Electrode Polarization in Glassy Electrolytes: Large Interfacial Capacitance Values and Indication for Pseudocapacitive Charge Storage

Transcription

1 Elctrod Polarization in Glassy Elctrolyts: Larg Intrfacial apacitanc Valus and Indication for Psudocapacitiv harg Storag. R. Mariappan, T.P. Hins,. Roling partmnt of hmistry, Univrsity of Marburg, Hans-Mrwin-Strass, -353 Marburg, Grmany. bstract W study th lctrod polarization bhaviour of diffrnt Na-a-phosphosilicat glasss by masuring th diffrntial capacitanc btwn blocking Pt lctrods. t low applid dc bias voltags, w dtct a linar capacitanc rgim with intrfacial capacitanc valus considrably largr than xpctd from man-fild doubl layr thoris and also considrably largr than found for ionic liquids with similar ion concntrations. With incrasing bias voltags, th diffrntial intrfacial capacitanc xhibits a maximum around 1 V and a strong drop at highr voltags. W suggst that ths faturs ar causd by psudocapacitiv procsss, namly by th adsorption of mobil Na + ions at th lctrods. Whil psudocapacitiv procsss ar wll known in liquid lctrochmistry, mor dtaild studis on solid lctrolyts should offr prspctivs for improvd nrgy storag in solid-stat suprcapacitors. 1. Introduction Ion transport in solid matrials, such as dfctiv crystals, glasss, polymrs and nanocomposits, plays an important rol for various typs of solid-stat lctrochmical clls, such as thin-film battris, suprcapacitors, ful clls and lctrochmical snsors. Th xprimntal charactrisation of ion transport procsss is oftn don by taking ac impdanc spctra of a solid sampl btwn blocking mtal lctrods,.g. platinum or gold lctrods. In this cas, th high-frquncy part of th impdanc spctra can usually b attributd to bulk ion transport in th solid matrial, whil th low-frquncy part rflcts blocking of th mobil ions by th mtal lctrod. This low-frquncy phnomnon is calld lctrod polarization [1, ]. Th blocking lads to an accumulation or dpltion of mobil ions clos to th lctrods, which is rflctd in a strong incras of th frquncy-dpndnt ral part of th masurd capacitanc with dcrasing frquncy [1, ]. Th motivation for studying lctrod polarisation phnomna is twofold: (i) Th lctrod polarization part of th impdanc spctra should contain additional information about th ion transport proprtis of th solid lctrolyt,.g. information about th numbr dnsity of mobil ions [3]. (ii) Th formation of ion accumulation/dpltion layrs may b usd to stor lctrical nrgy in suprcapacitors [4, 5]. Howvr, progrss in basic scinc as wll as in suprcapacitor applications has bn impdd by th currnt poor thortical undrstanding of lctrod polarisation in disordrd solid lctrolyts. Pionring thortical work in this fild was don in th 195s and 196s by Macdonald, Friauf, Ilschnr, aumont, and othrs [6-8]. Thy usd man-fild approachs analogous to th classical Gouy-hapman thory for dilutd lctrolyt solutions. Ths approachs ar basd on th assumption that a mobil ion intracts with an avrag fild gnratd by th lctrod and by othr mobil ions. Whil this assumption sms rasonabl for solid lctrolyts with low numbr dnsitis of point dfcts, th applicability to disordrd solids with high mobil ion concntrations is far from obvious. In this typ of solids, local intractions btwn mobil ions should play an important rol for th structur of th intrfacial layrs. Nvrthlss, a larg numbr of frquncy-dpndnt capacitanc data of ion-conducting glasss and polymrs wr traditionally analyzd and intrprtd utilizing th abov manfild approachs. From th capacitanc spctra, valus for th by lngth wr xtractd, and ths valus wr usd for calculating th numbr dnsity of mobil ions. Oftn, th obtaind numbr dnsitis wr considrably lowr than th total ion contnt of th sampl [3, 9, 1]. Howvr, rcnt thortical and xprimntal work on th doubl layr capacitanc of ionic liquids (ILs), anothr class of concntratd lctrolyts, provids strong vidnc that this kind of intrprtation of capacitanc data is not appropriat. Th diffrntial capacitanc pr unit ara,, is dfind as: dσ (1) d ϕ whr σ is th lctrod charg pr unit ara and ϕ th lctrical potntial diffrnc btwn lctrod and bulk of th lctrolyt. Molcular dynamic simulations of chargd sphrs btwn mtal lctrods rval that th linar diffrntial capacitanc obtaind for small potntial diffrncs ϕ can b considrably smallr than th by capacitanc [11, 1]: εε () L Hr, ε and ε dnot th vacuum prmittivity and th rlativ prmittivity of th IL, rspctivly. Th by lngth by: L (N V, + V, - L is givn ε ε k T (3) + N ) with k and T dnoting oltzmann s constant and th tmpratur, whil and ar th bulk numbr dnsitis of NV,+ NV, cations and anions, rspctivly. Typical by lngths for ionic o liquids ar about.5, i.. smallr than th radii of cations and anions. This indicats that th ionic radii play an important rol for th structur and capacitanc of doubl layr. Typical xprimntal capacitanc valus for ionic liquids clos to th point of zro charg ar in th rang from 1-3 µf/cm [13-14]. t highr lctrod chargs, th diffrntial capacitanc dpnds clarly on ϕ [13-15]. Th physical origin of th potntial dpndnc has bn discussd by diffrnt authors, in particular by Kornyshv and coworkrs, in trms of ovrscrning and lattic saturation cts [16-19]. To our knowldg, dtaild xprimntal studis of th potntial-dpndnt intrfacial capacitanc of solid lctrolyts btwn blocking lctrods hav not bn publishd so far. In this Lttr, w prsnt th rsults of such studis on ion conducting glasss, namly on sodium calcium phosphosilicat 1

2 glasss of diffrnt compositions. Ths glasss xhibit bioactiv proprtis, and thir bioactivity can influncd by lctrical polarization btwn blocking lctrods [, 1]. Our rsults dmonstrat that th diffrntial capacitanc of ths glasss xhibits thr rmarkabl faturs: (i) ftr prparing a frsh glass sampl with frshly sputtrd Pt lctrods and aftr hating th sampl to th dsird tmpratur, th diffrntial capacitanc dcrass with tim bfor raching a constant valu. (ii) t low applid voltags, th diffrntial capacitanc is about on ordr of magnitud highr than found for ILs with similar ion dnsitis (iii) t dc bias voltags around 1 V, th diffrntial capacitanc xhibits a maximum and drops strongly at highr voltags.. Exprimntal Na-a-phosphosilicat glasss of compositions (mol%) 46.4 SiO 5. Na O 5. ao 3. P O 5 (46S4), 4.1 SiO 6.3 Na O 9. ao.6 P O 5 (4S6) and 44.6 SiO 31. Na O 3. ao 1. P O 5 (45S11) wr prpard by hating dry mixturs of Na O 3, ao 3, SiO, and (NH 4 ) HPO 4 in a Pt crucibl and mlting thm in an lctric furnac btwn 163 K and 1673 K for hours. ftr complt homognization, th mlts wr pourd into prhatd stainlss stl molds with a cylindrical shap (diamtr about mm). Th obtaind bulk glass sampls wr thn annald 4 K blow thir rspctiv glass transition tmpraturs (dtrmind by diffrntial scanning calorimtry) for 1 hours. Th annald glass discs wr cut into slics with a thicknss of about 7 8 µm using a high-prcision cutting machin (Strurs ccutom 5) quippd with a diamond saw blad. Finally, both facs of th glass slics wr polishd with Si (msh 1) by high-prcision grinding using a lapping machin (Logitc PM5). For th ac impdanc masurmnts, Pt lctrods wr sputtrd onto both facs of th sampls. Th ac impdanc spctra of th glasss wr masurd in a frquncy rang from.1 Hz to 1 MHz using a Novocontrol lpha-k impdanc analyzr quippd with a POT/GL 15V/1 lctrochmical intrfac. low rms ac voltag of 1 mv and variabl dc bias voltags up to 14 V wr applid to th sampls. Th sampl tmpratur was controlld (±. K) by th Novocontrol Quatro ryosystm. 3. Rsults and iscussion For obsrving th lctrod polarization in th frquncy rang of our masurmnts (ν >.1 Hz), th sampls had to b hatd to lvatd tmpraturs. Fig. 1 dpicts th ral part of frquncy-dpndnt ac capacitanc '(ν) (pr unit ara) of th 46S4 glass masurd at T 573 K without applying a dc bias voltag. Th capacitanc was calculatd by using th following xprssion: 1 Z ''( ν ) 1 '( ν ) (4) π ν [ Z'( ν )] + [ Z' '( ν )] whr is th ara of th sampl facs, and Z'(ν) and Z''(ν) ar th ral and imaginary part of th complx impdanc, rspctivly. t high frquncis abov 1 khz, a capacitanc platau is found rflcting th bulk capacitanc of th sampl. With dcrasing frquncy, '(ν) incrass strongly, and blow.1 Hz, thr is a lvlling-off into a platau rgim rflcting th intrfacial capacitanc. Whn w carrid out masurmnts on a frshly prpard sampl with frshly sputtrd Pt lctrods, w obsrvd a drop of th intrfacial capacitanc with incrasing masurmnt tim. This is shown in Fig. for th 46S4 glass at T 573 K and ν.1 Hz. Th capacitanc '(.1 Hz) dcrass xponntially with tim and rachs a stabl valu aftr about 3 hours. Thrfor, masurmnts with applid dc bias voltag wr not startd bfor stabl ac capacitanc valus wr dtctd. In Fig. 3, th frquncy-dpndnt capacitanc of th 4S6 glass is shown for various applid dc bias voltags, V dc. In th bulk capacitanc rgim, th capacitanc is indpndnt of V dc, but in th frquncy rang blow 1 khz, th dc bias voltag xrts a significant influnc on th capacitanc. t dc bias voltags blow 3 V, rliabl capacitanc data could b obtaind down to 1 - Hz. t highr dc bias voltags, th capacitanc rlaxation shiftd to highr frquncis, and th low-frquncy part of th spctra bcam noisy. Th opn circls in Fig. 3 dnot th lowst frquncis whr nois-fr data could b obtaind. Th capacitanc valus at ths frquncis wr usd for plotting th voltag dpndnc of th diffrntial intrfacial capacitanc in Fig. 4 (closd symbols). lthough th xact capacitanc valus dpnd on th glass composition, w obsrv svral common faturs (i) t dc bias voltags blow 1 mv, thr is a linar rgim with a virtually bias voltag-indpndnt intrfacial capacitanc. Hr, w obtain larg capacitanc valus in a rang from 1 to 3 µf/cm. (ii) bov 1 mv, th diffrntial intrfacial capacitanc incrass with incrasing dc bias and rachs a maximum around 1 V. (iii) bov 1 V, th diffrntial intrfacial capacitanc dcrass strongly with incrasing dc bias. In ordr to tst whthr ths voltag-dpndnt changs in th diffrntial capacitanc ar rvrsibl or irrvrsibl, w prformd th following tst: ftr taking a capacitanc spctrum at a spcific bias voltag, a scond spctrum without applid dc bias was rcordd. Thn, th nxt spctrum was takn with a highr dc bias, followd again by a masurmnt without dc bias. Th opn symbols in Fig. 4 show th diffrntial intrfacial capacitancs obtaind undr zro dc bias, dirctly aftr having prformd a masurmnt at V dc (shown as closd symbol). If th changs in th diffrntial intrfacial capacitanc wr compltly rvrsibl, thn th opn symbols for a spcific glass should b all at th sam capacitanc valu. s sn from th figurs, th irrvrsibl cts du to th dc bias ar wak in th cas of th 46S4 and th 4S6 glass, whil thy ar mor pronouncd in th cas of th 45S1 glass. Nvrthlss for all thr glasss, th major part of th dc bias voltag dpndnc of intrfacial capacitanc is du to rvrsibl cts. In th following, w discuss th implications of ths xprimntal findings. First of all, w not that th linar capacitanc valus of our glasss obtaind at low voltags ar by about on ordr to magnitud highr than thos found in ionic liquids with similar ion dnsitis and by lngths. What valus for th intrfacial capacitanc do w xpct whn w considr a man-fild doubl layr? Th simplst approach is to assum a Hlmholtz layr with capacitanc and in sris to a diffus layr with capacitanc. In this cas, th ovrall diffus capacitanc in a two-lctrod configuration can b writtn as: 1 HL ε ε + (r + L ) HL diffus + Na Th radius of th sodium ions is rna o (5) + 1. Th numbr dnsity of Na + ions in our glasss is 3 N V 1, Na + cm, yilding a by lngth o. Whn w assum that th ctiv L ε ε N V, Na+ k T.5 dilctric constant ε is idntical to th lctronic polarisability of th sodium ions, w can stimat that ε. This would

3 rsult in 6 µ F/cm. Whn w assum that ε is idntical to th macroscopic high-frquncy prmittivity of th glass, ε 1, w obtain a linar doubl layr capacitanc not highr than 3 µ F/cm. Th xprimntally dtrmind doubl layr capacitancs of ILs ar indd in this rang, but th capacitancs of our glasss ar considrably highr. On may now argu that th distinction btwn a Hlmholtz and a diffus layr is somwhat arbitrary whn L r. This is crtainly corrct, + < Na but whatvr is th xact structur of th doubl layr, it is hard to bliv that its ctiv thicknss is smallr than 1- Å and that th ctiv prmittivity in th doubl layrs is highr than 1. In addition, w considrd th possibility that th tru intrfacial ara btwn our glasss and th Pt lctrods might b highr than th nominal ara. In ordr to gt information about this, w studid th surfac topography of our glass sampls bfor sputtring th Pt lctrods by mans of atomic forc microscopy (FM). Howvr for all glasss, w found that th tru surfac ara is not mor than 1% largr than th nominal on. onsquntly, w stat that man-fild thoris ar not sufficint to dscrib th glass / Pt intrfacs. In liquid lctrochmistry, capacitanc valus xcding 1 µ F/cm hav bn found in th cas of psudocapacitiv charg storag, i.. whn molculs or ions ar spcifically adsorbd at lctrods [4,, 3]. To our knowldg, such procsss hav not bn studid or discussd in any dtail for glassy lctrolyt matrials. In th cas of our Na + ion conducting glasss, th simplst approach is to assum a potntial-dpndnt Langmuir-typ adsorption of Na + ions at th platinum lctrods, which can b dscribd by a Nrnst-typ quation [4, 3]: RT 1 ϑ ϕ ϕ + ln (6) F ϑ Hr, ϕ dnots a standard potntial, whil ϑ is th fractional covrag of an lctrod by Na + ions. Whn is th ctiv ara ndd by a singl Na + ion at th lctrod surfac, thn th lctrod charg pr unit ara is givn by: σ ϑ (7) This rsults in th following xprssion for th diffrntial capacitanc: (8) d ϕ d ϕ RT 1 ϑ (1 ϑ) dσ dϑ F ϑ(1 ϑ) kt This quation implis that th diffrntial capacitanc xhibits a maximum at ϑ.5. In ordr to stimat th factor k T w assum that (5 ), i.., du th rpulsiv intraction btwn th adsorbd Na + ions, it is unlikly that th ions approach ach othr closr than a fw. t T 573 K this rsults in and in max ( ϑ.5) 3 µ F / cm, 1 F / cm k T µ which is in rasonabl agrmnt with our rsults shown in Fig. 4. t highly positiv and highly ngativ lctrod potntials, w hav ϑ and ϑ 1, rspctivly, rsulting in. Sinc adsorption phnomna xhibit, in gnral, a strong tmpratur dpndnc, it is not surprising that a chang in th sampl tmpratur lads to a thrmal rlaxation of th masurd intrfacial capacitanc, as shown in Fig.. In our prsnt xprimnts, w usd a configuration with two idntical blocking lctrods. Thrfor, w hav no information about th individual potntial drops at both lctrods, and only a smi-quantitativ comparison btwn xprimnt and thory can b mad. In ordr to larn mor about th psudocapacitiv procsss at th individual lctrods, w suggst two possibilitis: (i) Usag of on blocking and on non-blocking lctrod. In this cas, th voltag drop at th non-blocking lctrod should b ngligibl. (ii) Usag of on small-ara and on larg-ara lctrod. In this cas th voltag at th larg-ara lctrod should b ngligibl. This will b th subjct of futur xprimnts. 4. onclusions W hav studid th diffrntial capacitanc of diffrnt sodium ion conducting glasss btwn blocking Pt lctrods. W find that th linar intrfacial capacitancs ar considrably highr than xpctd from man-fild doubl layr thoris and also considrably highr than found for ionic liquids with similar ion concntrations. With incrasing bias voltag, th diffrntial intrfacial capacitanc xhibits a maximum around 1 V and a strong drop at highr voltags. W xplain ths faturs in a smi-quantitativ fashion by assuming psudocapacitiv charg storag, namly adsorption of Na + ions at th lctrods. From an application point of viw, our rsults point to th possibility to stor a considrabl amount of lctrical nrgy at th intrfac btwn mtals and ion conducting glasss. cknowldgmnts W ar gratful to th lxandr von Humboldt Foundation and to Grman Scinc Foundation (FG) for financial support. Rfrncs [1] E. arsoukov and J. R. Macdonald, Impdanc Spctroscopy, John Wily & Sons, 5 [] M. E. Orazm and. Tribollt, Elctrochmical Impdanc Spctroscopy, John Wily & Sons, 8. [3] H. J. Schutt and E. Grds, J. Non-ryst. Solids 144, 14 (199). [4]. E. onway, Elctrochmical Suprcapacitors, Kluwr cadmic / Plnum Publishrs, Nw York, 1999 [5] P. Simon and Y. Gogotsi, Natur Mat. 7, 845 (8). [6] J. R. Macdonald, Phys. Rv. 9, 4 (1953). [7] R. J. Friauf, J. hm. Phys., 139 (1954). [8] J. H. aumont and P. W. M. Jacobs, J. Phys. hm. Solids 8, 657 (1967). [9]. Pitarch, J. isqurt and G. Garcia-lmont, J. Non-ryst. Solids 34, 196 (3). [1] R. J. Klin, S. Zhang, S. ou,. H. Jons, R. H. olby and J. Runt, J. hm. Phys. 14, (6). [11] S. K. Rd, O. J. Lanning and P.. Maddn, J. hm. Phys. 16, 8474 (7). [1] M. V. Fdrov and.. Kornyshv, Elctrochim. cta 53, 6835 (8). [13] M. T. lam, M. M. Islam, T. Okajima and T. Ohsaka, J. Phys. hm. 111, 1836 (7). [14] M. M. Islam, M. T. lam and T. Ohsaka, J. Phys. hm. 11, (8). [15] V. Locktt, R. Sdv, J. Ralston, M. Horn and T. Rodopoulos, J. Phys. hm. 11, 7486 (8). [16].. Kornyshv, J. Phys. hm. 111, 5545 (7). 3

4 [17] M. V. Fdrov and.. Kornyshv, J. Phys. hm. 11, (8). [18] M. T. lam, M. M. Islam, T. Okajima and T. Ohsaka, J. Phys. hm. 11, 61 (8). [19] O. J. Lanning and P.. Maddn, J. Phys. hm. 18, 1169 (4). []. Obata, S. Nakamura, Y. Moriyoshi and K. Yamashita, J. iomd. Matr.Rs. 67, 413 (3). [1]. R. Mariappan and. Roling, Solid Stat Ionics 179, 671 (8). []. E. onway and W. G. Pll, J. Solid Stat Elctrochm. 7, 637 (3). [3].E. onway and G. Jrkiwi, Solid Stat Ionics 15, 93 (). Figur captions: '(ν) [µf/cm ] Intrfacial capacitanc ulk capacitanc ν [Ηz] FIG. 1: Frquncy-dpndnt ral part of th capacitanc pr unit ara, ' ( ν ), for th 46S4 glass at T 573 K. Th spctrum was takn at zro dc bias voltag using a rms ac voltag of 1 mv. '(.1 Hz) [µf/cm ] S4 at 573 K V rms 1mV τ 3 hrs ± 1 min Tim [hrs] FIG. : Rlaxation of th low-frquncy capacitanc of th 46S4 glass, aftr hating up a frshly prpard sampl to 573K. '(ν) [µf/cm ] S6 at 573 K c bias. V 5 mv.4 V.6 V 1. V 1.5 V 3. V 4. V 5. V 14. V slctd frq ν [Hz] FIG. 3: c bias voltag dpndnc of th capacitanc spctra of th 4S6 glass at T 573 K. Th opn circls dnot th frquncis slctd for plotting th voltag dpndnc of th diffrntial intrfacial capacitanc in Fig. 4. [µf/cm ] S1(E.77 V) at 543 K 4S6(E.83 V) at 573 K 46S4 (E.84 V) at 573 K 1 mv ac + dc bias 1 mv ac, no dc bias V dc (V) FIG. 4: c bias voltag dpndnc of th diffrntial intrfacial capacitanc,, for th thr glasss 46S4, 4S6, and 45S1. Th closd symbols rprsnt th capacitancs masurd undr applid bias voltag V. Th opn symbols rprsnt th capacitancs masurd at zro bias voltag, dirctly aftr having prformd a masurmnt at V. dc dc 4

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