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2015

Novel materials with effective super dielectric

constants for energy storage

Cortes, Francisco Javier Quintero

Cortes, Francisco Javier Quintero, and Jonathan Phillips. "Novel Materials with

Effective Super Dielectric Constants for Energy Storage." Journal of Electronic

Materials, v. 44, no. 5 (2015) pp.1367-1376

http://hdl.handle.net/10945/49628

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Novel Materials with Effective Super Dielectric Constantsfor Energy Storage

FRANCISCO JAVIER QUINTERO CORTES1 and JONATHAN PHILLIPS2,3

1.—Department of Chemical Engineering, University of Colombia, Bogota, Colombia. 2.—NavalPostgraduate School, Monterey, CA 93943, USA. 3.—e-mail: jphillip@nps.edu

To test a theory of the recently discovered phenomenon of super dielectricbehavior at very low frequency, the dielectric constants of several ‘pastes’,composed of porous alumina powders filled to the point of incipient wetnesswith water containing dissolved sodium chloride, were measured. The effec-tive dielectric low frequency constants of some of the pastes were greater than1010, dramatically higher than that of any material ever reported. Moreover,the total energy density reported for one capacitor generated with NaCl-basedsuper dielectric material is marginally higher than found in any prior report.These results are consistent with this recently postulated model of low fre-quency super dielectric behavior in porous, non-conductive materials satu-rated with ion-containing liquids: upon the application of an electric field, ionsdissolved in the saturating liquid contained in the pores will travel to the endsof pore-filling liquid droplets creating giant dipoles. The fields of these giantdipoles oppose the applied field, reducing the net field created per unit ofcharge on the capacitor plates, effectively increasing charge/voltage ratio,hence capacitance. This is simply a version of the theory of ‘polarizable media’found in most classic texts on electromagnetism. Other observations reportedhere include (1) the impact of ion concentration on dielectric values, (2) amaximum voltage similar to that associated with the electrical breakdown ofwater, (3) the loss of capacitance upon drying, (4) the recovery of capacitanceupon the addition of water to a dry super dielectric material, and (5) the linearrelationship between capacitance and inverse thickness. All observations areconsistent with the earlier proposed model of the super dielectric phenome-non. An extrapolation of results suggests this technology can lead to energydensity greater than the best lithium-ion battery.

Key words: Dielectric, capacitors, energy storage

INTRODUCTION

Recently, a material with an extraordinarydielectric constant at low frequency (ca. 0.001 Hz),greater than 108, was described.1,2 This material,dubbed a ‘super dielectric’ (SDM), was composed of ahigh surface area alumina powder saturated with asolution of boric acid (pH 5) to the point of ‘incipientwetness’. Capacitors generated with this materialwere demonstrated to behave as electrostatic

capacitors at low frequency below about 0.8 V.Extrapolating the data to 5-lm layers, a thicknessregularly attained with standard ‘ceramic’ capaci-tors suggested that this material could be used incapacitors easily capable of storing energy at about50 J/cm3. Moreover, a theory was advanced thatsuggested that a family of SDM exists, and thatsome members of this family of materials couldachieve far higher energy densities. The theory: Anyporous, non-electrically conductive solid saturatedwith a liquid containing dissolved ions is potentiallya SDM, because of the fundamental mechanism ofsuper dielectric behavior. Specifically, in an electric

(Received August 8, 2014; accepted January 8, 2015;published online January 31, 2015)

Journal of ELECTRONIC MATERIALS, Vol. 44, No. 5, 2015

DOI: 10.1007/s11664-015-3641-8! 2015 The Minerals, Metals & Materials Society (outside the USA)

1367

field, ions in the liquid drops move to form dipolesthat ‘oppose’ the applied field. This increases thecharge on the electrodes required to produce a givennet voltage, hence increasing the q/V ratio, that is,the capacitance. The maximum voltage such mate-rials can sustain is limited by the breakdown volt-age of the liquid phase. This postulate, developed byour team, is really just a modest modification of theclassic ‘ponderable media’ model of dielectricbehavior, described in standard physics texts.3

A simple illustration of the practical implicationsof the model: If the same alumina employed in thefirst study, were to be saturated with an electrolytewith a higher discharge voltage than water, forexample 2.5 V, but containing the same amount ofdissolved boric acid, a novel paradigm super capaci-tor (NPS) type capacitor of 5 lm thickness would beable to store >600 J/cm3. Clearly, the model shouldbe tested, as it suggests that the original reportrepresents only one example of a broad class ofmaterials. The arbitrary ‘first example’ of the earlierstudy is unlikely to represent an optimum formu-lation. Hence, testing aspects of the model may leadto the discovery of materials with even higherdielectric constants.

The work described here was deliberately limitedto permit a focus on the potential value of the superdielectric-based capacitors for electric energy stor-age. Thus, the study was limited to measuringcapacitance at !0 Hz. There is nothing unique tothis limitation. Indeed, standard carbon superca-pacitors are only viable at very low frequency,4,5

primarily because of the relatively high equivalentcircuit output impedance. Hence, the study does notaddress the issue of using an SDM-based capacitoras a circuit element, although such studies areclearly a component required to fully understandSDM.

The focus on energy storage also determined themethod employed to study the (effective) dielectricconstant. Energy storage in ceramic capacitors is afield of considerable debate. Recently, it wascogently argued that some capacitance data wasimproperly extrapolated without regard to satura-tion, maximum voltage, operating voltage and otherfactors,6 to yield dramatically exaggerated maxi-mum energy density for ferroelectric-based capaci-tors. In order to avoid these difficulties, the methodemployed allows a direct measure of the totalenergy output from the capacitor. Specifically, di-rect measurement of the RC time constant, where Ris resistance and C is capacitance, over full chargeand discharge cycles was selected. No algorithm isneeded, just the time integration of the collectedV2/R (V is voltage) data.

The use of standard ‘capacitance’ meters orimpedance spectroscopy was avoided as thesemethods do not produce a direct measure of energystorage. In both meters and impedance spectros-copy, the underlying algorithms are based on ana-lysis of RC time constants over very small voltage

and time intervals. In both, the charging rate oververy short charge times, hence nearly constantvoltage, is measured and deconvoluted to yieldcapacitance. Indeed, the value of the voltageamplitude has to be smaller than the thermal volt-age,7 about 25 mV at 25"C in order to work in arange where the current changes linearly withvoltage. The fact that the system has to reach a‘steady state’ with minor variations in voltageimplies that the information collected is valid for afully charged capacitor at a specific voltage, andthat is almost always 0 V.8

Clearly, any use of the data collected fromimpedance spectroscopy, etc. to determine storedenergy density requires an extrapolation of datacollected at a single voltage, and a relatively highfrequency (>10 Hz) to a range of voltages at !0 Hz.This is problematic. Indeed, in those rare instanceswhen the method is employed at a selected set ofvoltages, even for crystals in the ‘barium titanatefamily’, impedance spectroscopy shows capacitanceto continuously vary as a function of voltage, insome cases, very dramatically,6,9 and, theoretically,this should be the case for all ‘high’ dielectric con-stant materials.9 Moreover, these variations arefrequency-dependent, and the impedance spectros-copy is not able to determine maximum operatingvoltage at near 0 Hz.

The voltage/time data from the RC time constantmethod also yield capacitance as a function of volt-age, albeit at !0 Hz. For the material studied here,there is not a continuous variation of capacitancewith voltage. Indeed, there are only two significantcapacitance values, one from !1.1 V to !300 mV,and the other from !300 mV to 0 V. These dataindicate that the material is truly acting at 0 Hz like aclassic dielectric over broad voltage ranges. Finally, itis notable that preliminary investigation withimpedance spectroscopy shows the novel dielectricsdescribed in this manuscript maintain super highdielectric values (>108) to at least 1 kHz and thatdielectric loss is also insignificant below 1 kHz.10

As the study was focused on testing the postulatethat any ionic solution added to the same aluminaused in the first study could produce super dielectricbehavior at !0 Hz, only the source of the ions waschanged. All other parameters, particularly thealumina used, the use of water as the electrolyte,the ratio of water/alumina used to form the paste,etc., were (nearly) unchanged. A few samples madeof different dielectric layer thicknesses were studiedto demonstrate that interface effects were eitherminimal or non-existent. In sum, the prime focus ofthe study was the demonstration that a pH neutralsalt, sodium chloride (NaCl), dissolved in water canbe employed to create SDM. The results were com-pletely consistent with the earlier model; moreover,the (effective) dielectric constants observed for twoof the pastes (!1010), were nearly two orders ofmagnitude higher than reported in the first paperon super dielectrics, and the maximum operating

Cortes and Phillips1368

voltage more than 30% greater. This led to thecreation of a first-generation SDM-based capacitor,or NPS using an electrolyte of NaCl dissolved inwater with an energy density as high as any pre-viously reliably reported for a ceramic capacitor.

EXPERIMENTAL

Dielectric fabrication: The materials employed tocreate the specific dielectric employed in this study,alumina/NaCl solution SDM (Salt-SDM), were highsurface area aluminum oxide powder (Alfa Aesar,c-phase, 99.97%, 3 lm average particle size powder,surface area 80–120 m2/g), NaCl powder (Sigma-Aldrich, 10-mesh anhydrous beads, 99.999%), anddistilled deionized water. These constituents weremixed by hand in three ratios. In all cases, thisalumina:H2O ratio was the same: 1 g alumina:1.1 mL H2O. Three different NaCl ratios wereemployed: low salt: 0.01 g salt/1 g alumina; mediumsalt: 0.1 g salt/1 gm alumina; and high salt: 0.3 gsalt/1 g alumina. In each case, the mixing processwas as follows. First, water was added to a plasticcup, next salt was added and the mixtures wereagitated by shaking, not stirring, until all the saltwas dissolved in the water. Finally, alumina, in theproper ratio, was added gradually. This created aspreadable paste with little or no ‘free’ water(incipient wetness). It is interesting to note that saltand water are pH neutral.

As pore structure is a significant component of theproposed model, the surface area and pore structurewere determined from BET (liquid nitrogen tem-perature) isotherms collected at 77 K and analyzedusing a Quantachrome NOVA 4200e. Two sampleswere independently measured and both yielded re-sults within 5% for all parameters; specifically,these were a surface area of 39 ± 1 m2/g, a totalpore volume of 0.45 cm3/g, and an average pore ra-dius of 245 ± 3 A.

The dielectric paste was spread evenly on a 5-cm-diameter disc of GTA (Premium, 99.8% graphite)grade Grafoil (0.76 mm thick, >99.99% carbon). Asdescribed elsewhere11,12 Grafoil is a commerciallyavailable high purity carbon material (available insheets or rolls) made by compressing naturallyoccurring graphite flakes with a surface are of theorder of 20 m2/g. In the final step, a second sheet ofGrafoil was placed on top, then mechanically pressedto create a near constant thickness as determined bymeasurements made at multiple positions using ahand-held micrometer. This step completed the con-struction of a super dielectric-based capacitor. Thedielectric layer thickness, required to compute thedielectric constant, used in all computations wasbased on subtracting the Grafoil sheets thickness fromthe measured gross thickness of the capacitor. Themeasured thicknesses of the dielectric layers used inthe study of salt content effect are as follows: low salt0.64 ± 0.08 mm, medium salt 0.50 ± 0.06 mm, highsalt 0.46 ± 0.02 mm. The effect of thickness on

capacitance was studied as described in the ‘‘Results’’.It is notable that errors in the thickness measure-ments, about 10%, are the dominant error source.

Once constructed, the capacitors were placed inan electrically insulating plastic jig with bottomand top cylindrical aluminum electrodes of 5 cmdiameter and 5 mm thickness. A 250-g weight wasplaced on top in all cases. These capacitors werethen placed in simple circuits (Fig. 1) for mea-surements of charge and discharge over nearly thefull range of possible voltages. It is important tonote that in all cases in this study charging anddischarging was through a 7.5-kX resistor for thelow and medium salt capacitors, and a 20-kXresistor for the high salt capacitor and those atmedium salt and varying thickness. The use of asimple circuit, rather than a commercial meter, tomeasure capacitance and subsequently dielectricconstant, was dictated by the goal of this program:measuring the ability of the capacitor to storeelectrical energy. In order to evaluate the capacityfor electrical energy storage, maximum operatingvoltage and !0 Hz data are needed. These valuesare not available from meters.

The primary test platform was a NationalInstruments ELVIS II electronics prototyping boardimplemented with LabView 2011 software. Anadditional multimeter, Agilent U1252A, was regu-larly used for independent parameter verification. Itis further of note that the capacitance of severaltypes of commercial capacitors were measuredusing the above-described instruments and protocol,and in every case the measured value and the listedvalue were within 30%.

Discharge data were analyzed to determinecapacitance using the classic voltage decay equationfor a capacitor discharging through a constant load(R):

Ln V=V0ð Þ ¼ %t=RC (1)

Hence, the slope of a curve of the left side of Eq. 1versus t is 1/RC. As R is known and fixed, Cis readily obtained. The value of C and therequired dimensional measurements were used (see‘‘Discussion’’) to determine the dielectric constant.

Fig. 1. Testing circuit. With the switch ‘down’ the discharge voltageacross the capacitor is measured, and with the switch ‘up’ the voltageacross the capacitor during the charge is recorded.

Novel Materials with Effective Super Dielectric Constants for Energy Storage 1369

RESULTS

The charging and discharging behavior of fivecapacitors created with SDM, that is NPS, werestudied. The primary target of this study was toshow the effect of ion identity is not critical in cre-ating SDM. Another objective was to study theimpact of ion concentration on capacitive behavior.Thus, the NaCl concentration was varied by a factorof 30 over three Salt-SDM capacitors, while holdingall other parameters virtually constant. However,small differences in some parameters, particularlythe thickness of the dielectric layer (less than afactor of 1.5), was an inevitable consequence of theimprecise nature of the hand construction. Also, theimpact of dielectric layer thickness, over a factor ofsix, in which all other parameters were held con-stant, confirmed a major observation of the firststudy: the dielectric constant of SDM is nearlyindependent of layer thickness.1,2

It must also be noted that this study only relatesdirectly to energy storage. If we correlate ‘frequency’with time constant, these data are only strictly validbelow 10%3 Hz, as in all cases the RC time constantsin this work were more than 1000 s. Ongoing work,it should be noted, demonstrates that even at 1 kHzthese materials have dielectric constants >108.

Low Salt NPS Capacitor

Repeated charge/discharge cycles for this capaci-tor are shown in Fig. 2. Although the appliedcharging voltage was 4 V, the Salt-SDM-basedcapacitors never reached more than about 1.8 V.From Fig. 2, it is readily apparent that this capac-itor, which is exemplary of all studied, discharged instages; initially very rapidly, down to approximately1.1 V, then much more slowly. As discussed in detailbelow, the slow discharge region, that is below!1 V, can also be divided into two different dis-charge regimes.

To explore the discharge behavior in a quantita-tive fashion, the discharge voltage/time data fromthe three cycles shown in Fig. 2 were plotted, below1.1 V in a semi-log form (Fig. 3). For a constant

capacitance, these plots are linear, and show twolinear regions of different slope with an ‘elbow’between. In sum, the data can best be modeled asshowing three regions of capacitance. The firstregion is between the highest voltages reachedduring charging, !1.8 V, and about 1.1 V. In thisregion, the capacitance is low, and no effort wasmade to determine the actual value. The secondregion is for voltages between !1.1 V and !350 mV.In this region, the capacitance is very high andconsistent for all three cycles. The third region isvoltages below !300 mV. In this region, the capac-itance is ‘off scale’ relative to commercial ceramiccapacitors of the same size. Actual capacitance val-ues are given in Table I.

Medium Salt

The discharge behavior of the medium salt andlow salt dielectrics were qualitatively similar.Capacitors created with either discharged rapidlyabove a particular voltage, and both showed an‘elbow’ in the discharge curve at a low voltage thatcorresponded to a change in capacitance (Fig. 4).However, the quantitative values associated withthese features were different. For the medium salt,the high capacitance/slow discharge point in themedium salt was lower, about 0.9 V, ratherthan 1.1 V. Also, the dielectric constants for themedium salt were consistently higher. During thehigh voltage leg, the low salt dielectric constant wasfairly consistent over three discharge curves,equalling 3.5 ± 0.4 9 109, whereas the medium saltdielectric constant was never less than 2.7 9 1010,nearly eight times higher. The dielectric constant ofthe low voltage leg of the medium salt was at leastfour times higher than that observed at low salt.

In order to test the ‘liquid dipole’ aspect of thetheory, the medium salt capacitor was allowed to dry,its capacitance measured, and then the paste was‘re-wetted’ and its capacitance measured again.According to the theory, an NPS capacitor should

Fig. 2. Low salt cycles. Three cycles of charge and discharge areshown. The low salt NPS capacitor never charges above 1.8 V, butcan clearly discharge to zero and can be repeatedly recharged.

Fig. 3. Two regions of capacitance. The numbers refer to the dis-charge cycles in Fig. 2, and the V0 value in all cases was 1.1 V.Clearly, for cycles 2 and 3, there is a sharp change in capacitance atabout 350 mV. (The first cycle has a less ‘sharp’ elbow).

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have virtually no capacitance after drying, but capac-itance should be restored with the addition of water.All observations were consistent with these expecta-tions of theory, as described in more detail below.

To test the ‘dry state’, the medium salt capacitorwas allowed to sit in the room for 15 days in order to‘dry out’. Indeed, as shown in Fig. 5, at the end ofthis period, the ‘paste’ appeared dry and cracked. Inthis state, the medium salt NPS capacitor had ameasured resistance of !5 MX, and no measurablecapacitance. That is, after charging for more thanan hour, the capacitor discharged to !1 mV in lessthan 10 s. The measured near-zero capacitance isconsistent with the behavior anticipated by theory:in the absence of water in the pores, there can be no‘giant dipoles’, hence no super dielectric behavior.

As noted above, the following is a logical correla-tion to the giant dipole theory: A dried and ‘dead’

Salt-SDM-based capacitor can be restored to initialperformance by the addition of water. Indeed, as thesalt content is not modified by the drying process,the addition of water to the pores should re-dissolvethe salt and permit giant dipoles to form. Concom-itantly, super dielectric behavior should be restored.Hence, water was added to the dried paste of themedium salt NPS capacitor by evenly spreadingwater, roughly equal to the amount initially presentin the dielectric based on an initial measure of theweight of the paste employed in creating thedielectric, on one side of the Grafoil sheet which wasremoved to permit the inspection (Fig. 5). Thissheet, water side down, was then pressed back ontothe dielectric, reforming the capacitor. The result of

Table I. Key parameters including capacitance and dielectric constant

Saltlevel Cycle Voltage

Capacitance(f)

Dielectricconstant

Max error %capacitance and

dielectric

Low 1st discharge, high volts 1.1–0.3 0.086 3.1 9 109 ±20%Low 1st discharge, low volts <0.3 0.093 3.4 9 109 ±20%Low 2nd discharge, high volts 1.1–0.35 0.11 3.9 9 109 ± 20%Low 2nd discharge, low volts <0.30 0.306 1.1 9 1010 ± 20%Low 3rd discharge, high volts 1–0.35 0.09 3.3 9 109 ±20%Low 3rd discharge, low volts <0.30 0.45 1.6 9 1010 ±20%Medium 1st discharge, High Volts 0.8–0.3 0.98 2.7 9 1010 ± 25%Medium 1st discharge, low volts <0.3 2.25 6.3 9 1010 ±25%Medium 2nd discharge high volts 0.9–0.3 1.05 3.1 9 1010 ±25%Medium 2nd discharge low volts <0.3 2.25 6.3 9 1010 ±25%Medium After dry and Re-wet 0.9–0.3 0.80 2.2 9 1010 ±30%High 1st discharge, high volts 1.0–0.3 0.17 4.4 9 109 ±20%High 1st discharge, low volts <0.3 1.49 3.9 9 1010 ±20%High 2nd discharge, high volts 1.0–0.3 0.24 6.2 9 109 ±20%High 2nd discharge, low volts <0.3 4.7 1.2 9 1011 ±20%High 3rd discharge, high volts 1.1–0.3 0.19 4.9 9 109 ±30%High 3rd discharge, low volts <0.3 2.49 6.5 9 1010 ±30%

Fig. 4. Medium salt NPS capacitor discharge. 1 At low voltage(<0.3 V) the material has a very high dielectric constant. 2 At highvoltage (0.9 > V > 0.3) the dielectric constant is about 50% lower. 3After drying, this capacitor had approximately zero capacitance, butthe original high voltage capacitance was mostly restored, as shown,by the addition of water (see text).

Fig. 5. Dried paste: 15 days after the medium salt NPS capacitorwas created there was no measurable capacitance and, as shown,the paste is dried and cracked. Each line on the scale is 1/32.

Novel Materials with Effective Super Dielectric Constants for Energy Storage 1371

this restoration protocol can be seen in Fig. 4 (line3): it nearly restores the initial dielectric constant.There is one difference between the initial behaviorof the medium salt capacitor, and that of therestored medium salt capacitor: below about250 mV there is an ‘elbow’, but the data become verynoisy. Hence, no low voltage capacitance value isprovided. The origin of this behavior is not clear.

Another point should be made here. The loss ofdielectric behavior upon drying is not unique tothese capacitors. All electrolytic and supercapaci-tors are sealed to prevent drying and contamina-tion. Hence, in the event super dielectrics are everemployed commercially, they will also need to besealed.

Another study performed with medium saltcapacitors was of the impact of dielectric layerthickness, as shown in Fig. 6. Clearly, the behaviormatches the predicted behavior for dielectrics: alinear relationship between inverse thickness andcapacitance. In prior work, studies of the impact ofthickness on the dielectric performance of colossaldiamagnetic materials showed little impact ofdielectric thickness, indicating to the authors thatcolossal diamagnetism is largely an interfaceeffect.13 The linear behavior observed in the presentcase suggests that interface effects are notsignificant.

The final, and perhaps most significant, resultfound for the capacitors created with medium saltloading is the actual energy density measured. Thethinnest dielectric studied was 0.5 mm thick andhad a dielectric constant greater than 3 9 1010

below 0.9 V. Leading to a net energy density>0.4 J/cm3 (more in ‘‘Discussion’’).

High Salt

The qualitative discharge characteristics of thisNPS capacitor were similar to the other two. First,it can be, and was, repeatedly cycled, as per Fig. 2.Second, there was a region of low capacitance fromabout 1.8 V to 1.0 V. Third, the slow discharge

region could be divided into two sections: one of highcapacitance between about 1 V and 300 mV and theother of extremely high capacitance below 300 mV.

The quantitative behavior was unique. At ‘highvoltages’, roughly from 1 V to 300 mV, this capaci-tor showed performance similar to that observed forthe low salt case.

At best over this voltage range, the dielectricconstant was no more than two times that observedfor the low salt sample, and clearly far less thanthat observed for the medium salt sample. In sum,the measured dielectric constant over this voltageregion is not a linear function of salt concentration.Below 300 mV, there is a very sharp change in thedielectric value (Fig. 7). In this voltage range, themeasured dielectric is similar to that observed forthe medium salt, in fact an average 15% higher. Forthis low voltage range, there is apparently a positivecorrelation between dielectric constant and saltloading, one that perhaps reaches a limit asymp-totically with the concentration of salt.

DISCUSSION

There are four main points of this research. One,it confirms that super dielectric behavior at !0 Hzis repeatable. Two, various parameters can bemanipulated to increase the dielectric constant.Three, the results are consistent with the hypothe-sis that super dielectric behavior arises from theformation of dipoles in ion-containing liquid dropsin pores, and that consequently super dielectrics area broad family of materials. Four, it is reasonable toextrapolate the results to suggest the potentialenergy density of NPS capacitors might be enor-mous, possibly surpassing the current generation ofLi-ion batteries.

In the first paper on super dielectrics, an aqueousboric acid solution was used to create the aluminapaste.1 It was postulated that there was nothingessential about boric acid and that any solution

Fig. 6. Capacitance versus thickness. The measured capacitance,first cycle, for three capacitors constructed of medium salt dielectricsis linear over a large thickness variation, a factor of six. That is, thedielectric constant is invariant with thickness, indicating it is a trueintrinsic property.

Fig. 7. High salt NPS capacitor. The second discharge cyclebehavior is graphed as two regions of dielectric performance. 1 Thecapacitance is extremely high (>1 9 1011) below 300 mV. 2 Thecapacitance between 1.0 V and 300 mV (>6 9 109) is similar to thatobserved for low salt NPS capacitors at 300 mV.

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containing dissolved ions would perform as well. Inthis paper, aqueous solutions of NaCl were used tosaturate the same alumina powder, and the result-ing dielectric constants were about an order ofmagnitude higher than those produced with boricacid. These results are not regarded as simplyempirical evidence that NaCl will produce a betterdielectric constant than boric acid. More broadly,the results suggest that many parameters can bemanipulated to optimize the dielectric constant. Forexample, in the present work, it was establishedthat, up to a certain concentration, ‘more salt isbetter’. In fact, the results suggest that there maybe an optimum salt concentration. The ‘medium’salt capacitor had a higher energy density than the‘high’ salt sample, which suggests that there may bean optimum pore size, an optimum porous refrac-tory, an optimum electrolyte, an optimum salt, etc.

Although virtually all commercial dielectrics arehomogeneous materials, in particular barium tita-nate,14–18 the super dielectric-based capacitors arenot the only example of an inhomogeneous materialwith a high dielectric constant. There are two clas-ses of non-homogenous materials that reportedlyhave very high dielectric constants. The first classare standard dielectrics, particularly barium titia-nate to which particles of metal have beenadded.19–21 It was empirically demonstrated thatsuch mixed materials can have dielectric constantsnearly ten times larger than the host ceramic.20

Two apparently contradictory models have beenproposed to explain the increase of dielectric con-stant measured upon the addition of metal particles.The earlier model indicated that this effect will onlybe observed for nano-scale metal inclusions,21–23 butwas refuted by later experimental work thatemployed 50-lm Ni particles to achieve a similaroutcome.19 This led to the development of a ‘perco-lation’ model. Purportedly, some material proper-ties, in particular the dielectric constant, willdiverge as the loading of the minority material(metal particles in this case) approaches the perco-lation limit of approximately 27% by volume.24–26 Itis not clear that percolation27 can explain theresults of the present work, as it is not clear whatmaterial in the NPS capacitors would be creating apercolation path, nor why that component of the mixwas always near the percolation limit.

Another model class to consider are thoseemployed to explain the observed phenomenon of‘colossal dielectric behavior’.13,28–32 The origin of theobserved behavior is a matter of considerable dis-cussion. Most investigators concur that the intrinsicdielectric properties of these materials are not‘colossal’ and that the colossal values arise from arange of extrinsic properties such as the highdielectric values of interfaces, particularly inter-faces between dielectric and electrode and grainboundaries.31,32 Other extrinsic sources suggestedinclude the ability of trapped molecules, includingwater, to diffuse in porous networks in response to

changing fields. The process of production, andconcomitantly the amount of trapped water, of someof these materials can significantly increase theextrinsic dielectric value.32

All the data collected here are clearly consistentwith an older and simpler model (Fig. 8). In thefigure, a schematic cross-section of an NPS-typecapacitor, water drops of a variety of sizes andshapes are shown, each occupying a pore within thealumina framework. An enlargement of one dropshows the positively charged ions migrating towardthe electrode with the negative field, and the nega-tive ions migrating in the opposite direction. If thedegree of polarization is key, then more ions shouldallow the formation of more strongly polarizeddrops. Indeed, a ‘perfect’ system would be one inwhich the permittivity of the drops approachesinfinity, that is a perfect ‘Faraday’ response to anapplied field.

Effectively, the model presented here is only aslight variation on the classic model of dielectricbehavior, sometimes referred to as ‘ponderablemedia’.1,3 There is no basis in the data collected inthe present work to support a complex or novelmodel, as the classic model of ponderable/polariz-able media appears perfectly adequate to describeall observations. The unique behavior, that is the‘super’ dielectric values, stems from the uniquemorphology of SDM. They are multi-material mix-tures, not solid single crystal materials designed tocreate the largest dipoles, hence greatest ‘polariza-tion’. Thus, one component, the ionic liquid, aqueousNaCl in this study, contains the ‘polarizable ele-ment’ in the form of mobile ions in a liquid solution.The other component, the highly porous insulatingsolid, is the physical framework, or skeleton, thatholds the polarizable elements in place. Hence,SDM were designed to create the most polarizable,electrically insulating, multi-material.

It is not possible to assess with certainty thequantitative validity of the ‘polarizable mediamodel’, but a very simple computation suggests that

Fig. 8. Cross-section model of super dielectric in a parallel platecapacitor. In this model, alumina contains pores (circles, ellipses) arefilled with an aqueous NaCl solutions. In an applied field, ions in eachpore (right side expanded view) migrate to create a dipole thatopposes the applied field.

Novel Materials with Effective Super Dielectric Constants for Energy Storage 1373

SDMs should have far higher dielectric constantsthan traditional ‘high er materials’. Thus, if it issimply postulated that the ‘polarizability’ of a mediais proportional to the size of the dipoles(charge 9 separation length) times the density ofdipoles, then a comparison of ‘dipole moments/volume’ in SDM and in barium titante provides afirst-order quantitative estimate of differences indielectric constant. This is expressed as:

Dielectric constant ¼ Dipole length

& dipole charge & dipole density(2)

First, we provide a length comparison. Thedipoles in the SDM are more than 103 greater inlength than those in barium titanate. Specifically,given a pore diameter of 500 A (see ‘‘Experimental’’),and a charge separation in barium titanate of 0.1 A,the SDM dipoles are about 5000 times longer thanthose in barium titanate.

Second, it is easy to show that the total charge ina volume of barium titanate, and in the pores of a‘water drop’ of the same volume in an SDM, areabout the same. Given the amount of charge in ahigh salt SDM, we find a single 250 A radius dropcontains about 7.5 9 105 salt ions. The same volumeof barium titanate contains about 106 barium tita-nate primitive cells/dipoles. Finally, we assume thevoid space in imperfectly packed barium titanatematches the volume taken up by alumina.

Given the above computations, we find for theSDM: Dipole constant/drop volume = 500 A 9 7.5 9105 ions 9 1.

Similarly, for the barium titanate: Dipole constant/equivalent drop volume = 0.1 A 9 1 ion 9 106.

The ratio of these two values suggests that SDMshould have a dielectric constant more than 1000 timesgreater than barium titanate. As the measured dif-ference was another three orders of magnitude largerthan the ‘first-order’ computed value, the calculationalso suggests other factors must be considered.

At present, the model must be considered quali-tative and ‘conservative’. It does not consider theimpact of the fact that the ion-containing drops donot have a dipole field but are more like smallFaraday cages that form as charges migrate untilthe net internal field is zero. How would a huge setof Faraday cages, rather than a huge set of dipoles,impact the charge/voltage ratio? This question isbeyond the scope of the present article which is farmore focused on discovery than theory.

Additional data support this model. First is thefinding that, once all the water in the dielectricevaporates, the capacitance drops more than nineorders of magnitude. Moreover, simply re-addingwater to the capacitor nearly completely restoresthe original capacitance. Consistent with the model,it is clear that, once the media for charge transport,water, is removed, no ‘dipole mirror’ can form, hencethere is no increase in capacitance. The net

capacitance is probably that of alumina, i.e. verylow. Second, the model does suggest that more ionsin solution will strengthen the dipoles, making themmore effective. It is clear that more salt doesincrease the dielectric value, but only up to a point.In turn, this suggests that the model presented isnot sufficiently complex to explain all observations.

Another consistent observation: there is no sig-nificant capacitance above !1.1 V. It is postulatedin the model that this is caused by a breakdown ofthe water in the pores. It is well known that whenbreakdown occurs an electrolyte solution becomeshighly conductive and can no longer sustain a volt-age, or a dipole. Thus, the question becomes, is theobserved maximum voltage consistent with thebreakdown of an aqueous solution of NaCl? Thesethree values enable a calculation: (1) the breakdownvoltage of distilled water is !65 9 106 V/m,33 (2) asolution of NaCl breaks down at a voltage about10% lower than distilled water,34 and (3) the aver-age pore size in the alumina is approximately 250 A,or 25 9 10%9 m. These values indicate that theaverage drop should not be able to sustain a voltagegreater than !1.3 V. This is very close to theobserved value.

Another observation is that there is a ‘break’ inthe capacitance at approximately 300 mV. That is,below this value the capacitance significantlyincreases. One possible explanation for thisobserved behavior is that the alumina pore distri-bution is bimodal. One set of pores has an averagediameter of perhaps 250 A, and a second set anaverage diameter of 80 A. The smaller pores do notbecome ‘effective’ in creating capacitance until thevoltage drops below the breakdown voltage, whichfor 80 A pores is about 300 mV. Or, perhaps all thedrops are elliptical, with a long axis of 250 A and ashort axis of 80 A. Breakdown tends to occur acrosseither the long or short axes depending on orienta-tion relative to the applied field. In any event, theproposed model is reasonably close to observations,particularly given the uncertainty associated withmeasurements of pore size in powders.

The final point to consider is the potential energydensity of an NPS capacitor. In order to compare theenergy density of an NPS Capacitor to a battery orsupercapacitor these values found in the literatureof technology are needed: (1) it is common to makeelectrostatic capacitors that are 0.5 lm thick usingceramic powder, and (2) the other components ofceramic capacitor stacks (electrodes and insulators)are collectively of the same order of size or smallerthan the ceramic layer. Next, from the standardequation for energy in a capacitor:

E Jð Þ ¼ 0:5CV2 (3)

and the standard equation for parallel platecapacitance:

C ¼ e e0A=t (4)

Cortes and Phillips1374

the following key equation is derived:

Energy Jð Þ=Volume m3! "

¼ 0:5 e eo V2=t2 (5)

where e is the dielectric constant, eo the permittivityof free space (8.85 9 10%12 F/m), V is volts, and t isthe thickness of the layer in meters. Thus, given aconservative ultimate thickness of an NPS capacitorof 2.5 l, assuming only 1 V potential and assumingthat only one-half the volume of a ceramic capacitorstack is the dielectric layers, this yields anastounding value, approximately !9000 J/cm3.Moreover, it is likely that higher voltages can beachieved by use of larger pore sizes, better electro-lytes, etc., such that this energy density is unlikelyto be anywhere near the ultimate value that can beattained with this technology. Indeed, if the theorypresented here is correct, an ultimate energy den-sity greater than 50,000 J/cm3 is possible.

Clearly, the above discussion assumes a linearextrapolation of all data. As others have pointed out,breakdown and saturation tend to limit capacitorperformance as the thickness is reduced.6

Hence, it is argued the energy density achieved inthe present work is one of the highest ever achievedfor a classic electrostatic capacitor. Yet, it does notyet approach the value of the best commercial sup-ercapacitors with a reported energy density of!30 J/cm3.

Often, for example in Ragone plots,35 the energydensity of various devices, e.g., supercapacitors,Li-ion batteries, fuel cells, etc., are compared usingthe units W/kg. Assuming that the ultimate NPScapacitor stack, defined by the above conservativeultimate parameters of 1 V and 2.5 l thickness, is,by volume, 50% aluminum, 25% H2O and 25% alu-mina, yields an average density of !4 g/cm3, thisyields >700 W/kg. Presently, commercial Li-ionbatteries deliver less than 500 W/kg. On a volu-metric basis, the contrast is even greater. The bestLi-ion batteries are rated at !1000 W/L, whereasthe projected value for the NPS capacitor (1 V, 2.5 lthickness, etc.) is 2500 W/L. Hence, it is importantto continue testing NPS capacitors, with a focus onthinner layers of SDM.

CONCLUSION

The most significant finding of the present studyis empirical: a pH neutral aqueous solution of NaClin a porous alumina constitutes a material witheffective super dielectric behavior (dielectric con-stant >105) at approximately 0 Hz. Moreover, the0 Hz dielectric constant was a function of salt con-centration, reaching a maximum value, at nearly1 V, of greater than 2.5 9 1010 (25 billion), estab-lishing that super dielectrics have dielectric con-stants orders of magnitude greater than anypreviously observed.

This suggests that SDM, as per our earlier sug-gestion, are a broad class of materials: porous, non-

conductive materials saturated with ion-containingliquids. Moreover, they can be designed/optimizedfor energy storage by changes in the identity of thesalt, concentration of the salt, the identity ofthe refractory oxide, the pore distribution in therefractory oxide, identity of the electrolyte, etc. Thisis supported by the finding that one of the capacitorstested in the present work had a measured energydensity of >0.4 J/cm3, better than one of the mostreliable observation for barium titanate-typedielectrics of !0.2 J/cm3. And, it is notable that thebarium titanate-based dielectric was three orders ofmagnitude thinner than the best SDM-baseddielectric we could fabricate in our laboratory. Allthese empirical results are consistent with a simplemodel of ‘colossal polarization’, in which the superdielectric behavior is explained as resulting frompolarization of ions in the pore-filling liquid drops.The giant dipoles so formed ‘oppose’ the appliedfield, leading to a dramatic net increase in theamount of charge stored on the electrodes requiredto create a given net voltage.

The empirical findings also have practical conse-quences. Extrapolation based on the dielectric con-stants measured here suggest thin-layer NPScapacitors could have energy densities several timesgreater than the best lithium-ion batteries pres-ently available. This extrapolation does assume thedielectric values obtained in the present work aresustainable at layer thicknesses (e.g., 2.5 lm)widely found in today’s ceramic capacitors. Morestudy is warranted.

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Cortes and Phillips1376

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