Water-Induced Changes in the Charge-Transport Dynamics of

Article pubs.acs.org/Langmuir

Water-Induced Changes in the Charge-Transport Dynamics of Titanate Nanowires Henrik Haspel,† Valéria Bugris,† and Á kos Kukovecz*,†,‡ †

Department of Applied and Environmental Chemistry, University of Szeged, Rerrich Béla tér 1, H-6720 Szeged, Hungary MTA-SZTE “Lendület” Porous Nanocomposites Research Group, Rerrich Béla tér 1, H-6720 Szeged, Hungary

‡

ABSTRACT: The temperature dependence of dielectric processes in humid titanate nanowires was investigated via broadband dielectric spectroscopy under quasi-isosteric conditions in the temperature range of 150−350 K. It was found that the dynamic parameters obtained from low-temperature measurements cannot describe the dielectric behavior of the system above 273 K, implying changes in the dynamics of the corresponding dielectric processes. The calculated activation energies and pre-exponential factors counterintuitively increase linearly with the amount of adsorbed water, and a compensation effect was also found to apply to all contributions in the TiONW spectra.

1. INTRODUCTION The dielectric properties of an adsorbent depend strongly on the species bound on its surface. Water adsorption changes the adsorbent’s electrical conductivity according to a universal characteristics in many hydrophilic materials (e.g., oxides,1−4 zeolites,5 glasses,2,3 carbohydrates,6 and proteins7,8). Principally the same behavior was found for a variety of adsorbates other than water (i.e., quinoline,1 methanol,2 ammonia,2,5 nitromethane,3 dioxane,3 acetonitrile,5 and benzene3). The conduction mechanism has been the subject of an ongoing debate for decades, and many theories have been put forward so far: surface-enhanced autoprotolysis,9,10 proton hopping within surface groups or absorbed water molecules,11 electric-fieldconfinement-induced ion release in adsorbed water layers in 1D12 and 2D13 systems, and electronic semiconduction mostly in biological materials7,8,30 or the hopping of holes and other charge carriers in DNA14 and hyaluronic acid.15 Although it would be of great importance in the description of adsorption phenomena,2,3 catalysis,1,5 paper-based electronics,6 pharmaceutical excipients,6 and biological systems,7,8 no widely accepted conduction theory exists to this date. Furthermore, similar dielectric spectra were found in a wide range of humid adsorbents (e.g., various solid oxides− hydroxides16,17 (mainly silica18−20 and alumina4), zeolites,21,22 clay minerals,23 glasses,24 and biopolymers25). The suggested origin of the emerging dielectric loss processes is, however, somewhat speculative, and hence no sound theory for the underlying microscopic processes exists. Recently, we reported on room-temperature dielectric measurements of titanate nanowires26 (TiONW) under changing relative humidity (RH) conditions.27,28 Because it is well known that the temperature dependence provides much information on the possible origin of a dielectric process, here © 2014 American Chemical Society

we present temperature-dependent broadband dielectric spectroscopy results measured in the range of 150−350 K under quasi-isosteric conditions in the same TiONW model system.

2. EXPERIMENTAL SECTION 2.1. Materials and Characterization. The investigated hydrothermally synthesized nanowires were the same as those used in our former studies on the dielectric properties of this system.27,28 The mesoporous titanate nanowires (TiONW) had an average length of a few micrometers and an average diameter of 60 nm with a trititanate structure described by the formula (Na,H)2Ti3O7. A specific surface area of 180 m2/g was obtained from nitrogen adsorption measurements using the Brunauer−Emmett−Teller (BET) model, and a specific surface area of approximately 350 m2/g was obtained from the moisture sorption isotherm using the Guggenheim−Anderson−de Boer (GAB) equation. The monolayer capacity was calculated to be ∼94 mg/g (at about 22 RH%) with water as the adsorbate. 2.2. Electrical Measurements. The dielectric properties were measured in a concentric cylindrical capacitor by a Novocontrol AlphaA frequency response analyzer with the application of 50 mV (rms) voltage at a frequency of between 1 mHz and 1 MHz. To avoid a density-dependent conductivity variation,29 the sample was measured in powder form without pressing it into a pellet. The relative humidity (RH) dependence of the dielectric properties was measured in a closed, grounded metal vessel containing saturated salt solutions, which maintained the desired RH levels between 6 and 100 RH%. The samples were allowed to equilibrate to a constant electrical response.28 Low-temperature measurements were carried out in a homemade cryosystem with stability better than 0.5 K after quenching the samples with liquid nitrogen and then increasing the temperature stepwise from 90 to 273 K in 2.5 K steps. High-temperature dielectric spectra were recorded above 273 K in 5 K steps under isothermal conditions Received: August 25, 2013 Published: February 4, 2014 1977

dx.doi.org/10.1021/la4048374 | Langmuir 2014, 30, 1977−1984

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in a Julabo F12 refrigerated circulator with an estimated temperature error of ±0.1 K.

ε*(ω) = ε′(ω) − iε″(ω) 2

= ε∞ +

3. RESULTS AND DISCUSSION Representative dielectric loss spectra of TiONWs are shown in Figure 1. As we have pointed out recently,28 under near-

∑ i=1

⎛ σ ⎞ − ia⎜ dc S ⎟ (1 + (iωτi) ) ⎝ ε0ω ⎠ Δεi

α β

(1) −12

where Δε is the dielectric strength, ε0 = 8.8542 × 10 F/m is the permittivity of vacuum, τ is the relaxation time, ω = 2πf is the angular frequency, 0 < α, β ≤ 1 are the broadening parameters, σdc is the conductivity, and S ≤ 1 determines the slope of the conductivity tail in the double-logarithm formalism. It was between 0.6 and 0.9 in this work. Factor a has the dimensionality (rad Hz)S/(Hz). Process 3 cannot be fitted in these relatively hightemperature spectra, so its effect was taken into account as an asymmetrical high-frequency flank of the loss peak of process 2. As seen in Figure 1a, the determination of the parameters characterizing the dielectric relaxations in eq 1 is notably hindered by the overlapping peaks of processes 1−3 in combination with the limited measuring frequency range. To overcome this difficulty, low-temperature spectra were chosen to be evaluated in the electric modulus formalism.32 The imaginary part of the electric modulus of the same spectrum as plotted in Figure 1a (i.e., TiONW measured at ∼11 RH% and 193 K) was redrawn in Figure 2a to demonstrate the obvious

Figure 1. Dielectric loss spectra of TiONWs measured at temperatures of (a) 193, (b) 298, and (c) 350 K and at a relative humidity of 11 RH %. Panel b shows the dependence of the loss spectrum on the relative humidity of the environment and hence the water content of the titanate nanowires measured at 298 K and 11 and 62 RH%. Solid lines denote fits of entire spectra as a superposition of (a) three or (b, c) two HN functions and a conductivity contribution. The constituent dielectric processes are indicated on each panel. Data were redrawn from ref 28.

ambient conditions these spectra contain at least one dielectric loss in the middle frequency range with a sharp rise at low frequencies in both the storage and loss spectra. The broadband dielectric response of TiONW can then be described by the superposition of at least three dielectric relaxation processes, denoted as processes 1, 2, and 3 in the spectrum measured at 193 K (Figure 1a), and another low-frequency dispersion (LFD) caused by imperfect charge transport. High-frequency process 3 arises from the dipolar relaxation of a real polar moiety of the system, whereas the two loss processes in the middle frequency range (i.e., processes 1 and 2) were suggested to have a common interfacial origin. Figure 1 demonstrates that the conductivity increases with increasing temperature and the peaks of processes 1 and 2 slide toward higher frequencies. The increasing water content has a similar effect on the dielectric properties as the temperature variation, which was recently rediscovered30 and confirmed in ion-conducting polymers by the validity of the so-called time-humidity-superposition principle.31 With increasing water content, the conductivity increases and the interfacial loss peaks are shifted toward higher frequencies, as illustrated in Figure 1b for room temperature at 11 and 62 RH%. The measured spectra were fitted with a model function consisting of two Havriliak−Negami (HN) functions and a conductivity contribution with a fractional exponent to describe the imperfect conduction of the LFD

Figure 2. Imaginary part of the complex electric modulus spectra of TiONWs quenched from 11 RH%, (a) measured at 193 K and (b) its temperature dependence from 155 to 244 K. The constituent dielectric processes (processes 1−3) are also shown (a). Solid lines denote fits of the spectra with the superposition of three HN functions in the modulus formalism defined in eq 2.

benefit of this representation. All three processes are clearly seen in the imaginary modulus spectrum, whereas the evaluation of spectra remains possible up to about 250 K. Above that point, the measuring method did not allow us to fix the water content of the sample. The conductivity (LFD) shows itself as a peak in the imaginary modulus spectra, but at such low conductivity values as that in TiONW, especially in the low-temperature regime, the corresponding peak is located well below the frequency window of the measurement.33 The 1978


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lack of the interfering response of the charge-transport process is a further advantage of the use of the electric modulus. A description of the dielectric relaxations is possible with the same empirical relaxation functions as defined in eq 1. When we use the three HN functions, eq 1 turns into34 M *(ω) = M′(ω) + iM″(ω) 3

= M∞ −

∑ i=1

ΔMi (1 + (iωτM)α )β

(2)

where M*(ω) is the complex electric modulus and M′(ω) and M″(ω) are its real and imaginary parts, respectively. τM is the modulus relaxation time, and τM = τ(ε∞/εs)1/x, where x = α, β in the case of Cole−Cole and Cole−Davidson functions, respectively.34 Lesser known is the fact that τM is the “real” relaxation time for a dielectric process whereas τ in eq 1 is the so-called retardation time in the framework of the linear response theory.34 Because ε∞ is always lower than εs for any dielectric process, τM ≪ τ and therefore the modulus peaks are always located at higher frequencies than the corresponding permittivity peaks, gradually shifting out of the accessible frequency window with increasing temperature. In Figure 2b, the imaginary modulus spectra of TiONW measured in the low-temperature region between about 150 and 250 K are depicted. The effect of the increasing temperature on the acceleration of the relaxations is seen. Dielectric measurements on humid materials are often carried out at fixed relative humidity and varying temperature. Because water-induced dielectric changes seem to be related to the number of adsorbed water molecules in these systems,27,28 measuring the temperature-dependent dielectric properties at a fixed amount of adsorbed water would be desirable. However, it is experimentally more feasible to maintain a fixed relative humidity atmosphere in the sample holder, which enables the achievement of quasi-isosteric conditions in a narrow temperature range. To predict the amount of adsorbed water in TiONWs at each RH and temperature value, the characteristic adsorption curve was obtained from the water adsorption isotherm measured at 298 K. The adsorption potential is then calculated according to Polányi35 ε=

∫p

p0

⎛ p⎞ V dp = −RT ln⎜⎜ ⎟⎟ ⎝ p0 ⎠

Figure 3. Characteristic adsorption curve for water vapor on TiONWs as calculated from the adsorption isotherm measured at 298 K (open black symbols). The solid line denotes the fit of the GAB equation to the measurement points. Open symbols correspond to the amounts of adsorbed water at different relative humidities and temperatures predicted from the Polányi potential via the GAB parameters. The inset shows the logarithm of the characteristic adsorption curve, where there is a steep increase in the amount of adsorbed water (i.e., the third adsorption stage is seen).

1.6, and 168.6 ± 2.2 mg/g were obtained for 11, 22, 33, 43, and 75 RH% atmospheres, respectively. Therefore, quasi-isosteric conditions were indeed maintained during the high-temperature (273−350 K) measurements. Constant water coverage in the low-temperature regime (i.e., below 273 K) was realized by quenching the material of known water content from room temperature to cryogenic temperatures. The sample was then allowed to warm to room temperature gradually while recording spectra in 2.5 K steps.36 The applied method, however, was unable to guarantee a constant water content between ∼250 and 273 K. Spectra from this region were, therefore, excluded from the study. The temperature dependence of the dielectric processes (i.e., processes 1−3 and conductivity) is shown in Figure 4 in both the high- and low-temperature ranges. They all follow Arrhenius behavior, thus for the conductivity we can write σ σdc = 0 e−Ea / kBT (4) T where σdc is the dc conductivity, σ0 is the pre-exponential factor, Ea is the activation energy, and kB is the Boltzmann constant. Because hopping transport of the carriers was suggested in such ionic conductors, the linear temperature dependence of the preexponential factor is explicitly denoted in eq 4.37 The Arrhenius equation for dielectric relaxations takes the form of

(3)

where ε is the work done by the adsorption forces in delivering the molecules from the gas phase to the sorbed phase on the adsorbent surface, p and p0 are the actual and saturation vapor pressures, R is the ideal gas constant, and T is the absolute temperature. If the adsorbed amount is plotted as a function of the adsorption potential for a given adsorbent−adsorbate pair, a temperature-independent master curve is obtained. The potential theory allows the prediction of an adsorption isotherm at different temperatures. Figure 3 depicts the water sorption isotherm measured at 298 K along with the surface water coverage calculated from the GAB monolayer capacity on the right axis. Solid lines are fits of the GAB equation to the data in the 6−90 RH% regime. Above 90 RH%, a steep increase in the amount of adsorbed water, the so-called third adsorption stage, occurs, which is more visible in the logarithmic representation in the inset graph of Figure 3. The adsorbed amount of water at all RH values and measurement temperatures was calculated by the Polányi potential. Values of 70.4 ± 4.2, 96.0 ± 2.1, 109.9 ± 1.4, 120.7 ±

τ = τ0e+Ea / kBT

(5)

where τ0 is the pre-exponential factor. The validity of eq 5 is independent of the framework of evaluation; in Figure 4b the permittivity and in Figure 4c the modulus relaxation times are shown. Practically no changes in the activation energy of process 3 were observed throughout the study. However, the activation energy of conductivity, processes 1 and 2, varies with the amount of adsorbate in both the low-temperature (Figure 4a,b) and high-temperature (Figure 4c) ranges. Above 273 K, it varies roughly between 0.2 and 0.4 eV for processes 1 and 2 at 11 and 75 RH%, respectively. However, activation energies of about 0.38 and 0.46 eV were obtained from low-temperature measurements for samples cooled from 11 and 75 RH% atmospheres, respectively. The low-temperature values are in 1979


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Figure 4. Arrhenius plots of (a) conductivity and (b, c) processes 1−3 for TiONW measured in different relative humidity environments (i.e., at different water contents of the sample). (a, b) Above 273 K, the permittivity formalism (eq 1) was used, and below 250 K, the modulus formalism (eq 2) was used, and hence the modulus relaxation times are depicted in c. Solid lines are fits of the linearized Arrhenius equation to the data.

in either of the latter quantities. It has been pointed out recently that carrier concentration has the major effect on the water-induced charge transport in TiONW, whereas the ionic mobility changes only slightly as a result of moisture adsorption. In this study, however, practically constant water coverages were maintained during temperature scans, and hence it is suggested that changes in the charge-transport properties are mainly driven by changes in the activation energy of the diffusion of ionic species. In the methanol/silica system, NMR measurements indeed confirmed the water coverage dependence of the diffusion activation energy. 38 The comparison of these two seemingly different systems (water/ TiONW and methanol/silica gel) is justified by the identical variations in conductivity and ionic mobility upon water sorption (see Figures 3 and 7 in refs 27 and38, respectively). The abrupt change in the dynamics at around 260 K is then a consequence of the different dynamics of ionic diffusion in the low- and high-temperature regions. Furthermore, a 4-fold difference in the low- and high-temperature activation energies of a dielectric relaxation was found also in the NaX zeolite.39 Although the variation of a dielectric process activation energy with the amount of adsorbate is a widely observed phenomenon, there is no consensus about the direction of the change in the corresponding potential barrier heights. A decreasing conductivity activation energy was reported in oxides,2,3,40 clays,40,41 zeolites,5,22,40 and proteins,7,42 with an increasing or practically constant activation energy in collagen8 and silica−alumina catalyst particles,1 respectively. Even a variation according to a maximum curve was found in textiles43 and Vycor glass.24 The change in the activation energy of the dielectric relaxation times shows similar diversity because it was found to decrease in clays23 and polymer composites,44 increase in α-Fe2O3,45 Ag2O,17 silica,46,47 calcium-silicate-hydrate gel,48,49 and hydrated ovalbumin.50 The simultaneous exponential dependence of processes 1 and 2 and conductivity on both the adsorbed amount of water28

good agreement with those obtained recently via the evaluation of low-temperature permittivity spectra.28 Measurements of samples dried with activated zeolite from 11 RH% to an almost dry state (results are not included in Figure 4c for clarity) in fact provided the same temperature dependence as for 11 RH% (i.e., 0.39 and 0.35 eV for processes 1 and 2, respectively). It is noteworthy that whereas a pronounced change in the activation energy happened at 11 RH% only a slight change could be observed in the relaxation dynamics at 75 RH%; the extent of the relaxation dynamics change varies with the amount of adsorbed water. Discontinuity in the temperature dependence for the relaxation time of a loss process attributed to the orientational relaxation of water molecules was observed in the Cr2O3/water and ice/bulk water systems.16 The change in the dynamics was thought to arise from the 2D phase change of the adsorbate. When the adsorbate was suggested to be amorphous over the whole investigated temperature range, as in the case of amorphous ice,16 a continuous change in the adsorbate dynamics was observed at around the melting point with a strongly decreasing activation energy. In TiONW, calorimetric measurements did not reveal any phase transition below 53 RH % for strongly bound or capillary water or below 90 RH% for liquidlike water,27 thus the adsorbate remains amorphous in the 11, 22, 33, 43 RH% series even at very low temperatures. Because the typical relaxation times of processes 1 and 2 are orders of magnitude higher than that of bulk liquid water and have totally different temperature dependences in the lowtemperature region than crystalline or amorphous ice (see Figure 13 and corresponding references in ref 16), the interfacial origin of the middle-frequency processes seems to be the most plausible explanation. This also implies that the change in the dynamics of these processes is governed by the change in the charge transport dynamics itself. Because dc conductivity is expressed as σdc = enμ, where e is the charge, n is the carrier concentration, and μ is the carrier mobility, changes in conductivity could be governed by changes 1980


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and temperature (Figure 4a,b) implies linearly changing activation energies with ongoing water adsorption, as has already been pointed out for middle-frequency relaxation processes in silica19,44 f ∝ e−(Ea − b′w)/ kBT

as well as for conductivity in ion-conducting polymers σdc ∝

1 −(Ea − b*w)/ kBT e T

(6) 31

(7)

where w is the amount of adsorbed water, b′ = bkBT and b* = bkBT are the exponents of the water content dependence, and f is the frequency of the loss peak maximum in the spectra in ref 46. The above works, however, took only decreasing activation energies into account, taking no notice of the counterintuitive case of increasing activation energy. If we assume, in accordance with our experimental findings, that both the activation energy and the pre-exponential factor change linearly with the amount of adsorbed water, then we can write for the conductivity (C ± Dw) ln σ dc= (A + Bw) − kBT ⎛ ⎞ ⎛ C D ⎞ = ⎜A − ⎟ + ⎜B ∓ ⎟w kBT ⎠ ⎝ kBT ⎠ ⎝

Figure 5. Variation of (a) the activation energies and (b) the corresponding pre-exponential factors for the contributing dielectric processes above 273 K with the adsorbed amount of water in TiONW. Solid lines are linear fits to the data.

The correlation of Arrhenius parameters is a frequently observed phenomenon. A linear relationship between the logarithm of the pre-exponential factor and the activation energy is often found in physical/chemical processes and also for conductivity52 and dielectric relaxation:47,53

(8)

where A + Bw = ln σ0, C + Dw = Ea at water content w, and A and C are the pre-exponential factor and the activation energy in the dry state (w = 0), respectively. A similar equation applies to the relaxation processes as well. The term (A − C/(kB T)) on the right-hand side of eq 8 is ln σdc in the dry state at temperature T, with an Arrhenius-like temperature dependence. The second term here is the slope of the conductivity characteristics. An Arrhenius temperature dependence was indeed found at all studied water coverages (Figure 4). Furthermore, the 1/T temperature dependence of the second term in the right-hand side of eq 8 was also confirmed in hydrated collagen.8 The sign of D in eq 8 did not introduce any controversy into the physical picture of the water-related dielectric phenomena because the actual sign of the temperature coefficient is determined by the interrelation of the barrier height and the energy difference between the equilibrium states in the potential energy landscape.51 Furthermore, considering that both decreasing2,3,5,7,23,40−42,44 and increasing8,17,46,50 activation energies can be measured in different adsorbents, the nonmonotonous activation energy variation24,43 is thought to be a consequence of the change in the mutual variation of these energy differences. Furthermore, it was also suggested earlier that two processes with distinct activation energies (i.e., carrier generation and migration) determine the overall dynamics of the charge transport process in vapor-adsorptioninduced surface conduction.3 Dielectric spectroscopy alone, however, is unsuitable for resolving these closely related microscopic steps. In Figure 5, the activation energy and pre-exponential factor for all dielectric processes in the high-temperature range (i.e., above 273 K) is depicted against the amount of adsorbed water. Linearly increasing parameters were found for all studied water contents, similar to that in hydrated collagen.8 Essentially the same dependency is seen for the parameters of processes 1 and 2, which is thought to be further evidence of their common origin.28

log10 σ0 = aEa + b

(9a)

log10 τ0 = −αEa + β

(9b)

where σ0 and τ0 are the pre-exponential factors and a, b, α, and β are parameters. This is the so-called compensation effect or, for transport properties, the Meyer−Neldel rule. Although the phenomenon was thoroughly reviewed in the literature,54 concerns have continuously been emerging on its artifactual nature.55,56 The phenomenon was, however, confirmed in the water adsorption of hydrophilic surfaces57 and the surface diffusion of adsorbed molecules.58 The distinct straight lines in Figure 6 confirm the existence of the compensation effect in the TiONW−water system. The identical variation of the pre-exponential factors of processes

Figure 6. Correlation between the pre-exponential factors and the activation energies of the dielectric processes investigated in this study. The distinct straight lines indicate the validity of the Meyer−Neldel rule. 1981


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adsorbent’s surface18,23−25 and the accumulation of charges at the interfaces in the sample17,19,20 are mainly suggested as their possible origin. In zeolites, the relaxation of loosened ionic species21,22 was also proposed as the possible underlying mechanism. A further difficulty is the essentially similar spectra of completely different processes, such as the relaxation of associated ions and ion vacancy sites in ionic crystals.60 We hereby suggest, according to the results in Figure 7, that if multiple contributions in the spectra of an investigated material appear then the interrelation of these loss processes should be checked.

1 and 2 with their activation energies differs from the behavior of conductivity, thus supporting their common origin further. Recently, we indeed suggested the common and interfacial origin of processes 1 and 228 on the basis of the definite relationship between the relaxation times of processes 1 and 2 and the conductivity (Figure 9 in ref 28). However, a powerlaw-type correlation between long-range charge transport (dc conductivity) and molecular relaxation was also found in selfassembled transient intermolecular networks, where macroscopic charge transport originates from microscopic movements.59 Hence, here we propose another type of representation in order to reveal the interrelation between processes 1 and 2 more clearly. In the case of a common origin, a definite relationship exists not only between relaxation times and conductivity but between the relaxation times themselves. Therefore, we plotted the logarithm of relaxation times of processes 2 and 3 against that of process 1 in Figure 7 for the

4. CONCLUSIONS Temperature-dependent broadband dielectric spectroscopic measurements have been carried out on loosely packed titanate nanowires under quasi-isosteric conditions. The dynamics of the dielectric processes found in the spectra of humid TiONW was discussed in the temperature range between 180 and 250 K and in the relatively high-temperature range of 273−350 K. It was found that all investigated processes follow the Arrhenius equation in both the low- and high-temperature regimes; nevertheless, the dynamic parameters obtained from the lowtemperature measurements cannot describe the dielectric behavior of the system above the melting point of water. This implies a change in the dynamics of the processes. Further evidence was presented on the common interfacial origin of the middle-frequency peaks, which then implies change in the dynamics of the long-range charge-transport processes. It was suggested that this change originates from the coveragedependent ionic mobility on the adsorbent surface. The Arrhenius parameters of the investigated dielectric processes (i.e., activation energy and pre-exponential factor) vary linearly with the amount of adsorbed water. It has been pointed out that this behavior is a natural consequence of the interrelation between the water and temperature dependence of these processes. The compensation effect for conductivity and the middle-frequency losses was also demonstrated to be valid over the whole investigated adsorption range.

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AUTHOR INFORMATION

Corresponding Author

Figure 7. Correlation between relaxation times of processes 2 and 3 with process 1. Data measured at 298 K under various RH conditions were replotted from ref 28 (a) and for the temperature dependent results from Figure 4 in both the low- and high-temperature regions (b).

*Fax: 36 62 544 619. Tel: 36 62 544 620. E-mail: kakos@chem. u-szeged.hu. Author Contributions

The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript.

data measured at 298 K under various RH conditions and for the temperature-dependent results of Figure 4 in both the lowand high-temperature regimes. The relaxation times of processes 2 and 3 in panel b were shifted along the y axis, normalizing the curves to τ1 = 0.01 s. The specific value of the normalizing factor has only a negligible influence on the results and hence does not alter our conclusions. Between processes 1 and 2, a linear dependence was found with a slope of unity (i.e., τ2 ≈ τ1), which means that these two loss processes are two distinct appearances of the same phenomenon. We simply look at the same effect from different aspects. Between processes 1 and 3 a linear relationship was also found with a slope of 0.46 (τ2 ≈ 0.46τ1). It is then indeed a different process. Assignments of the middle-frequency processes (processes 1 and 2 in TiONW) are often contradictory in the literature. Dipolar relaxation of water molecules slowed down by the

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support was provided by the OTKA NK 106234 and NN 110676 projects and the TÁ MOP-4.2.2.A-11/1/KONV2012-0047 program.

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REFERENCES

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