Water Sorption Induced Dielectric Changes in Titanate Nanowires

Water Sorption Induced Dielectric Changes in Titanate NanowiresHenrik Haspel,† Valeria Bugris,† and Akos Kukovecz*,†,‡

†Department of Applied and Environmental Chemistry, University of Szeged, Rerrich Bela ter 1, H-6720 Szeged, Hungary‡MTA-SZTE “Lendulet” Porous Nanocomposites Research Group, Rerrich Bela ter 1, H-6720 Szeged, Hungary

ABSTRACT: Broadband dielectric spectroscopy (BDS) meas-urements have been carried out on a nanostructured hydrophilicmodel system to gain insight into the atomistic level mechanismof adsorption-induced dielectric changes. Titanate nanowires(TiONWs) were investigated between 10 mHz and 1 MHzunder various humidity conditions. The processes contributingto the measured dielectric response were identified, and theirdependence on water surface coverage was discussed in detail.Three relaxation processes and an imperfect ionic conductionwere found in the investigated frequency window. Exponentialrelationships were found between the different dielectricquantities and the amount of adsorbed water. The conductivityvariation originates from the exponentially increasing charge carrier concentration, while the relaxations in the middle frequencyrange have a common, interfacial origin. The high-frequency loss process arises from the orientation relaxation of a real dipolarmoiety of the system.

1. INTRODUCTION

The dielectric properties of a solid are markedly affected by thevarious species adsorbed on its surface. The most commonexamples are hydrophilic materials in which the adsorption-induced low-temperature charge transport processes arethought to be dominated by surface conduction. In thesematerials conductivity changes of 4−9 orders of magnitudearound room temperature are due to the ongoing adsorption ofpolar molecules. Some of the commercially available humiditysensors are also based on this kind of variation.The phenomenon has been investigated over the past

century from as early as the 1910s.1,2 Considerable progress hasbeen made through each decade of the century (1920s,3,4

1930s,5−7 1940s,8−11 1950s,12−15 1960s,16−24 1970s,25−28

1980s,29−31 1990s32−37), and progress continues in the 2000sas well.38−49 Although this progression also addressed someaspects of the microscopic mechanism of the adsorption-induced conduction variation, studies were mainly limited togathering extensive experimental data on a broader set ofhydrophilic materials, e.g., oxides,12,13,21,24−26,28,29,31,40,43,59

zeolites,17,34 ionic solids,19 heteropolyacids (HPA),33

glasses,15,20−23,32 minerals,21,50 ceramics,36,37,41 metal−organicframeworks (MOF),49,51 polymers,10,11,14,26,35,38,44 and biopol-ymers47 (textiles,1−8 carbohydrates,9,16,30,42 proteins,10,11,18,27,52

DNA39,45,46,48). It is clear from the large body of experimentalwork already done in this field that the behaviors of materialswith diverse electronic properties (insulators, semiconductors)show striking similarities, suggesting a common conductionmechanism in chemically different systems. This implies thatthe function of the solid materials in the sorption-inducedcharge transport processes is solely to provide the surfacewhere charge carrier generation and migration can occur. This

is further supported by the essentially identical behavior ofthese materials for a wide variety of adsorbates besides water,i.e., formic acid,10,11 ammonia,17,20,25 methanol,8,20,23 quino-line,13 acetonitrile,17 nitromethane,22 dioxane,22 isobutylalcohol,28 and benzene.22 The microscopic description of theunderlying conduction mechanism would be of greatimportance in the fields of studying adsorption phenom-ena,15,21−23,34 sensors,29,31,33,35−38,40,41,59 composite materi-als,32,43 catalysis,13,17,20−22,24,25,28,34,43,53 industrial processes,54

fuel cell applications,44,49 paper-based electronics,16,30,42 andbiological systems.10,11,18,27,39,45−48,52 Although many humiditysensing mechanisms were already established,55 many aspectsof the low-temperature moisture-induced dielectric processes inhygroscopic solids are unknown. The missing detailedmechanism provides further challenges for researchers workingin these fields.The dielectric properties of the adsorbent change drastically

during the adsorption of polar molecules. Analyzing thedielectric variations creates the possibility to investigate theseprocesses more thoroughly. Dielectric relaxation spectroscopy(DRS) is a powerful technique to characterize the variation ofthe dielectric properties of the material56 as a function ofadsorbate content in both the frequency and temperaturedomains. Analysis of dielectric spectra, combined with detailedknowledge on the type and amount of water in/on the sample,helps in gaining deeper insight into the charge transportmechanism.

Received: May 7, 2013Revised: July 2, 2013

Article

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Here we report our results on the water-induced dielectricphenomena in a nanostructured hydrophilic ionic material(titanate nanowires, TiONW) investigated via broadbanddielectric spectroscopy. The nanotubular or wirelike morphol-ogies of titanates, particularly their mesoporous forms, providehigh specific surface areas for adsorption and the relateddielectric phenomena, i.e., charge carrier generation, ionmigration, and dielectric relaxation. A high level of under-standing has already been obtained of the surface chemistry ofsuch one-dimensional titanate nanosystems.57 Besides theirwell-known crystalline structures, the type and position of ionicspecies making up the structure were also identified.58 Theinterpretation of dielectric spectra of the humid sample and thecritical discussion of the origin of their constituent dielectricprocesses are presented in the light of an extensive review ofthe available literature. This work can be regarded as acontinuation of our recent study59 on adsorption-inducedconduction phenomena in the TiONW model system.

2. EXPERIMENTAL SECTION2.1. Titanate Nanowire Synthesis. The nanowires were

prepared60 by mixing 2 g of anatase TiO2 into 140 cm3 of 10 M

aqueous NaOH solution until a white suspension was obtained,and then aging the suspension in a closed, cylindrical, Teflon-lined autoclave (diameter 4 cm, height 14 cm) at 130 °C for 72h while rotating the whole autoclave intensively at 10 rpmaround its short axis. The product was finally washed withdeionized water and neutralized with 0.1 M HCl acid solutionto reach pH 7, at which point the slurry was filtered, and thenanowires were dried in air at 70 °C.2.2. Characterization. The completion of the nanowire

synthesis was verified by field emission scanning electronmicroscopy (SEM) using a Hitachi S-4700 Type II FE-SEM.Samples for SEM were coated with a thin (<4 nm) Au−Pdlayer deposited by an Ar+ plasma sputter to avoid chargingeffects. Elemental analysis was performed using a Rontec QX2energy dispersive X-ray spectrometer. The nitrogen adsorptionisotherm was measured at 77 K using a QuantaChrome Nova2200 surface area analyzer. The sample was outgassed at lowtemperature (at 298 K) for 24 h to remove adsorbedcontaminants and physisorbed water.61 The water content ofthe samples was determined from thermogravimetric analysis(TGA) measurements as presented in a recent publication.59

The specific surface area of the sample was calculated from theadsorption isotherms using the Guggenheim−Anderson−deBoer (GAB) equation62 for the moisture sorption and theBrunauer−Emmett−Teller (BET) model63 for the nitrogenadsorption. The pore size distribution function was obtainedfrom the desorption branch of the nitrogen sorption isothermvia the Barrett−Joyner−Halenda (BJH) theory.642.3. Electrical Measurements. The dielectric properties

were measured by inserting the samples into a concentriccylindrical capacitor and measuring the complex impedance ofthe cell using a Novocontrol Alpha-A frequency responseanalyzer (FRA) equipped with a ZG2 interface and a somewhatmodified BDS1200 sample holder. In order to avoid densitydependent conductivity variation,65−70 the sample wasmeasured in powder form without pressing it into a pellet.The response analyzer applies a sinusoidal 50 mV (RMS)voltage with a frequency between 1 mHz and 1 MHz to thesample cell electrodes. The FRA measures the phase andamplitude relations between the applied generator signal andthe detected sample current. The complex permittivity and the

complex electric modulus are then calculated from the rawimpedance data. The relative humidity (RH) dependence of thedielectric properties was measured in a closed, grounded metalvessel containing saturated salt solutions, which maintained thedesired RH levels71 between 6 and 100% RH. The sampleswere allowed to equilibrate to constant electrical response. Lowtemperature measurements were carried out in a home-builtcryostat setup during heating from 90 to 298 K with anestimated error of ±0.5 K. The current−voltage curves weremeasured using a Keithley 2612A Dual-channel SystemSourceMeter Instrument in a two-probe arrangement between0 and 20 V at room temperature. The transient currentmeasurements (ITIC) were conducted by an ACM InstrumentsGill AC multipurpose electrochemical station applying a voltageof 3 V across the sample, and the resulting current wasmeasured. The measurement details, the measured currentdecays, and the evaluation procedures were publishedrecently.59

3. RESULTS AND DISCUSSION3.1. Microstructure. The investigated titanate nanowires

originated from the same batch as the ones used in our previousstudy.59 In Figure 1 we present the basic characterization dataof this material.

The starting anatase particles were converted into nanowireswith an average length of a few micrometers and an averagediameter of ∼60 nm (Figure 1a). The powder X-ray diffraction(XRD) profile of the product material (not reproduced here)agreed well with previous literature results and thus proved theformation of the trititanate structure. The EDS measurement inFigure 1a, inset, indicates that sodium ions from the alkalinetreatment remained in the structure. The silicon peak is due to

Figure 1. (a) Typical SEM image of the investigated titanatenanowires. The inset depicts the EDS spectrum of the sample. (b)Nitrogen adsorption−desorption isotherm of TiONWs. The inset inpanel b shows the corresponding pore size distribution curve ascalculated by the BJH method. The second peak is an artifact causedby the tensile strength effect (TSE).

The Journal of Physical Chemistry C Article

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the sample holder. Therefore, we conclude that the studiedsample consisted of trititanate nanowires (TiONW) describedby the formula (Na,H)2Ti3O7.

57

A type IV nitrogen adsorption isotherm featuring a type Ahysteresis loop was obtained and is presented in Figure 1balong with the corresponding BJH pore size distribution curve.A specific surface area of 180 m2/g was obtained using the BETmodel. However, the recent evaluation59 of the moisturesorption isotherm in the GAB model resulted in a monolayercapacity of ∼94 mg/g (at about 22% RH) which correspondsto a specific surface area of approximately 350 m2/g whenconsidering the water molecule surface area of 0.111 Å2/molecule.72 We pointed out earlier that the actual value ofsurface coverage strongly depends on the definition of themonolayer and the model in which it is calculated. It is also notclear whether the monolayer coverage in water adsorptionmeans a molecular monolayer or bilayer of water. Moreover,the occurrence of hydrophobic regions in an essentiallyhydrophilic material leads to water clustering73 and, further-more, the preferred adsorption of water molecules on surfaceions has to be taken into account as well.74−76 The latter meansthat water is adsorbed at ionic sites first, developing waterplaques on the TiONW surface and hence increasing theamount of water required to form a monolayer.The pore size distribution curve in Figure 1b, inset, is

characterized by a sharp peak at ∼3.5 nm and two broaderpeaks at ∼2 and ∼18 nm, respectively. We assign the firstbroader peak to the wall defect related pores of the nanowiresand the third one to the adsorption of nitrogen in the interwirespace. Due to the mesoporous character of the sample, watercapillary condensation in the upper regime of the investigatedRH range was also presumed. The peak at ∼3.5 nm is a knownartifact arising from the tensile strength effect (TSE) caused bythe sharp drop in the desorption branch of the nitrogensorption isotherm at p/p0 ∼ 0.45.77

3.2. Dielectric Measurements. In order to obtain detailedinformation on the electrical properties of loose-packed titanatenanowires, we measured their dielectric spectra at varioushumidity levels at 298 K.The permittivity or dielectric constant is a complex function

of frequency, defined as

ε ω ε ω ε ω* = ′ − ″( ) ( ) i ( ) (1)

where ε′(ω) is the real part and ε″(ω) is the imaginary part ofthe complex dielectric function. In the case of highly conductivesystems it might be useful to evaluate dielectric data in theelectric modulus formalism. The complex electric modulus(M*(ω)) is given by the inverse of the complex permittivity:

ω ω ωε ω

ε ωε ω ε ω

ε ωε ω ε ω

* = ′ + ″ =*

= ′′ + ″

+ ″′ + ″

M M M( ) ( ) i ( )1( )

( )( ) ( )

i( )

( ) ( )2 2 2 2(2)

It is important to note that although ε*(ω) is commonlyassociated with the dielectric relaxation, in fact it describes thetrue dielectric retardation in the framework of the linearresponse theory.78 Recently, there has been a renewed interestin its use for interpreting dielectric spectroscopy data.79−81

Since dielectric properties are dependent on both frequencyand temperature, measurements varying these parameters arevital. Temperature scans provide information about thedielectric processes which show up in the dielectric spectra of

the material of interest. These processes must be taken intoaccount in the evaluation of the isothermal measurements.Isochronal runs, i.e., the temperature dependence of the realand imaginary parts of the complex permittivity and electricmodulus of TiONW, were performed at eight fixed frequencies(0.1 Hz−1 MHz) from 120 to 280 K. Figure 2a,b depicts thelogarithm of the real and imaginary parts of the complexpermittivity, and Figure 2c shows the imaginary part of thecomplex electric modulus.

Three distinct relaxation processes denoted as processes 1, 2,and 3 can be identified in the investigated frequency region. Inthe high-temperature−low-frequency regime a steep increase inboth the real part and the imaginary part of the permittivityappears. This behavior was referred to as low-frequencydispersion (LFD) by Jonscher82 and appeared in the dielectricresponse of a wide variety of materials,83 often in the presenceof humidity.50,52,65,67,107 The weak process 3 is partly maskedby the more intensive process 2 and is more pronounced in theimaginary modulus formalism in Figure 2c. The conductivitypeak would show up only at higher temperatures in themodulus plot, and therefore, it is not depicted here.In the frequency domain, isothermal spectra between 5 mHz

and 1 MHz were recorded at 19 different relative humidities.Representative real and imaginary permittivity spectra recordedat 11% RH and 298 K (Figure 3a,b) as well as at 193 K (Figure3c) are presented in double logarithmic representation inFigure 3. Arrhenius plots for processes 1−3 are depicted inFigure 3d. It should be noted that the water content of theinvestigated sample was not exactly the same as in the roomtemperature measurements at 11% RH due to experimentaldifficulties. The relaxation times for processes 1 and 2 are notshown for higher than about 247 K, since a curvature in thetemperature dependence of the relaxation times was observed.This might be due to water loss with increasing temperature ordue to a sign of the saddlelike temperature dependencereported by various authors in the past decade.95,101,106 The

Figure 2. Temperature dependence of the (a) real and (b) imaginaryparts of the complex permittivity and (c) the imaginary part of theelectric modulus of TiONW. The processes emerging in theinvestigated temperature and frequency range are marked on eachpanel.


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origin of such unusual behavior is the subject of an ongoingdebate in the scientific literature.96 The dielectric spectra of wettitanate nanowires bear a great resemblance to the spectrapublished in the past 60 years for a wide range of adsorbent−adsorbate systems, e.g., various solid oxides−hydroxides84−89

(mainly silica90−96 and alumina28,97−99), zeolites,65,100−102 clayminerals,76,103−106 sand/soil,107 glasses,32,108,109 and biopoly-mers.66,67,110,111 At near-ambient conditions these spectracontain at least one dielectric loss in the middle frequencyrange with a sharp rise at low frequencies in both the storageand loss spectra. Two relaxation processes (processes 1 and 2)can be identified in TiONW at room temperature in the middleand high frequency ranges of Figure 3a,b, whereas process 3 canbe resolved only at very low temperatures (Figure 3c). In thelow frequency regime a clear evidence of LFD is seen both inthe real (Figure 3a) and imaginary permittivity spectra (Figure3b). On the basis of the slope values (0.7−0.9) and the type ofsample, the dispersion is suggested to arise from a combinedeffect of an imperfect (or quasi-dc) conductivity contributioncaused by mobile charge carriers and the blocking of chargecarriers at the electrode−sample interfaces leading to theformation of the electrochemical double layer.56,82 The latterphenomenon is referred to as electrode polarization (EP) indielectric spectroscopy.The spectra were fitted with a model function in order to

quantitatively characterize the dielectric properties of TiONW.Two relaxations and the LFD need to be taken into account inthe evaluation procedure near room temperature. The LFD canbe satisfactorily described by a quasi-dc conductivity con-tribution causing an interfacial relaxation at very lowfrequencies and the electrode polarization.56,112

Therefore, we constructed our model function with thesuperposition of two Havriliak−Negami (HN) functions, aconductivity contribution with a fractional exponent, and, forthe description of EP, an additive power-law term:56

∑ε ω εεωτ

σε ω ω

* = +Δ

+− +α β∞

=

⎛⎝⎜

⎞⎠⎟a

A( )

(1 (i ) )i

i

i

iS S

1

2dc

0

(3)

where ε∞ is the permittivity at infinite frequency, Δε is therelaxation strength (Δε = εS − ε∞, where εS is the staticdielectric constant), ε0 = 8.8542 × 10−12 F/m is the permittivityof vacuum, τ is the relaxation time, ω = 2πf is the angularfrequency, 0 < α and β ≤ 1 are the broadening parameters, σdcis the specific conductivity, and S ≤ 1 determines the slope ofthe conductivity tail in double logarithm formalism. S is oftenless than 1 for quasi-dc ionic conduction. It was between 0.7and 0.9 in this work. The factor a has the dimensionality (radHz)S/(Hz), and 0 ≤ A is the magnitude of the EP contribution.Good fits were achieved at all measured humidity levels. Thesolid lines in Figure 3 are fits of eq 3 to the experimental data,while dashed, dash−dotted, short-dashed, short-dotted, anddotted lines represent the contributing dielectric processes, i.e.,process 1, process 2, process 3, conductivity, and EP,respectively.Although the origin of a relaxation cannot be assigned

unambiguously in DRS, it can be guessed from the dielectricstrength, shape parameter, and typical relaxation time regime ofthe investigated process. Such an assignment can only bevalidated by comparing it with results of independent methods,e.g., NMR or neutron scattering. Various and often contra-dictory assignments of the dielectric processes corresponding toprocesses 1 and 2 can be found in the literature. The origin ofthe loss peaks in the middle frequency range was suggested tobe the dipolar relaxation of water molecules slowed downthrough interaction with the adsorbent surface (see refs 28, 76,84, 86, 88, 91, 92, 94, 95, 97−99, 103, 105, 108, 110), or byaccumulation of charges at the interfaces of the heterogeneoussample.32,85,86,88−90,93,95,96,100,101,104 The latter is the so-calledMaxwell−Wagner−Sillars (MWS) process observed in manyheterogeneous systems of very different natures.113 In the caseof zeolites, the mid-frequency processes are thought to becaused by the relaxation of loosened ionic species.65,101,102 In

Figure 3. (a) Real and (b, c) imaginary parts of the complex dielectric function for titanate nanowires measured at 11% relative humidity at (a, b)298 and (c) 193 K. Full lines denote the fitting of eq 3. The constituents (processes 1−3, conductivity, EP) of the spectra are also indicated.Arrhenius plots for processes 1−3 are presented in panel d, where solid lines are fits to the data. The obtained activation energies are shown at eachdata set.


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TiONW, the asymmetrical broadening parameter of all threepeaks is 1, which means that only symmetrically broadened, i.e.,Cole−Cole, functions114 have to be taken into account in eq 3.Process 1 has, furthermore, a very large dielectric strength in aheterogeneous material featuring various interfaces (TiONW/water, TiONW/air, air/water); thus it can be assigned to theinterfacial polarization of the accumulated charges at the grainboundaries. Process 2 shows up as a shoulder in the highfrequency wing of process 1, while process 3 appears at evenhigher frequencies. Relaxations similar to process 2, viz., a lossat frequencies higher than the MWS loss, were found by severalauthors and were assigned either to the relaxation of ionicspecies101,102,108 or to the dipolar orientation polarization ofadsorbed water molecules with restricted motion in the case oftransient metal oxides Y2O3,

85 Cr2O3,86 and Nd2O3.

88 Thelatter argument was based upon the fact that the dielectricstrength of this process decreases almost linearly withdecreasing amount of adsorbed water and disappears at zerocoverage. Since titanate nanowires contain structural waterbesides adsorbed moisture, it is not possible to reach zerocoverage while leaving the microstructure intact.57,58 However,a similar behavior was found upon drying, which proves thatthese processes are certainly related to the water content of thematerial. Regarding the dielectric strength of process 2 (about10−15), it is 1−2 orders of magnitude higher than that forprocess 1 and 4−6 times higher than that for process 3 in thecase of C−S−H gels.118 It significantly increases further withincreasing amount of adsorbed water. Hence we put forward atthis point that this process has an interfacial origin as well.More evidence on this assumption are to be presented in thediscussion of Figure 9. Process 3 has a dielectric strength of0.2−0.4, which is more than a magnitude lower than those forprocesses 1 and 2. Moreover, its relaxation time seems to becloser to that of strongly bound water molecules showing upwell above 1 MHz in dielectric measurements undertakenaround room temperature in Vycor glass,108 silica−alumina115and montmorillonite116 gel suspensions, timber,117 humidoxides,85,88 zeolites,101 molecular sieves,95,96 alumina,99 andsilica particles.73 Therefore, it is concluded to originate from areal orientation relaxation process.Further conclusions can be drawn from the activation plot of

the relaxations. Arrhenius-type temperature dependence wasfound for all processes, and the activation energies werecalculated from fits of the Arrhenius equation to the data.Energies of 0.37, 0.43, and 0.19 eV were obtained for processes1, 2, and 3, respectively as indicated in Figure 3d at each dataset. The activation energy of process 3 is considerably lowerthan that for the “universal” water relaxation (∼0.5 eV)118 andis almost equal to the activation energy of process 1 foundrecently in C−S−H gel (0.2 eV),119 which was assumed tooriginate from the relaxation of some intrinsic dipolar group(surface OH or bound water). Considering the structure andcomposition of our sample, we argue that process 3 arises froma real dipolar moiety of the investigated system. Process 3cannot be fitted in room temperature measurements, but itseffect has to be taken into account. Therefore, we fitted process2 with a HN function describing this way the high-frequencyasymmetry caused by the low-frequency flank of process 3.Since process 3 is out of our accessible frequency range, itsvariation with water adsorption was not investigated in thisstudy.Dielectric investigations on damp zeolites pointed out65 that

“there is a measure of nonlinearity in the response with respect

to the amplitude of the exciting electric field”. Therefore, westudied the dependence of the dielectric spectra on the appliedmeasuring voltage at ambient conditions. The results aredepicted in Figure 4. Above approximately 100 mV (the actual

value depends on the RH) detectable changes in the dielectricspectrum occur. Only the low-frequency part of the spectrum isaffected by the amplitude of the voltage signal, while adsorbedwater, as we will see later, affects all processes in the dielectricresponse. The mid-frequency loss (process 1) becomes rapidlyovertaken by the voltage dependent dispersive regime, viz., theLFD process with increasing measuring voltage. Contradictoryresults were reported in the literature for the current−voltagecharacteristics of wet materials. In some cases linear, i.e.,ohmic,5,23,26,35,39 behavior, while in other cases clearly non-linear, nonohmic3,24,39,45,46,65 behavior was reported. Thenonlinear shape of the curves was explained on the one handby the redistribution of the ions at the electrode−sampleinterfaces39 and, on the other hand, by the increased amount ofadsorbed water on the sample surface.23,45 In the inset of Figure4b the current−voltage characteristics of TiONW are presentedfor three consecutive voltage sweeps in the 0−20 V range. Inthe first run the current was below the measuring limit of theinstrument at low voltages and ohmic behavior was observedabove 9 V excitation amplitude. In the second run tens ofnanoamps current was measured from 4 V onward, and afurther kink is visible in the curve, separating stages withdifferent slopes. The current was higher than that in the firstrun by a factor of about 2 in the whole voltage regime.In the third run similar behavior was observed with a current

10−20% higher than that in the second one. To the best of ourknowledge, there is no generally accepted explanation for thenonlinear character of the low-frequency dispersion in theliterature today. However, the shape of the I−V curves indicatesthat chemical reactions were taking place in the material underhigh voltage excitation. Furthermore, the curves in the secondand third voltage sweeps start at nonzero currents, which weremost likely caused by the generation of charges in the sample in

Figure 4. Voltage dependence of the dielectric response at ambientRH. The inset of panel b depicts three consecutive current−voltagecharacteristics measured in the concentric measuring cell used for thedielectric measurements.


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the previous runs. The possibility of chemical reactions isfurther supported by the well-known observation that theelectrical current at high excitation fields in a damp material isrelated to electrochemical reactions,45,120,121 which wassuggested for the LFD at the electrode interface aswell.50,82,83 Measurements presented in the following sectionswere all performed using an excitation of 50 mV, thus being farbelow the threshold voltage of any detectable dielectricchanges. Despite the nonlinearity of the LFD, its water-dependent characteristics appeared to be independent of themeasuring voltage except for an offset. This implies theapplicability of the approximation used in the construction ofthe fitting function, eq 3. The use of this model function causedonly an apparent increase in the conductivity with increasingmeasuring voltage, while the long-range charge transportprocess was left intact. This makes the voltage independenceof processes 1 and 2 understandable. However, there is stillmuch left to be understood about the details of the interrelationbetween the LFD and MWS processes.The spectra in Figure 3 show that even at the depicted low

RH level (11% RH) the LFD (∼conductivity and EP) could besignificant. Since the contributions of these processes increasewith increasing RH, they can mask other relaxations and hinderthe proper evaluation of the measurements. This is trueparticularly at very high RH. In order to overcome thisdifficulty, we have chosen to evaluate all measurements in thecomplex electric modulus formalism.78,79 In Figure 5 the real

and imaginary parts of the complex electric modulus are plottedfor different humidity levels at 298 K. Solid lines are fits of eq 2to the data using the model function eq 3.The lower and higher frequency relaxation peaks in the

depicted frequency window correspond to process 1 andprocess 2, respectively. Both peaks shift toward higherfrequencies with the increasing humidity of the surroundingatmosphere indicating the decrease of relaxation times of the

processes upon water adsorption. This is a well-knownphenomenon and was observed in a wide range of systemswhere dielectric measurements were made under variedhumidity conditions (see refs 32, 52, 65, 76, 84−86, 88,90−94, 98, 100, 103−105, 107, 108, 110, 111, 117). Themaximum frequency shift can be estimated from Figure 5 to bemore than 2 orders of magnitude in the whole RH range. Theconductivity manifests itself as a peak in the modulus formalismand is located below the presented frequency window. Therelaxation times of processes 1 and 2 are determined from thecomplex modulus fit, while conductivity was calculated fromthe loss spectrum.

3.3. Coverage Dependence of the Conductivity. Sinceadsorption-induced conduction processes were thoroughlyreviewed recently,59 here we highlight only some relevantdetails in brief, emphasizing the main points concerning themechanism and origin.1. The change in the dielectric properties of the used material

could be caused by swelling, physisorption, chemisorption, orcapillary condensation of the adsorbate.2. The similarities in the LFD response to various adsorbates

imply a common surface conduction mechanism.3. Most solid materials including trititanate structures122

exhibit both electronic and ionic conduction (mixed ionic−electronic conductors, MIEC).123

4. However, it is quite likely that in large band gapsemiconductors and insulators ionic conduction dominates nearroom temperatures from low relative humidity on-ward.15,20−26,28,42,65,68−70,91,100,102,120,121

5. Conduction may be attributed either to protons or toexchangeable cations (Na+, K+) balancing the charge of thelattice.21,22,24,25,28,42,65,68−70,91,100,102,124

6. However, the origin of the charge carriers is not clear.Protons could be present in the structure as counterions or begenerated by the dissociation of adsorbed water molecules atcoordinatively unsaturated metal sites, but only at very low RH.Hence a surface enhanced water autoprotolysis mechanism wassuggested, enabling water dissociation also at very high relativehumidities.24

7. The microscopic details of the transport of the generatedor structural charge carriers are also unknown. Hopping,43

vehicle,125 and Grotthuss mechanisms126,127 were suggested byvarious authors.8. Since there is some uncertainty about the origin of the

relaxation processes, the adsorption-induced variation of theseprocesses raises further questions.9. It is also debated if the variation of the dielectric properties

should be discussed as a function of relative humidity or watercontent. Different authors present their results against eitherRH,3,12,33,35,38,39,41,45,46,48,50 log(RH),19,40,43 adsorbedamount,9−11,13−15,17,18,20−28,30,32,34,40,42,44,47,54,108 or log-(adsorbed amount).5−8,16,42 Our recent results on TiONWrevealed that no structural water changes occur in the 6−100%RH range. Therefore, any variation of the dielectric propertiesshould be related solely to water physically adsorbed onTiONW, so we discuss our results in terms of the adsorbedwater content. In Figure 6 the surface coverage dependenciescalculated from the water adsorption isotherm via the GABmonolayer of 93.9 mg/g are also depicted. The results differfrom the one calculated according to the BET theory by afactor of 2 as was pointed out in section 3.1.Coverage dependent conductivity has been widely inves-

tigated in the past. The characteristics uncovered by

Figure 5. (a) Real and (b) imaginary parts of the complex electricmodulus for titanate nanowires at various relative humidities at 298 K.The full lines are fits of eq 2 to the data using the model function eq 3.Increasing humidity shifts spectra toward higher frequencies.


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independent authors resemble one another to a great extent,even in the case of different adsorbates. The conductivity of amaterial increases exponentially with coverage below the onseto f t h e d e l i q u e s c e n c e o f t h e a d s o r -bate9−11,13,14,17,18,20−28,32,40,42,44,47 (the so-called third sorptionstage62), where a distinct change in the characteristics occurs. Inthis high coverage regime exponential17,21,25,42 or lineardependency15,23 was identified. In some cases there is nodiscontinuity in the characteristics; hence they can be describeda s a s a t u r a t i o n c u r v e i n t h e l o g a r i t h mplot.9−11,13,20,22,24,28,30,44,47,54,108 Our results for dc conductivity(σdc) are presented in Figure 6 as a function of both watercontent and water surface coverage. Since the measured sampleconsisted of nanowires, adsorbed water in various thermody-namic states,59 and air, the conductivity in Figure 6 character-izes the electrical properties of this mixture rather than that ofthe pure nanowires.A two-stage linear relation was found between the logarithm

of conductivity and water content, similar to those previouslypublished for water and ammonia adsorbed on differentmontmorillonites, silica, glass powder,21,25 glass-bead-filledHDPE composite,32 and microcrystalline cellulose (MCC)tablets.42 The onset of the deliquescence of water onto thesurface (∼90% RH) divides the response into two linearsegments. The conductivity can be described by an exponentialformula in each segment:

σ σ= C wexp( )i idc 0, (4)

where σ0,i and Ci are constants of the ith segment and w is theamount of adsorbed water. Solid lines in both segments ofFigure 6 are fits of eq 4 to the data. The inset in Figure 6 zoomson the data and the corresponding fit at low coverages.Although both segments exhibit an exponential dependence,the lower slope of the third adsorption stage indicates thatincreasing the amount of liquidlike water causes less increase inconductivity in this regime than the binding of more structuredwater in the first one or two molecular layers.The water sorption induced conductivity change could arise

from an increase in either the ionic mobility or theconcentration of the charge carriers. Recently we haveshown,59 in accordance with earlier findings,42,128 that the

increase in charge carrier concentration is the dominantcontribution, whereas the mobility change has a much smallerinfluence only. The following model was suggested to explainthe exponential dependence of the conductivity from theamount of adsorbed water:21

σρ

=⎛⎝⎜

⎞⎠⎟n

v ez akT

l ez nkTA

( )exp

( )dc

2 2 2

(5)

where v is the number of “jumping attempts” per second, a isthe distance between two equilibrium positions (∼8 Å), l is thevertical distance from the surface, k is the Boltzmann constant,T is the absolute temperature, A is the specific surface area ofthe sample, and ρ is its density. It was assumed that the chargecarriers originate solely from the dissociation of adsorbed watermolecules and their concentration is directly proportional tothe number of water molecules Nwater adsorbed per unitvolume:21,28

α=n Nwater (6)

where α corresponds to the degree of dissociation of theadsorbate. In the adsorbed layers a dissociation degree 6 ordersof magnitude higher than that in liquid water was found.21,28

However, our measurements revealed a stronger than linearadsorbate dependence of the TiONW conductivity. In Figure 7

the logarithm of the charge carrier concentration versus theadsorbed water molecule concentration is depicted. A two-stagelinear relation similar to the conductivity in Figure 6 wasobtained. The segments are divided by the onset of the thirdadsorption stage. Since ionic mobility was found to increaseabove 90% RH, it seems that the moderate conductivityincrease in this regime originates from the less effective chargecarrier generation in the almost bulklike water layers.Clement et al. suggested that the linearity of the ln(σdc/

Nwater) vs Nwater plot proves the validity of the Fripiat model21

in the hopping regime. This proportionality was verified earlierfor the NH3/SiO2 and CH3OH/SiO2 systems,

20 but no furtherconclusions were drawn. In the inset of Figure 7 the plot wasconstructed from our data using only the points below the thirdadsorption stage. Even though the invalidity of eq 6 for theTiONW system was proven above, a linear relationship wasobtained from which a dissociation degree of 2.9 could becalculated by fitting eq 6. It is clearly seen that this simplepicture is unable to correctly describe the adsorption-induced

Figure 6. TiONW conductivity as a function of the amount ofadsorbed water. The inset zooms on the region found before the onsetof the third sorption stage. The coverage dependence according to theGAB theory is given in the top axis. Solid lines are fits of eq 4 to thedata; the vertical dashed lines denote the completed GAB layers.

Figure 7. Variation of charge carrier concentration on the numberdensity of adsorbed water molecules. The onset of the third adsorptionstage divides the characteristics into two segments as indicated by thedashed vertical line. The inset shows the representation of Clement forour data.


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conduction phenomena. In the light of these findings, we arguethat the Fripiat model could not be verified by the Clementplot, since the exponential dependence of both conductivityconstituents yields an adequately linear Clement plot.In order to describe the origin of the charge carriers, a further

surface enhanced dissociation model was proposed.24 It isassumed that protons originate from the dissociation of surfacehydroxyls to a greater extent and of water molecules to a lesserextent. The adsorption of polar molecules increases thepermittivity of the adsorbent, which in turn reduces thedissociation energy to protons. Thus the dissociation and,therefore, the conductivity are enhanced by the adsorbed watermolecules. The validity of the model could be tested by plottingthe logarithm of conductivity against the reciprocal of theadsorbent relative permittivity, where linear dependency shouldbe obtained. It is, however, not obvious which value of the realpermittivity should to be used in a system exhibiting LFD.Moreover, the model states that the conductivity falls roughlyexponentially with increasing surface OH concentration,whereas an opposite effect was found in kaolinite dehydrox-ylation experiments.129 On the other hand, conductivityincreases parallel with increasing dipole moment of theadsorbates were indeed found in porous Vycor glass,22 andproton exchange between surface functional groups andadsorbed molecules was observed in the case of methanol/silica,128 water/sulfonated polystyrene,44 and water/SBA-15130

systems. The exchange rate is dependent on coverage, andaccording to NMR measurements,128,129 an adsorbate moleculeis protonated many times during its stay on an adsorption site.During water adsorption in acid-functionalized SBA-15130 andin isostructural series of functionalized metal−organic frame-works (MOF),51 the charge carrier (proton) generating stepwas identified as the dissociation of the acidic functional groups.The dc conductivity of these materials varied according to thepKa of the functional groups, and the governing parameter ofthe sorption-induced conductivity was suggested to be theincreasing carrier concentration. Although the mechanism ofproton conduction−proton transport was thoroughly re-viewed131 and both vehicle and Grotthuss mechanisms wereidentified, there is still an ongoing discussion on the nature ofthe underlying processes. Recent theoretical calculationsshowed that the interfacial adsorbates are also involved in thelong-range Grotthuss-type transport as bridging molecules.This latter mechanism is referred to as a carrier-mediated132 orinterfacial133 Grotthuss mechanism in PVPA and boehmite,respectively. To the best of our knowledge no widely acceptedtheory exists that describes the exponential increase in thecharge carrier concentration with ongoing adsorption.3.4. Coverage Dependence of the Relaxation Pro-

cesses. As suggested earlier in section 3.2, processes 1 and 2might have an interfacial origin. Moreover, it is well-known thatthe MWS relaxation time is a very complex function ofconductivity and depends strongly on the structure of thesample.113 Equation 7 was derived to describe the relaxationtime of the corresponding dielectric loss process in a compositeof nonconductive particles immersed in a nonconductingmedium with a conductive water interlayer between them(HDPE + glass bead + moisture):32,134

τϕ

ϕε

σ ϕε ε ε ε ϕ=

−+ − −

13

2[( 2 ) ( ) ]f

f

0

dc lf m f m f

(7)

where τ is the relaxation time, ϕf and ϕl are the volumefractions of the filler and the interlayer, εm and εf are thedielectric constants of the medium and the filler, and σdc is theinterlayer conductivity. Although titanate nanowires are notstrictly nonconductive particles, the wet polymer−glass beadsystem was assumed to be a good model for them becausesurface ionic conduction dominates the electrical properties ofTiONW. The theory does not hold strictly even in the originalcase, so only qualitative conclusions can be drawn. According toeq 7 the interfacial relaxation time is essentially inverselyproportional to ϕl (the amount of adsorbed water) if the waterlayer conductivity has the same constant value at all relativehumidities. However, the volume fraction of the adsorbed layerand its conductivity both increase during adsorption. The latteris shown in Figure 6, where the strong dependence ofconductivity on water coverage is clearly seen. It implies that,according to this model, the interfacial relaxation times dependvery strongly on the amount of adsorbed water. In Figure 8 therelaxation times of processes 1 and 2 are depicted as a functionof both water content and water surface coverage.

Two-stage linear relations were found between the logarithmof relaxation times and water content, similar to that of theconductivity in Figure 6. The third adsorption stage divides thecharacteristics into two segments, and each segment can bedescribed by an exponential formula:

τ τ= ′C wexp( )i iMWS 0, (8)

where τ0,i and C′i are constants for the ith segment. The solidlines in Figure 8 are fits to the data according to eq 8. Similarbehavior, i.e., exponential variation of the interfacial relaxation

Figure 8. Variation of relaxation times of (a) process 1 and (b) process2 with the amount of adsorbed water. The onset of the thirdadsorption stage, indicated by the dashed vertical line, divides thecharacteristics into two segments. Insets enlarge the region before theonset of the third sorption stage. On the top axis the coveragedependency is also given according to the GAB theory. Solid lines arefits of eq 8 to the data; the dashed vertical lines denote the completedGAB layers.


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times with increasing amount of adsorbates, was found in awide variety of systems, e.g., HDPE−glass beads,32 silicagel,90,93 alumina,98 clay minerals,76,103,105 zeolites,65,100 pro-teins,52 and cellulose.111

The observed shift of the relaxation times is thus suggestedto be governed mainly by the water coverage relatedexponential increase of the adsorbed layer conductivity. Thesimilarity in the shape and the practically identical slopes ofeach segment of the characteristics of processes 1 and 2 clearlysuggest a common origin of these processes. Further strongsupport for their common and interfacial origin is presented inFigure 9, where the relaxation times of processes 1 and 2 areplotted in a double logarithmic representation againstconductivity.

Again, the data sets are divided into two segments at theonset of the third sorption stage. Linear correlation between thelogarithm of relaxation times and the logarithm of conductivitywas found in both segments. According to eq 7 relaxation timeswould be inversely proportional with a slope of −1 toconductivity if ϕl (the interlayer volume fraction) had thesame constant value at all water contents. In our case for thefirst segments slope values of ∼−0.4 and for the secondsegments values of ∼ −4.1 are obtained which can beinterpreted as a weaker and a stronger than inverseproportionality for the first region and the second region,respectively. It can be concluded that at the onset of theadsorbate deliquescence not only the conductivity and therelated interfacial relaxation times change drastically, but theunderlying mechanism of the mid-frequency loss processes isaffected as well. Although no unambiguous explanation for theabrupt change observed at high dc conductivity in Figure 9 isavailable yet, we suggest on the basis of Figures 8 and 9 that themid-frequency processes in the room temperature dielectricspectra of damp materials have a common, and most probably,interfacial origin. Therefore, any subsequent theory on theorigin of these processes has to take the identical behaviors oftheir relaxation times with conductivity into account.

4. CONCLUSIONSBroadband dielectric spectroscopy measurements were carriedout on titanate nanowires (TiONW), and the variation of thedielectric response with the amount of adsorbed water wasexamined. Processes contributing to the damp TiONWdielectric spectra were identified, and their origin was critically

discussed. There are three relaxations in the medium- and high-frequency regimes and a further dispersive feature (low-frequency dispersion (LFD)) toward low frequencies. Weargue that LFD is caused by imperfect charge transport in thesample, while the high-frequency loss arises from the dipolarrelaxation of a real polar moiety of the system. The two lossprocesses in the middle frequency range were suggested to havean interfacial origin. The water content dependence of thetitanate dielectric response was investigated in detail. Theconductivity varied exponentially with water content in twoseparate regions, the latter of which was identified as the thirdadsorption stage in the moisture sorption isotherm. Theexponential increase in conductivity was attributed to theexponential dependence of charge carrier concentration on theamount of adsorbed water molecules. The atomistic origin ofthe increase in the carrier concentration, however, still remainsan open question. The relaxation times of the mid-frequencyloss processes also vary exponentially with the adsorbedamount of water in two separate regions. On the basis oftheir similar features these processes are suggested to have acommon origin. The shape of the logarithm of relaxation timesvs the logarithm of the conductivity plot indicated that thiscommon origin is of an interfacial nature.

■ AUTHOR INFORMATIONCorresponding Author*Fax: 36 62 544 619. Tel.: 36 62 544 620. E-mail: [email protected] ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSFinancial support was provided by the OTKA NK 106234project and the TAMOP-4.2.2.A-11/1/KONV-2012-0047program.

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Figure 9. Variation of relaxation times of processes 1 and 2 with dcconductivity. The identical power-law dependences between thequantities further support the assumption of a common and interfacialorigin of these processes. The discontinuity at 90% RH denotes theonset of the third sorption stage.


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mailto:[email protected]

mailto:[email protected]

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Water Sorption Induced Dielectric Changes in Titanate Nanowires