backflow of charge). As the electric po- 0 (cid:0) (cid:1)
larization further decreases, the voltage across the elec- Output is therefore higher if the dark state polariza-
trodes increases until it reaches the value V . Then the tion P0 and the average value of the polarization profile
2 s
chargestartstoflowthroughtherightdiode,whichleads P (t ) in the illuminated state differ more, that is if as
s on
to its being pumped into battery V at constant voltage muchpolarizationaspossibleis lost. The workdelivered
2
(Fig. 2). If the connection of the sample with the bat- depends on the volume AL of the working material.
teryV wereabsent,thevoltageacrossthe samplewould If I is the incident solar flux, and U is the energy
2 sun in
rise to a value we simply denote by V corresponding input per unit volume of the sample required to trans-
on
to V (t) with t = t , the duration of the illumination formthe polarizationstate ofthe workingmaterial,then
on on
phase of the cycle. t is determined by energy balance I At = U AL.
on sun on in
The charge transferred to the battery V is equal to The period of a cycle τ = t +t = U L/I +t
2 on off in sun off
∆q =C(V −V ),whereC isthetotalcapacitanceofthe thenfollows. Here,t isthecharacteristictimeforrelax-
on 2 off
sample. TherearetwoinsulatinglayersofcapacitanceC ation of polarization to its dark state value. The power
b
andaliquidcrystalofcapacitanceC connectedinseries. efficiency is then η =W /(τI A).
L m sun
The equivalent capacitance is given by 1/C = 2/C + The power efficiency of this cycle is significantly re-
b
1/C =(2b/ε +L/ε)/(ε A), where A is the area of the duced, due to the fact that no work is done during the
L 1 0
electrode. Takingintoaccountthatb≪L,andtypically time t . To avoid such kind of difficulties one can use
off
3
k n small θ. When the temperature is increased and crosses
athresholdvalue,the SmC*phasemostoftenundergoes
a second-order phase transition to the non-polar SmA*
phase.
q
The spontaneous polarization of a SmC* phase doped
with photosensitive molecules (for example, an azo or
P thioindigo dye) can be changed by light irradiation;1,2
S pure systems of dyes have also been used.3 Some dye
molecules can make transitions from the linear (trans)
ground state to the excited bent-shaped (cis) state by
absorbing a photon. The cis state isomers can disrupt
theSmC*ordering,whichleadstoachangeofP ,whence
s
thenamephotoferroelectriceffect. Iftheinteractionwith
FIG.3. AsmecticC*liquidhost. Guestdyemoleculeswitha
light is sufficiently strong it can completely destroy the
photoactivecenterindicated bya circleare also shown,some
SmC*phase,causingatransitiontothenon-polarSmA*
of them in the linear (trans) state, and others in the bent
phase. Dyemoleculesintheexcitedcis statere-isomerize
(cis) excited state.
thermallybacktothegroundtrans statewithsomechar-
acteristic time. Upon removal of light, the electric po-
larization eventually regains its initial dark state value.
anarrayofphotoferroelectricsamples. Theycouldbese-
Recently,ithasbeenarguedthatthemechanismandde-
quentially illuminated and then allowed to relax back to
tails of light absorption are crucial to understanding the
thedarkstate,eitherviaamovablefocusingmirror,orby
opticaldepressionofelectric polarization.8 Inparticular,
rotatinganarrayofsamples. Itisclear,however,thatthe
ithas been shownthatthe spontaneouspolarizationdis-
described setting will reduce to some extent the desired
plays a non-uniform profile through the sample.
enhancement of power efficiency. As typically t <t ,
on off
one should use an arrayof at least m=t /t samples. Here we suppose that the sample is confined between
off on
For such a device the power efficiency η is given by the twoparallelplates sothat the smectic layersareperpen-
above formula, but in which the cycle time τ is equal to dicular to the plates – the bookshelf geometry (Fig. 4).
t , that is The smectic layers usually shrink to some extent at the
on
tilting transition from the paraelectric SmA* to polar
W (P0−P (t ))2 SmC*phaseandformafoldedchevronstructure.9Given
η = m = s s on . (8) thatmaterialswithoutsubstantiallayershrinkage10have
U AL 4ε εU
in 0 in
also been found, in our simple analysis we shall neglect
Toobtainanumericalestimateofthepowerefficiency(8) thisshrinkage. Chargepumpsmadeofsampleswithlarge
we confine ourselvesto photoferroelectricliquid crystals, electricpolarizationinthedirectionperpendiculartothe
the main properties of which we sketch. electrodes have larger efficiency. A perpendicular polar-
Liquid crystals are anisotropic fluids which usually ization can be achieved by applying a voltage between
consistofrod-likemolecules. Theliquid-crystallinestates the electrodes. Indeed, a simple extension of the ap-
areobservedattemperaturesbetweenthesolidstateand proach of reference [11] reveals that for voltages higher
the ordinary isotropic liquid state. In the simplest ne- than Vc = 2bPs0/(ε0ε1) the sample’s polarization is per-
matic phaselong-rangetranslationalorderis absent,but pendicular to the electrodes. For b = 10nm, ε1 = 10,
the long molecular axes are orientationally ordered, on and for a SmC* material with Ps0 = 550nC/cm2 we get
average about a unit axial vector n, the director. In ad- asmallvoltageVc =1.25V. Weseethatthepolarization
dition to nematic orientational order, the molecules in willhavetherequireddirectionprovidedthatthevoltage
smectic phases are arranged into layers. In the smec- V1 (Fig. 2) is greater than Vc.
tic A phase (SmA), the molecules are organized as two- Typically one deals with SmC* hosts doped with dye
dimensional anisotropic liquids within the layers, with molecules, whose number fraction is a few percent. The
the nematic director n being parallel to the normal k of behavior of the average polarization after time t can
on
the layers. Inthe smectic C phase(SmC), n is no longer bedescribedtheoretically.8 Hereweshallsimplysuppose
parallel to k, but is tilted by an angle θ with respect to thatthelightissufficientlyintensesothatthereisatime
k (Fig. 3). The tilt angle θ is a function of temperature t (<t )suchthatP (t )vanishes. Inotherwords,we
on off s on
T. At a givenT, the director n is located on the surface canregardt astheminimaltimeneededforasufficient
on
of a cone centered around k with opening angle θ(T). depletion of the trans dye population to eliminate the
A SmC liquid crystal composed of chiral molecules is polarization. Taking P (t ) = 0, formula (3) for the
s on
referred to as a SmC* (Fig. 3). As first pointed out by voltageV reducestoV =V +LP0/ε ε. Forinstance
on on 1 s 0
Meyer6, the emergence of a (local) spontaneous electric for a SmC* material with P0 = 550nC/cm2 and ε =
s
polarizationP in SmC* is allowedalong k∧n since the 4 in a cell of thickness L = 2µm one obtains a V −
s on
plane ofk andnisnota mirrorplane. The spontaneous V ≈ 310V, which is much larger than V . Therefore,
1 1
polarizationisafunctionofthetiltangle,7andP ∝θfor the optimal voltage V is Vopt ≈155V.
s 2 2
4
ofdye species can be stabilizedby bonding them into an
elastomericSmC*host–alooselylinkedsolidthatisstill
abletochangeitsdegreeoforder. Suchsolidsalsoreduce
b theriskofchargetransportunderfields(V2/Lhere)asin
x dielectricactuationusingrubber.5 Lowerenergyphotons
P wouldgivecorrespondinglyhigherefficienciesη ∼2−5%.
L S Let us briefly consider the case of a non-zero polar-
z ization profile through the sample. We adopt a sim-
n
ple model for this profile, namely, we assume that the
y
polarization is eliminated in a layer of thickness ∆L,
while in the rest of the sample it is uniform and equal
to the dark state polarization P0. Then we can write
s
P = LP (x)dx/L = P0(L−∆L)/L. As I t A can
s 0 s s sun on
berouRghlyestimatedasUinA∆L,forthepowerefficiency
wegetη =(P0)2∆L/(4ε εU L). Theefficiencyis,there-
s 0 in
FIG. 4. Bookshelf geometry of a SmC* sample with layers fore, reduced by a factor of ∆L/L with respect to (9).
normaltotheelectrodes. Theliquidcrystalsituatedbetween
Our pump could equally work on cycles of tempera-
glass plates, coated with insulating layers, is placed between
turechangethatchangethespontaneouspolarization. In
two electrodes. The spontaneous polarization P lies in the
s this casethe input energyis U =n C(T)dT,where
xy–plane,thatis,intheplaneofthesmecticlayers. Toensure in tot
that the polarization is directed along the x axis, a voltage C(T) is the specific heat per moleculeR at temperature
acrosstheelectrodeshigherthanV =2bP0/(ε ε )isneeded. T, and the integral goes from the dark state tempera-
c s 0 1
ture of ferroelectric material to the temperature where
thespontaneouspolarizationis eliminated(SmC*-SmA*
phase transition temperature for liquid crystals). The
Supposing that P (t )=0, the efficiency (8) is
s on
heatthatis unavoidablygeneratedbyopticalabsorption
(P0)2 thusaddstotheefficiencyofouropticalenergyharvester.
η = s . (9) In summary, we have proposeda light-poweredcharge
4ε εU
0 in pump for energy conversion, using a photoferroelectric
workingmaterial. Theefficiencyisexplicitlygiven,which
Provided that t is shorter than the characteristic time
on
makes clear directions for further increase.
ofthermal recoveryof spontaneouspolarization,andthe
processofbackphotoconversionfromthecis tothetrans M.K. thanks the Winton Programme for the Physics
of Sustainability and the Cambridge Overseas Trust for
stateofdyemoleculescanbeneglected,theinputenergy
can be expressed as U =n ~ω. Here n is the number financialsupport,andM.W.thanksthe Engineeringand
in d d
of trans dye molecules per unit volume that need to be Physical Sciences Research Council (UK) for a Senior
converted to cis to eliminate P , and ~ω is the energy Fellowship. The authors thank David Walba for advice.
s
each dye molecule absorbs from the light beam. 1T.Ikeda, T.Sasaki, andK.Ichimura,Nature361,428(1993).
Togetanumericalestimateoftheefficiencywetakeas 2A. Langhoff and F. Giesselmann, J. Chem. Phys. 117, 2232
an example a polar SmC* host W314 doped with a few (2002).
mol%ofaracemicmixtureofW470azodyes12,13 (higher 3A. Saipa, M. A. Osipov, K. W. Lanham, C. H. Chang, D. M.
Walba, andF.Giesselmann,J.Mater.Chem.16,4170(2006).
dyeloadingsleadtolowerconversionduetofluxattenua- 4T. Hiscock, M. Warner, and P. Palffy-Muhoray, J. Appl. Phys.
tion3,8). Thesetwocompoundshaveaverysimilarstruc- 109,104506(2011).
ture, the N=N double bond of W470 being the only dif- 5T. G. McKay, B. O’Brien, E. Calius, and I. Anderson, Smart
ference. Thepolarizationofthe W314hostatT =31◦C Mater.Struct.19,055025(2010).
is roughly 550nC/cm2 and is one of the highest outside 6R. B. Meyer, L. Leibert, L. Strzelecki, and P. Keller, J. Phys.
(Paris)Lett. 36,L69(1975).
bent-core molecules.14 The trans absorption maximum 7S.T.Lagerwall,Ferroelectricandantiferroelectricliquidcrystals
of W470 dyes is located at 365nm, which corresponds (Wiley-VCH,NewJersey,1999).
to photons of 3.4eV. We assume that the quantum effi- 8M.Kneˇzevi´candM.Warner,J.Chem.Phys.137,144902(2012).
ciency for the trans to cis transition is equal to 1. The 9T. P. Rieker, N. A. Clark, G. S. Smith, D. S. Parmar, E. B.
Sirota, andC.R.Safinya, Phys.Rev.Lett.59,2658(1987).
relative molecular mass of W314 is 603, and assuming a
10A.deVries,A.Ekachai, andN.Spielberg,Mol.Cryst.Liq.Cryst.
densityofroughly103kg/m3,weobtainatotalmolecular Lett.49,143(1979).
number density ntot = 1027molecules/m3. If only, say, 11M.Cˇopiˇc,J.E.Maclennan, andN.A.Clark,Phys.Rev.E65,
2% of molecules need to be convertedto cis to eliminate 021708(2002).
the polarization, we obtain n =2×1025molecules/m3. 12D.M.Walba, M.B.Ros,N.A.Clark,R.Shao,K.M.Johnson,
d M. G. Robinson, J. Y. Liu, and D. Doroski, Mol. Cryst. Liq.
Taking the dielectric constant of W314 in the direction Cryst.198,51(1991).
perpendicular to the director n(see Fig.4)as ε=4,the 13K.W.Lanham,Master’sthesis,UniversityofColorado,Boulder
efficiency (9) is η ≈ 2%. Multiple layers with different (1999); C. H. Chang, Master’s thesis, University of Colorado,
dyes which absorb photons of different energies would Boulder(2000).
14T.Niori,J.Sekine,J.Watanabe,T.Furukawa, andH.Takezoe,
capture more of the broad solar spectrum. A gradient
J.Mater.Chem.6,1231(1996).