Non-Arrhenian Ionic dc Conductivity of Homoionic Alkali Exchanged

May 4, 2010 - and Laboratoire Synthe`se et Catalyse, UniVersité IBN KHALDOUN Tiaret, BP 78, 14000 Tiaret, Algeria. ReceiVed: March 4, 2010; ReVised ...
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J. Phys. Chem. C 2010, 114, 9431–9438

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Non-Arrhenian Ionic dc Conductivity of Homoionic Alkali Exchanged Montmorillonites with Low Water Loadings S. Balme,† M. Kharroubi,†,‡ A. Haouzi,‡ and F. Henn*,† Institut Charles Gerhardt UMR 5253 CNRS-UM2-ENSCM-UM1, e´quipe Physicochimie des Mate´riaux De´sordonne´s et Poreux, UniVersite´ Montpellier II, Place Euge`ne Bataillon, 34095 Montpellier cedex 5, France, and Laboratoire Synthe`se et Catalyse, UniVersite´ IBN KHALDOUN Tiaret, BP 78, 14000 Tiaret, Algeria ReceiVed: March 4, 2010; ReVised Manuscript ReceiVed: April 15, 2010

Dc conductivity of the whole series of homoionic alkali exchanged montmorillonites is investigated by means of Complex Impedance Spectroscopy. Conductivity of the samples is measured at the dry state and at various water loadings between 0 and 6 absorbed water molecules per cation. Dc conductivity of all the dehydrated samples follows an Arrhenius behavior. In contrast, the hydrated samples exhibit a non-Arrhenius temperature dependence of dc conductivity that is fruitfully fitted by using the VTF’s empirical law. It is then shown that the critical temperature, TVTF, increases with water loading until the later equals approximately 3 for the Li+ and Na+ samples and higher values for the K+, Rb+, and Cs+ samples. So, it appears that the departure from the Arrhenius behavior is directly related to the number of water molecules in interaction with the alkali extra-framework cations. For water loadings higher than 3, activation energy for dc conductivity tends to values of about 0.2-0.3 eV for all samples independently on the alkali extra-framework cations. In contrast, activation energy appears to be very sensitive to the considered alkali sample for water loadings lower than 1 and, in that case, closely related to the dehydration enthalpy of the samples. 1. Introduction Smectites1 are clay minerals which the properties significantly depend on their hydration state. This phenomenon can be related to their lamellar crystallographic structure and to the presence of extra-framework cations (EFC) located in their interlayer space. Indeed, it is well acknowledged that water molecules intercalate in the interlayer space and strongly interact with EFC. When water loading exceeds certain values which depend on the nature and the density of EFC, smectites swell or even exfoliate to form a colloidal suspension when they are dispersed in aqueous solution.2 In such cases, the native EFC can be exchanged with other cations present in the surrounding solution. Likewise, large molecules can interact with the smectite innersurface and be trapped inside the interlayer space. These two properties can be very useful for water decontamination and have thus been the subject of numerous works.3 Besides, it must be underlined that the fundamental understanding of water molecule behavior confined in nanoscopic spaces makes smectites model materials for experiments as well as molecular simulations.4-7 Investigations on the water molecule adsorption mechanism and on water molecule dynamics confined in this smectite interlayer space have thus attracted much attention with use of either experimental or computational techniques.8-11 Basically, all studies point out the key role played by EFC. For instance, we recently determined from a systematic Thermo-Gravimetric Analysis (TGA) study of the whole series of homoionic alkali exchanged montmorillonites from the Wyoming deposit the heat of dehydration as a function of the alkali EFC and we highlighted, in accordance with other reported data, the peculiar * To whom correspondence should be addressed. E-mail: francois.henn@ univ-montp2.fr. Tel: 33 4 67 14 48 55. † Universite´ Montpellier II. ‡ Universite´ IBN KHALDOUN Tiaret.

behavior of the K+-sample.12 Nevertheless, many questions remain posed about the structure and dynamics of the water molecules which are confined, in strong interaction with EFC, in the smectite interlayer space sheet. EFC dynamics inside the interlayer space is known to be very sensitive to the presence of water molecules. Likewise, water molecule adsorption and dynamics visibly depend on the EFC characteristics.13-15 Therefore, we can expect the investigation of ionic dc conductivity, i.e., ion dynamics, as a function of the water loading and as a function of the temperature to be a fruitful way to obtain insight into the water/EFC subsystem confined in the smectite interlayer space. The present paper aims at investigating dc conductivity, measured by means of Complex Impedance Spectroscopy (CIS), on the entire series of homoionic alkali exchanged montmorillonites containing low amounts of water molecules, i.e., water loadings corresponding to less than a monolayer of adsorbed water molecules. The reason for studying only low water loadings is 2-fold: on the one hand, the influence of swelling can be neglected, and on the other hand, the cation influence is thought to be larger. Studies on ionic dc conductivity and dielectric properties of montmorillonites have already been reported at the dry16 as well as at various water loadings.13,17,18 However, none of them thoroughly examines the entire series of homoionic alkali exchanged samples and the effect of low water loadings. So, the influence of the alkali cation on the first stages of water adsorption, or the last stages of water desorption, via the measurement of ionic dc conductivity was not systematically scrutinized. Moreover, most of the reported data correspond to conductivity measurements carried out under constant water partial pressure while we investigate, in the present article, the last stages of dehydration obtained by a specific thermal treatment.

10.1021/jp101979t  2010 American Chemical Society Published on Web 05/04/2010

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The paper is constructed as follows. Section 2 describes the materials and the experimental methods used in this study. Section 3 first reports conductivity data at the dry state and then as a function of the water loading for the whole series of homoionic alkali exchanged montmorillonite samples. Temperature dependence of dc conductivity is also investigated as well as the resulting activation energy. Finally, section 4 discusses the data before conclusion. 2. Materials and Methods 2.1. Homoionic Clay Preparation and Chemical Analysis. The whole series of alkali exchanged montmorillonite samples studied in this work is the same as that investigated in our previous paper12 where the reader will find all the details about the sample preparation and chemical analysis (see Table 1 in ref 12). In brief, the natural montmorillonite was supplied by the Clay Minerals Society as source clay SWy-2-montmorillonite (Wyoming). It was first treated by water dispersion, sedimentation, and centrifugation12,19 in order to extract the e2 µm clay fraction. The later was then repetitively dispersed and stirred in 1 M MCl (M ) Li+, Na+, K+, Rb+, or Cs+) aqueous solution in order to exchange the alkali EFC. The chemical composition of each alkali exchanged montmorillonite was determined by elemental analysis (Central Analysis Laboratory, CNRS, France) and by application of the Mauguin method.20 2.2. Conductivity Measurements and in Situ Dehydration Procedure. Dc conductivity is extracted from ac conductivity signal recorded at various constant temperatures T in the 10-2 to 106 Hz frequency range, using a Novocontrol Broad-band Dielectric spectrometer (BDS 4000). Ac conductivity is measured on a pellet obtained by compaction, up to 5 tons, of the considered homoionic alkali e2 µm clay fraction powder. A 0.1 µm thick film of platinum is sputtered on both sides of the pellet in order to ensure a good electrical contact between the sample and the metallic plates of the spectrometer. Before each measurement, the pellet is dried at 473 K for 2 h. Then it is placed in a closed recipient with water at the bottom and left in this saturated water vapor atmosphere for 48 h at room temperature. The hydrated pellet is then positioned into the spectrometer cell that is maintained, until the end of the experiment, under a dry N2 flow, where the temperature is under remote control. Water loading, i.e., the number of adsorbed water molecules per EFC, denoted nH2O, is then obtained by in situ dehydration during 2 h at a given Treatment Temperature (TT). After reaching TT, the sample is quickly cooled, at about 20 to 30 deg min-1, to 173 K. This modus operandi ensures that the water loading, fixed by TT, is not modified during the “cooling” ramp. The value of nH2O corresponding to a given TT was previously determined from TGA carried out on the same montmorillonite series under the exact same experimental conditions and reported elsewhere.12 TT applied in the present study ranges between 303 and 333 K for the various hydrated samples and equals 473 K for the dehydrated ones. Depending on the alkali exchanged sample, these values of TT correspond to nH2O between 0 and about 3 to 6 water molecules per EFC. These hydrated states correspond to low water loadings for which no swelling is observed.21,22 Ac conductivity is first measured at TT at the end of the dehydration step. Then, the sample is cooled to 173 K and ac conductivity is measured at constant temperature T between 173 K and TT every 10 deg. In solid state ionic conductors, the real part of ac conductivity σac′(ω,T) results, in the first approximation, from the superposi-

Figure 1. Log-log plot of ac conductivity versus frequency for various measurement temperatures, from 353 to 473 K every 20 deg, in the case of the fully dehydrated Na+-montmorillonite (a) and Arrhenius plot of dc conductivity as a function of the inverse temperature for each fully dehydrated alkali exchanged sample (Li+ (9), Na+ (b), K+ (1), Rb+ (O), Cs+ (0)) and fits (straight lines) using eq 2 (b).

tion of dc conductivity σdc(T) and polarization conductivity σpol′(ω,T) contributions:

σac′(ω, T) ) σdc(T) + σpol′(ω, T)

(1)

Dc conductivity σdc(T) corresponds to long-range redistribution of ions, i.e., ionic diffusion, while σpol′(ω,T) arises from local ionic rearrangements causing dipolar reorientation and thus resulting in the intrinsic bulk polarization. In addition to these intrinsic conductivity contributions, σac′(ω,T) also exhibits, at low frequency, a frequency-dependent behavior that is known to result from the interfacial polarization effect due to the accumulation of ionic charges at the interface between the ionically conducting material and the metallic current collector. Basically, the higher the ionic dc conductivity, the larger the effect due to interfacial polarization. It is thus necessary to measure σac′(ω,T) over a relatively broad frequency range (see Figure 1) to be able to disjoint the different conductivity contributions and, hence, to extract the proper value of σdc(T). Following the Nernst-Einstein model for ionic dc conductivity, the temperature dependence of σdc(T) can be expressed as

σdc )

(

-∆Eaσdc σ0 exp T kBT

)

(2)

where ∆Eaσdc is the activation energy, σ0 is a pre-exponential factor, and kB is the Boltzmann constant. Equation 2 is only valid if the studied system is in a steady state. If not, empirical functions such as the so-called VTF23 law can be used to describe the temperature dependence of σdc(T). This point will

Conductivity of Montmorillonites

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TABLE 1: Experimental Values of ∆Eaσdc Obtained from the Arrhenius Plot of dc Conductivity for the Whole Series of Dehydrated Homoionic Alkali Exchanged Montmorillonite, i.e., Treated at TT ) 473 K for 2 h under Continuous Dry Nitrogen ∆Eaσdc ( 0.02 (eV)

Mont-Li+

Mont-Na+

Mont-K+

Mont-Rb+

Mont-Cs+

1.08

0.94

0.85

0.82

0.80

be detailed in sections 3 and 4 which are focused on the hydrated samples ionic dc conductivity. 3. Results 3.1. Dry State. First, a systematic study of the ionic dc conductivity of the entire series of dry alkali-exchanged montmorillonites is proposed. According to previous articles,12 it is assumed that after 2 h at TT ) 473 K under a continuous dry Nitrogen flow, all the samples are fully dehydrated. For measurement temperatures lower than 273 K (not reported here), all the samples only exhibit a frequency-dependent contribution, i.e., σpol′(ω,T), in the whole explored frequency range. However, at temperatures higher than about 300 K, σac′(ω,T) spectra show a dc conductivity plateau at low frequency (Figure 1a). Noteworthy, the poor dc conductivity of all the dehydrated samples makes the interfacial polarization effect rather weak and, hence, the determination of σdc(T) straightforward. Given that all the samples show the same behavior, we only report the ac conductivity spectra measured at various temperatures for the dry Na+-montmorillonite sample (Figure 1a). The dc conductivity dependence on temperature is reported in Figure 1b. It can then be seen that eq 2 is obeyed in the whole explored temperature range and, hence, that the activation energy ∆Eaσdc can be easily determined from a simple linear fit (Table 1) of the Arrhenius plot (Figure 1b). So far, we have no explanation for the peculiar behavior of the dry Rb+-montmorillonite sample, which exhibits a dc conductivity level close to that of the Na+montmorillonite sample. 3.2. Hydrated State. It is well-known that EFC have a great influence on smectite hydration and dehydration.24,25 The present study is focused on the last dehydration states, i.e., on low water loadings. In such cases, the adsorbed water molecules are all located inside the interlayer space26 in strong interaction with EFC. So, one may expect that the presence of water molecules in the EFC vicinity influences the ionic dc conductivity. Furthermore, because of the specific EFC/water interaction, one may also anticipate that the influence of water on dc conductivity will be remarkably cation dependent. Indeed, it is well-identified that the alkali cation hydration energy and that the structure of the alkali cation first solvation shell are extremely cation dependent.27 A typical example of ac conductivity spectra obtained for the hydrated samples is given in Figure 2a. First of all, the comparison with the dry state (Figure 1a) indicates that ac conductivity increases by several orders of magnitude upon hydration. Second, we can also notice a strong low frequency effect due to interfacial polarization emerges. This is coherent with the increase in dc conductivity, which favors the accumulation of ionic charges at the sample/metallic electrode interface. Nevertheless, σdc(T) can be determined, at the intermediate frequency plateau, for various measurement temperatures (see Figure 2a). The temperature evolution of σdc(T) is plotted in Figure 2b. In contrast to the dry state (Figure 1b), we observe that eq 2 is not obeyed. To analyze these non-Arrhenian behaviors, we choose the empirical Vogel-Tamman-Fulcher (VTF) law that is often used for the analysis of conductivity or viscosity measurements in materials as glasses, polymers, or melts.23 In these materials, the non-Arrhenian behavior is

commonly assumed to arise from the slow thermal evolution of the structural relaxation taking place throughout the structure. Thus, the potential landscape representing the material is continuously renewed with the temperature and, hence, the height of the potential barrier, i.e., activation energy, related to ions displacement.28 In the case studied here, this means the dynamical and/or structural configurations of the interlayer space in which water molecules and EFC are in strong interaction vary constantly, i.e., are not in a steady state. VTF’s law for dc conductivity is basically expressed23,29 as:

σdc )

(

-∆Eaσdc,VTF σ0,VTF exp T kB(T - TVTF)

)

(3)

where ∆Eaσdc,VTF, σ0,VTF, and TVTF are the characteristic VTF parameters. TVTF illustrates the departure from the Arrhenius behavior (eq 2), i.e., when TVTF ) 0 eq 3 is similar to eq 2. To quantify the non-Arrhenian behavior of our hydrated samples, dc conductivity data are fitted with eq 3. A typical

Figure 2. Log-log plot of ac conductivity versus frequency at various measurement temperatures from 173 to 303 K every 10 deg (a) (note: the sudden decrease of ac conductivity observed at high frequency for the measurement temperatures 173 and 183 K is an experimental electrical artifact) and Arrhenius plot of dc conductivity as a function of the inverse temperature. Solid squares are the experimental data points. The dash line corresponds to the Arrhenius behavior (eq 2) calculated from the lowest measurement temperatures only and the open square corresponds to the resulting extrapolated value of dc conductivity at T ) TT (b). Case of the Na+-montmorillonite partly dehydrated at TT ) 303 K.

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Figure 3. Logarithm of the product σdcT as a function of the measurement temperature for the Na+-montmorillonite partly dehydrated at TT ) 308 (squares) and 333 K (circles). Full and dash lines are the VTF fits (eq 3) which take into account only the solid symbols. The open symbols correspond to the experimental data comprised between TT - 50 K and TT that are excluded from the VTF fit procedure.

example is reported in Figure 3 for the Na+-montmorillonite sample treated at two different TT values. The experimental data used for the VTF fitting procedure (eq 3) are systematically taken considering the point corresponding to the first measurement at TT and all the points from the lowest temperature (at which it is possible to determine σdc) to TT - 50 K. This modus operandi guarantees that the effects due to the possible loss of water that could occur at the higher temperature, i.e., between TT - 50 K and TT, are not taken into account. First of all, it can be observed (Figure 3) that eq 3 matches well with our experimental findings. The values of ∆Eaσdc,VTF and TVTF extracted from the fit of the experimental data are reported in Table 2. A more detailed discussion about these values and their evolution will be given in section 4. However, it is worth noting here that all of them change drastically with the water loading: ∆Eaσdc,VTF decreases and TVTF increases when nH2O increases. It is also worth pointing out that dc conductivity is, as expected, very sensitive to the presence of water molecules even at extremely low loadings. For instance, no loss weight, i.e., no departure of water molecules, could be detected from TGA experiments carried out at some given TT (see the asterisks (*) in Table 2) while the ionic dc conductivity measured under the same conditions significantly differs from that of the dry state. This observation indicates that interaction between the very last remaining adsorbed water molecules and EFC is strong enough to influence the ionic dc conductivity. 4. Discussion 4.1. Dry State. The evolution of ∆Eaσdc, obtained for the dehydrated samples (see TT ) 473 K in Table 1) as a function of the alkali EFC radius,30 is plotted in Figure 4a. It can then be observed that ∆Eaσdc regularly decreases with the cation radius. A recent work published by Salles et al.15 on the same type of samples shows similar results. The slight discrepancy with data reported by some of us in a previous paper19 could be explained on the one hand by the difference in EFC chemical composition and on the other hand by the difference in experimental dehydration modus operandi. The cation dependence of ∆Eaσdc can be explained assuming that ∆Eaσdc is directly related to the Columbic attraction between EFC and the negative charge of the smectite sheet.31 If the global Columbic attraction was built from the exact same network of

Figure 4. Evolution of the dc conductivity activation energy (∆Eaσdc, eq 2) (9 and left axis) and interlayer space (d001) taken from ref 33 (O and right axis) as a function of the alkali EFC radius RC (a) and as a function of the inverse EFC radius (b) for the whole series of fully dehydrated homoionic montmorillonites. The lines are just to guide the eyes.

negative and positive charges, ∆Eaσdc would vary linearly with the inverse of the alkali EFC radius. Figure 4b shows that this is not the case. The departure from linearity is likely to result from the fact that the crystallographic features of montmorillonite allow the smallest cations, i.e., Li+ and to a much less extent Na+,15 to penetrate inside the clay sheet32 and therefore to be embedded in traps that are not strictly located at the center of the interlayer space. The EFC influence on ∆Eaσdc is well correlated to the evolution of the interlayer distance at the dry state33 (Figure 4a) that also exhibits a peculiar behavior for the Li+ sample. Noteworthy, the fact that natural clay minerals are also known for being rather heterogeneous in terms of charge distribution from one layer to another does not affect the Arrhenius dc conductivity behavior. 4.2. Hydrated State. The main experimental outcome of this study is that the dc conductivity temperature dependence of all the hydrated montmorillonite samples is non-Arrhenian and, in addition, that it can be well fitted by using VTF’s law (eq 3). As far as we know, no such dc conductivity behavior has ever been reported in these materials. The first assumption that could be made to interpret this nonArrhenius behavior is that some water molecules evaporate during the course of the experiment so that the sample dc conductivity continuously decreases. If this was true, we would expect (i) eq 2 to be obeyed only at the lowest measurement temperatures for which water evaporation is unlikely because of the extremely low water partial pressure and (ii) the dc conductivity measured at the beginning of the experiment to be different from that obtained at the end. Hypothesis (i) is not verified since the Arrhenius plot of the hydrated samples shows

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a

The asterisk (*) in the nH2O columns means that the weight loss due to the departure of water was below the TGA sensitivity apparatus and hence could not be determined (see ref 12).

7 8 20 35 73 87 111 0.69 0.65 0.64 0.60 0.3 0.24 0.20 13 25 35 71 94 106 118 0.9 1.1 1.4 1.8 2.8 3.4 6.3 333 328 323 318 313 308 303

0.68 0.56 0.51 0.40 0.26 0.26 0.25

5 9 45 59 83 98 96

(*) 0.6 0.9 1.3 2.4 2.8 5.4

0.67 0.51 0.41 0.30 0.25 0.25 0.23

16 50 57 84 93 97 105

(*) (*) (*) 0.26 0.78 1.72 2.42

0.67 0.51 0.44 0.34 0.34 0.25 0.23

0 35 50 66 78 84 96

(*) 0.1 0.3 0.8 1.1 2.1 3.1

0.68 0.63 0.61 0.49 0.29 0.24 0.15

(*) 0.1 0.6 1.1 1.7 2.6 3.7

TVTF ((1 K) ∆Eaσdc,VTF ((0.02 eV) TVTF ((1 K) nH2O ((0.1) TT (K)

∆Eaσdc,VTF ((0.02 eV)

TVTF ((1 K)

nH2O ((0.1)

∆Eaσdc,VTF ((0.02 eV)

TVTF ((1 K)

n H 2O ((0.1)

∆Eaσdc,VTF ((0.02 eV)

TVTF ((1 K)

nH2O ((0.1)

∆Eaσdc,VTF ((0.02 eV)

nH2O ((0.1)

Mont-Cs+ Mont-Rb+ Mont-K+ Mont-Na+ Mont-Li+

TABLE 2: nH2O (taken from ref 8), ∆Eaσdc,VTF, and TVTF Obtained at Different Dehydration Temperature Values TT from the Fit of the dc Conductivity Experimental Data (eq 3, see text and Figure 3) for the Whole Series of Hydrated Homoionic Alkali Exchanged Montmorillonitea

Conductivity of Montmorillonites

Figure 5. Evolution of TVTF obtained from the VTF fit of the experimental dc conductivity (see text, eq 3, Table 2 and Figure 3) as a function of nH2O, the number of adsorbed water molecule per alkali EFC for the whole series of partly dehydrated homoionic montmorillonites: Li+ (9), Na+ (b), K+ (1), Rb+ (O), Cs+ (0). The lines are just to guide the eyes.

no linear domain even at the lowest temperature. Hypothesis (ii) could be partly confirmed since we observe that dc conductivity measured at T ) TT at the beginning of the experiment is slightly higher than that measured at the end (Figure 2b). However, assuming an Arrhenius behavior, the hypothetical dc conductivity at T ) TT that can be extrapolated from the data obtained at low temperature turns out to be much higher than that measured at the beginning (Figure 2b), thus indicating a water uptake. Obviously this is absolutely impossible in regards to the experimental conditions used in this study since the sample is continuously maintained under dry N2 flow so that no water uptake can account for such a dc conductivity increase. Furthermore, if significant water uptake or evaporation took place, our data would not be reproducible. To sum up, we cannot totally exclude that a small number of water molecules evaporate upon experiments, especially at the highest measurement temperatures comprised between TT - 50 K and TT. That is the reason why the experimental values of dc conductivity between TT - 50 K and TT are not taken into account for the VTF fitting procedure. Meanwhile, the non-Arrhenian behavior observed here is sufficiently marked and reproducible to be an intrinsic feature of our samples within the experimental conditions used in our study. TVTF characterizes the departure from an ideal steady state system. So, it can be deduced from the increase of TVTF with the water loading (Figure 5) that the larger nH2O is, the less stable the EFC/water subsystem that results from the experimental conditions used in this study, i.e., dehydration at TT followed by a relatively fast cooling. The evolution of TVTF also appears dependent on EFC. For a given value of nH2O, TVTF is always lower for the Li+ sample. For the smallest cations, i.e., Li+ and Na+, TVTF tends toward an asymptotic value of about 100 K when nH2O is about 3. Obviously, this is not the case for the biggest ones, i.e., K+, Rb+, and Cs+, for which the asymptotic value of TVTF, if it existed, would be higher than 100 K and would be reached for values of nH2O higher than 3. Therefore, it comes out from the evolution of TVTF with nH2O that the presence of water molecules in interaction with alkali EFC results in nonsteady states in which the departure from thermodynamics equilibrium increases with the water loading and the considered alkali cation radius until an asymptotic behavior is attained when the cation is solvated by a minimum of 3 water molecules. It can be reasoned that the nH2O threshold value of 3, for the smallest cations, or more, for the largest ones,

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is likely to be related to the number of water molecules needed to complete the first hydration sphere of the considered alkali EFC in the confined geometry imposed by the interlayer space. Sanchez et al.5 report data obtained on various clay minerals by means of neutron scattering. They observe, for the Na+montmorillonite, a non-Arrhenius behavior of the water diffusion coefficient and show that their fully hydrated samples exhibit both a glass-type and a “fragile-strong” transition at Tg ) 108 K and Ts ) 205 K, respectively. At first sight, this value of Tg appears very close to that of TVTF ≈ 97 K obtained in our present work (see Table 2). However, they ascribe the glass transition to water located at the clay grain surface and not to that confined in the interlayer space, whose phase change is attributed to the fragile-strong transition at Ts. Others neutron scattering experiments reported by Bordallo et al.6 show that water molecule dynamics confined in the interlayer space of a Na+-montmorillonite is strongly influenced by the exchangeable cations and that a deviation in the normalized scattering function is observed at temperatures below 200 K (see Figure 4a in ref 6). It must also be emphasized that Frunza et al.34 report a nonmonotonous temperature dependence of water molecule dynamics from ac conductivity measurements of hydrated layered oxide materials. Although these experimental findings cannot be quantitatively compared with ours, it can be, however, qualitatively concluded that, in all cases, the EFC/water subsystem confined in the nanoscopic interlayer space of montmorillonite behaves as a complex nonsteady state system, at least in regards to its dynamical properties. The reason for this remarkable phenomenon can be inherent to confinement and/or partly induced, in our case, by the relatively fast cooling step to which the sample is submitted before dc conductivity measurements. Unfortunately, we cannot investigate the effect of the cooling ramp and, at the same time, control the water loading throughout the experiment. Therefore, it is not possible to examine the effect of confinement (at constant water loading) independently on the cooling step. Let us now analyze the evolution of the activation energies calculated from the VTF fit of the experimental dc conductivity data (see Table 2). Figure 6 reports the evolution of ∆Eaσdc,VTF as a function of nH2O, for each homoionic alkali montmorillonite. For loadings lower than 3, we observe a decrease of ∆Eaσdc,VTF when the water loading increases. For nH2O > 3, the values of ∆Eaσdc,VTF tend to an asymptotic value of about 0.2-0.3 eV for all the samples independently on the considered alkali exchanged sample. Noteworthy, these asymptotic values of ∆Eaσdc,VTF are close to that reported by Su and Chen13 for dc conductivity measurements carried out in relative humidity between 40% and 70%. As for the water loading dependence of TVTF (Figure 5), it seems that the value of nH2O ) 3 is like a threshold beyond which the nonsteady state features of the EFC/water subsystem do not evolve. The influence of the alkali EFC can be highlighted by plotting the evolution of ∆Eaσdc,VTF with the cation radius for different fixed values of water loading (Figure 7). First, it can be clearly seen that the higher nH2O is, the less the cation influence on the activation energy, i.e., for nH2O ) 2.5 all the samples exhibit roughly the same activation energy roughly between 0.2 and 0.3 eV. Figure 7 also indicates a peculiar behavior for K+montmorillonite, which appears to be much less sensible to the water loading. This result is fully consistent with the previous data reported from experiments12,35 and molecular simulations24 which clearly outlined the peculiar behavior of K+-montmorillonite that was attributed to the reluctance of K+ cations to fully

Balme et al.

Figure 6. Evolution of ∆Eaσdc,VTF obtained from the VTF fit of the experimental dc conductivity (see text, eq 3, Table 2, and Figure 3) as a function of nH2O, the number of adsorbed water molecule per alkali EFC for the whole series of partly dehydrated homoionic montmorillonites: Li+ (9), Na+ (b), K+ (1) (a) and Rb+ (O) and Cs+ (0) (b). Results are divided in two plots for the sake of readability. The lines are just to guide the eyes

Figure 7. Evolution of ∆Eaσdc,VTF as a function of the alkali EFC radius RC for various nH2O values (from top to bottom: nH2O ) 0.25, 0.5, 1, 1.5, 2, and 2.5). The lines are just to guide the eyes.

hydrate24 probably because of the competition occurring between the K+ solvation and the interlayer cohesion energies. Finally, the influence of nH2O on dc conductivity can be well highlighted by calculating the activation energy difference between the dry (Table 1) and the different nH2O states (table (∆Eaσdc) ) ∆Eaσdc(dry) - ∆Eaσdc(nH2O), as a function 2), ∆ndry H2O of the alkali cation radius (Figure 8). Thus, the most remarkable (∆Eaσdc) (left axis finding is that the cation dependence of ∆ndry H2O in Figure 8) varies consistently with that of the dehydration enthalpy, ∆Hdehyd, obtained from TGA experiments (see Table 3 in ref 12 and the right axis in Figure 8) when nH2O < 1. It can also be seen that the largest effect is observed for K+-

Conductivity of Montmorillonites

Figure 8. Evolution of ∆dry nH2O(∆Eaσdc) (see text section 4.2 for definition) (solid symbols and left axis) for various nH2O values (solid lines from bottom to top: nH2O ) 0.25, 0.5, 1, and 2.5) and of the dehydration enthalpy ∆Hdehyd taken from ref 8 (] and right axis) as a function of the alkali EFC radius RC. The lines are just to guide the eyes.

montmorillonite. This means that experimental data extracted from both TGA and dc conductivity indicate that interaction of the first adsorbed water molecules is stronger with K+ compared to the other alkali EFC in the confined configuration imposed by the interlayer space. This outcome evidently emphasizes that the influence of the last remaining water molecules on the activation energy for dc conductivity is strongly correlated to the dehydration enthalpy when less than 1 water molecule per cation remains adsorbed. This provides additional proof that these water molecules directly interact with EFC and, hence, that the dehydration enthalpy of our samples is governed by EFC/water interaction. 5. Conclusion Dc conductivity of the whole series of homoionic alkali cation exchanged montmorillonite samples is measured at the dry state and as a function of the water loading. All the dry samples follow an Arrhenius behavior where the corresponding activation energy does not strictly vary with the inverse cation radius, thus indicating that the Columbic interaction network which governs the potential barrier for cationic diffusion slightly differs for Li+- and, to a less extent, Na+montmorillonites. This deviation probably results from the more or less deep embedding of the alkali cation, depending on its size, into the montmorillonite sheet. In contrast to the dry states, the dc conductivity thermal activation of all the hydrated samples turns out to be nonArrhenian. The empirical VTF law (eq 3) thus appears to be suitable to account for the experimental behavior. The critical temperature TVTF, extracted from the fit of the experimental data, increases until the water loading per cation, nH2O, equals approximately 3 for the smallest cations, i.e., Li+ and Na+, and higher values for the biggest ones, i.e., K+, Rb+, and Cs+. In the case of Li+ and Na+ samples, the asymptotic TVTF value is about 100 K, whereas it seems to be higher for the other homoionic montmorillonites. First, it must be emphasized that these asymptotic TVTF values are qualitatively comparable to other critical temperatures obtained from neutron scattering diffusion experiments on fully hydrated montmorillonite samples.5 Second, the threshold values of nH2O, i.e., 3 for Li+ and Na+ or higher for K+, Rb+, and Cs+, would correspond to the number of water molecules required for the completion of the cation first hydration shell when it is confined in the interlayer space. Therefore, it appears that the ionic dc con-

J. Phys. Chem. C, Vol. 114, No. 20, 2010 9437 ductivity is very responsive on the one hand to the EFC/water solvation features and on the other hand to the confined water molecule dynamics which is expected to be rather complex and typical of systems in nonsteady states. Furthermore, the peculiar behavior of K+-montmorillonite is evidenced in agreement with previous work. Finally, evolution of the activation energy for the ionic dc conductivity as a function of the water loading shows that it is extremely sensitive to the last remaining water molecules. So, it is clearly demonstrated that the difference in activation energy between the dry and the last dehydrated states, i.e., nH2O ) 0.25 and 0.5, varies with the cation size in the same manner as the dehydration enthalpy12 does. These outcomes emphasize that, at least in these materials, the variation of dc conductivity as a function of the lowest water loadings is akin to the surface thermodynamics of the material inner-surface. Dc conductivity measurements by means of Complex Impedance Spectroscopy thus appear to be a powerful tool for characterizing (i) the water molecules dynamics confined in the nanoscopic interlayer space and (ii) the surface thermodynamics due to the extra-framework cation/water interaction. Acknowledgment. The authors are grateful to the French and Algerian Ministries for Foreign Affairs for their financial support via the CMEP/PHC Tassili scientific exchange program. References and Notes (1) Guven, N. ReV. Mineral. 1988, 19, 497. (2) Cases, J. M.; Berend, I.; Besson, G.; Francois, M.; Uriot, J. P.; Thomas, F.; Poirier, J. E. Langmuir 1992, 8, 2730. (3) Nakazawa, T.; Takano, M.; Nobuhara, A.; Torikai, Y.; Sato, S.; Ohashi, H. Activation energies of diffusion of tritium and electrical conduction in water-saturated compacted sodium montmorillonite. In Proceedings of the 7th Iinternation Conference on RadioactiVe Waste Management and EnVironmental Remediation; ASME: New York, 1999. (4) Swenson, J.; Bergman, R.; Longeville, S. J. Chem. Phys. 2001, 115, 11299. (5) Sanchez, F. G.; Juranyi, F.; Gimmi, T.; Van Loon, L.; Seydel, T.; Unruh, T. J. Phys.: Condens. Matter 2008, 20. (6) Bordallo, H. N.; Aldridge, L. P.; Churchman, G. J.; Gates, W. P.; Telling, M. T. F.; Kiefer, K.; Fouquet, P.; Seydel, T.; Kimber, S. A. J. J. Phys. Chem. C 2008, 112, 13982. (7) Marry, V.; Rotenberg, B.; Turq, P. Phys. Chem. Chem. Phys. 2008, 10, 4802. (8) Michot, L. J.; Delville, A.; Humbert, B.; Plazanet, M.; Levitz, P. J. Phys. Chem. C 2007, 111, 9818. (9) Porion, P.; Michot, L. J.; Faugere, A. M.; Delville, A. J. Phys. Chem. C 2007, 111, 13117. (10) Porion, P.; Michot, L. J.; Faugere, A. M.; Delville, A. J. Phys. Chem. C 2007, 111, 5441. (11) Boulet, P.; Greenwell, H. C.; Stackhouse, S.; Coveney, P. V. THEOCHEM 2006, 762, 33. (12) Kharroubi, M.; Balme, S.; Henn, F.; Giuntini, J. C.; Belarbi, H.; Haouzi, A. J. Colloid Interface Sci. 2009, 329, 339. (13) Su, P. G.; Chen, C. Y. Sens. Actuators, B 2008, 129, 380. (14) Cadene, A.; Rotenberg, B.; Durand-Vidal, S.; Badot, J. C.; Turq, P. Phys. Chem. Earth 2006, 31, 505. (15) Salles, F.; Devautour-Vinot, S.; Bildstein, O.; Jullien, M.; Maurin, G.; Giuntini, J. C.; Douillard, J. M.; Van Damme, H. J. Phys. Chem. C 2008, 112, 14001. (16) Fan, Y. Q.; Wu, H. Q. Solid State Ionics 1997, 93, 347. (17) Bidadi, H.; Schroeder, P. A.; Pinnavaia, T. J. J. Phys. Chem. Solids 1988, 49, 1435. (18) Belarbi, H.; Haouzi, A.; Giuntini, J. C.; Zanchetta, J. V.; Niezette, J.; Vanderschueren, J. Clay Miner. 1997, 32, 13. (19) Haouzi, A.; Kharroubi, M.; Belarbi, H.; Devautour-Vinot, S.; Henn, F.; Giuntini, J. C. Appl. Clay Sci. 2004, 27, 67. (20) Mauguin, C. H. Bull. Soc Fr. Mineral. Cristallogr. 1928, 51, 285. (21) Tambach, T. J.; Bolhuis, P. G.; Hensen, E. J. M.; Smit, B. Langmuir 2006, 22, 1223. (22) Sato, T.; Watanabe, T.; Otsuka, R. Clays Clay Miner. 1992, 40, 103. (23) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. J. Appl. Phys. 2000, 88, 3113.

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