RF-microwave dielectric relaxation spectroscopy of xerogel Na0.33V2O51.6H2O

Solid State lonics 38 (1990) 143-148 North-Holland

RF-MICROWAVE

DIELECTRIC RELAXATION SPECTROSCOPY

OF X E R O G E L Nao.~3V2Os-l.6HzO J.C. B A D O T and N. B A F F L E R Laboratoire de Chimie de la Matiere Condensbe, UA 302-CNRS, ENSCP. 11 rue P. et M. Curie, 75231 Paris 6~dex 05, France

Received 25 September 1989; accepted for publication 26 January 1990

The dielectric properties of Na0.33V205 - 1.6H20 have been studied in a broad frequency range (103-1010Hz). The dielectric spectra exhibit: i)a low frequency effect due to the diffusion of Na + cations; ii)two dielectric relaxations due to the two kinds of water (strongly and weakly bonded water); iii) a dielectric relaxation which would be due to a fast intrasite motion of Na + cations. One explanation of these mechanisms with respect to the experimental results is proposed.

i. Introduction The vanadium oxide gels formed by polycondensation of vanadic acid correspond to the formula V 2 0 5 - n H 2 0 . According to the value of n, we have a gel (n<300) or a colloidal solution (n>300). By drying at room temperature, a xerogel with the formula V 2 0 5 - 1 . 6 H 2 0 is obtained. Electron microscopy observations have shown that the xerogel is formed of entangled fibers which are ribbonshaped with dimensions I fix 102x 103 .~ [ 1J. When the xerogel is deposited on a flat substrate, X-rays diffraction studies show a layered structure resulting from the arrangement of the ribbons parallel to the substrate [2] The basic distance is a function of water content in the gel, e.g. d=l 1.6A for the V205-1.6H20 xerogel and d=8.8A for the V 2 0 5 - 0 . 6 H 2 0 xerogel formed after a stronger drying. The difference Ad=2.8A between these two values corresponds to the dimensions of the water molecule (interlayered water). Different kinds of bonded water were observed by thermal analysis (DTA and TGA): weaklybonded water (interlayered water) and water stronglybonded to the ribbon. The strongly-bonded water assures the cohesion of different parts of ribbon. The ribbon structure has been put in evidence by electron and X-ray diffraction: it is close to the V205 orthorhombic structure [ 1]. The existence of H30 + ion has been proved by infrared spectroscopy [3,4]. The equilibrium of the system is made by electrostatic compensation of the repulsive forces between negatively charged solid particles and the attractive forces between the solvent cations (H3 O+ counter-ions) and the negative charges of the solid network (0.33 e / V 2 0 5 ) . The conductivity of the xerogel is due to the H 3 0 ÷ diffusion into the interlayered water between the oxide ribbons. The conductivity is remarkably high : t~=3x 10-3[)-I.cm "l at room temperature with an activation energy of O.35 eV [5]. These values depend upon the water content in the gel and on the water-pressure above the sample I6].

A dielectric study in the broad frequency range (103-10 l0 Hz) has recently been performed on V2Os-I.6H20 xerogel in order to discern the dielectric relaxations of the various protonic species present in the gels [7]. We have also demonstrated the potential of this method for the study of protonic conductors such as HUP(H30 UO2PO4-3H20) and hydrogenosulfates(CsHSO4,...) 18,9]. The dielectric spectra in V2Os-1.6H20 xerogel exhibit three types of behaviour: i) a low-frequency effect due to long range diffusion of the oxonium ions (H30+); ii) two dielectric relaxations due to the two kinds of water (strongly and weakly bonded to V205 ribbon); iii) a dielectric relaxation due to a fast reorientation of the dipolar H3 O+ ions. One explanation and discussion of the mechanisms with respect to experimental results have been proposed [7]. Vanadium oxide xerogels have the same ion-exchange properties as clays: at room temperature, H30 + ions can be easily exchanged by cations such as Na +, K +, Li+,...(10). In this .paper, we determine the dielectric relaxation of each protomc species in the sodium exchanged xerogel (Na0.33V205-1.6H20). The comparison between xerogel and its homologous sodium exchanged allows to discriminate ions and water motions and to determine the influence of the ion exchange on water motions and conductivity mechanism.

2. Synthesis and structure of Na +-xerogel 21 .Ion exchange in xerogels

The xerogel obtained by polycondensation of vanadic acid is deposited on a glass substrate and dried at room temperature. The thin film of xerogel is introduced in a NaCI solution (0. I M). The ion exchange is realized at room temperature in a few minutes. The thin film is washed with distilled water in order to eliminate the CI" ions on the film surface and dried at room temperature [ 11 ].

J.C. Badot, N. Balfier I Rf-microwavedielectric rela-~cation

144

X-rays diffraction studies (reflection geometry) show the same layered structure than the H30+-xerogel with a basic distance d=10.9A. This distance decreases up to 8.8/~ when the xerogel is dried at 150°C. The discrepancy between these two values, Ad=2.1]~, corresponds to the departure of one water-monolayer (hereafter called Xwater). This value is lower than in the case of H30 ÷xerogel (Ad=2.8A) because an electrostriction effect in water network (water molecule compression) is produced by Na ÷ ions. Two different kinds of bonded water were observed by thermal analysis (DTA and TGA): i) water "weakly bonded" to the ribbon corresponding to 1.3H20 / V205 (X-water). ii) water "strongly bonded" to the ribbon corresponding to 0.3H20 / V205 (hereafter called Y-water). Thus, the hydration layer of the Na ÷ ion in the interlayered space is constituted by four water molecules (X-water), e.g. 0.33 Na ÷ for 1.3 H20.

bl

o

b)

@_C

22. Structure of the interlayered water network(X-water) in Na +-xerogel In orthorhombic bronze a - N a x V 2 0 5 structure [121 (cf.fig. l) Na ÷ ions are localized in tunnels constituted by VO5 pyramids: the vertices of the pyramids make an oxygen square plane whose dimensions are 3.6x3.6A. Assuming the structural analogy between the oxide network in xerogel and the orthorhombic V205, it seems reasonable to localize the Na + ions of the xerogel in the same way as in the or-bronze: the water molecules form also a square of 3.6 x 3.6A with their OH-groups orthogonal to b

a)

dc

l.©

©C I °

c

Fig. 2. Localization of Na ÷ ions and water molecules in Na÷-xerogel in: a) (a,c) bisectrix-b plane. b) a-c plane. oxide ribbon (cf.fig.2a). Each water molecule forms two H-bonds with two ribbons (cf.fig.2a). It is thus possible for Na ÷ cations, which statistically occupy a third of the sites, to jump from one square to the other in the c-direction with a distance of about 3.6A (cf.fig.2b). 3. Electrical m e a s u r e m e n t s

ONa Fig. 1. Localization of Na+ ions in orthorhombic bronze ~-Na×V205

The samples are compacted pellets with a diameter 2a=3mm and a thickness d=lmm.The experiments were made with brass plugs covered with Au thin film electrodes between 190K and 300K under N2 flux. The cell is a circular coaxial line whose inner conductor is interrupted by the sample (cf.fig.3).It is loaded with the characteristic impedance ZO=50D. The same cell is used in the broad frequency range 103-1010Hz. In the sample, the electric field is parallel to the common axis of the sample and the inner conductor (cf.fig.4), as fully described in references [7] and [81. The knowledge of the sample impedance Zb allows the determination of dielectric complex permittivity ~* as detailed in references [71, 1131

J.C. Badot, N. Baffler / Rf-microwave dielectric relaxation

In this frequency range, it is thus possible to use complex impedance representation for the determination of the direct-current conductivity o(0).

sample t

x\\

\ \ \ ~/\\\

145

\ \ \

1

32.High frequency range (106-1010 Hz)

\ \ " \

The study of the real part e'(¢0) and the imaginary part e"(c0) was performed between 106 and 10 I0 Hz with following relation: £*(~) - £~

Fig. 3. Localization of the sample in the coaxial line. and [ 141 according to the formula: Zb=(G b+iCb¢0) - 1

ic°la0dJ0(ya) 2rt-'/aJ 1(ya) where y = k(e' - iE") I/2 , t.10 = 4rcxl0 -7 H.m t k = o~/c with c = 3x108 m.s -I

( 1)

e* = e' - ie" is the complex relative permittivity of the sample. J0 and Jl are respectively zero and first order Bessel functions. Gb and Cb are respectively the conductance and the capacitance of the sample.

1

= ~

(2)

es - ~oo 1+ io~z where E,oand es are limit values of ~:*(o)) as ~ approaches and 0 respectively, z is known as the (Debye)relaxation time and fp=(27tx -1) denotes the loss-peak frequency. The relaxation time x is a measure of the nominal time scale on which molecular reorientation can place. The Cole-Cole plot, e' vs ~", is a semi-circle centered on the ~' axis. If the dipoles interact more strongly with each other the equation (2) is slightly modified according to the empirical expression:

e*(w) -e,~ es - e ~

1 1+ (ic0'~)1-~ '

(0
(3)

31. Low frequency range (103-106 Hz) The conductivity of Na÷-xerogel is determined by the complex method with a LF impedance analyzer model HP4192A. In this frequency range and generally for frequencies below IGHz, where Iyal << I, the formula (1) is reduced to the expression of the parallel-plate capacitor (quasi-static approximation): Zb =

d 0*(60) xa 2

where 0*(0)) = i~ c0 e*(oJ)

where 0t is an empirical parameter which measures the degree of discrepency from the Debye model. 4. D e t e r m i n a t i o n

of dc-conductivity

C o m p l e x i m p e d a n c e diagrams, Z " = f ( Z ' ) , are characterized by circular arcs centered below the Z'-axis (cf.fig.5). The intersection of the circles with the Z'-axis permits to obtain the de-resistance R(0) of the sample. The de-conductivity 0(0) is obtained by the expression R(0) =d

°' Jz ,~

20_ 7 s

3

f

I 0.1

0.2

0.3

0.4

Z'CM~.~ b)

~°~I

6 ~3 2

I

=

Ez - ' - ~ ' - - He Fig. 4. Sample electromagnetic field distribution (Ez,Hm: electric and magnetic fields respectively).

" 0.Sz,(Mn)

~2}

Fig. 5. Complex impedance plots (Z" vs Z') for Na+xerogel at 296K(a) and 278K(b). Numbers indicate frequency in kHz.

146

2°i

J.C. Badot, N. Baffler/Rf-rmcrowave dielectric relaxation

~ I-.-

Na÷-xerogel at room temperature. The decomposition of the diagrams reveals two kinds of behaviour: one is represented by a straight line (domain 1) and the other by semi-circles or circular arcs (domains 1', 2, 3 and 4) characterizing dielectric relaxations. In our previous work [7], the decomposition procedure has been extensively discussed. The experimental data, at various temperatures, are given in table l-a in comparison with those of H 3 0 ÷ - x e r o g e l (cf.table I-b) obtained in previous work [7]. - Domain 1: this domain occurs in the low frequency part of the spectra and is represented by a straight line with a slope

.3.0

_o 4D

5"03

315

Table

4

lO~,T Fig. 6. Temperature dependence of the conductivity of the Na÷-xerogel. / ( o ( 0 ) . S ) where d is the thickness and S (S=Tta 2) the surface of the sample. Experiments are done at various temperatures. The dc-conductivity of Na+-xerogel (o(0)=7x10 .6 f~-t .cm -I at T=296K) is approximatively two orders of magnitude lower than the dc-conductivity of H30+-xerogel

(o(0)=10 3 ~ l . c m l at T=300K). The temperature dependence of dc-conductivity, e.g. logoq'=f(103/1 ") (cf.fig.6), follows an Arrhenius law in the temperature range with an activation energy Wo=0.48eV. This conductivity corresponds to Na t ions diffusion in the X-water network. Results are in good agreement with previous studies on Na ÷ diffusion in other hydrates, e.g. NaUP and Na-vermiculite [8,151.

I~: Relaxation times and parameters f o r Na+-xerogel

TCK) (s) W(eV) Ar . . . . . . . . . . . . . . . . . . . . . . . . 296 0.16 278 Domain 4 Intrasite >la+ jump

Domain 3 X.H20

Domain

2

Y_H2D

Domain I ' Na'-jump

5. Evidence of various relaxations ~

1.1xi0 - l l

0

20

263

3.2 0.2

223

1.2xlO - I I

0.3

208 193

1.3xi0 - I ! 2xi0-11

0.3 0.4

188

2.3xi0 - ; I

296 278 263

| . I x l C -I0 2.4xi0 -IC 3.7xi0 -I0

296

1.1xi0 -9

278 263

2.3xi0 -9 3.2xic -9

296

1.1xi0 -8

278 263

4x10 -8 1 , I x i 0 -7

0.1

20

0.4

0.25

I0

0

0.28

37

0.2

45 0.48

53 72

0

= 10

Figure 7 shows the typical Cole-Cole plots, ~:"=f({), for Table Ib:

°°l:I /

T(K)

296

002:I , /

20

6o

,'

mE' 7

00

8000 ~

'

2o

~o

....--.~~..-

" 60

...... ~"". r

oo

~oo

-..

;2o

r(s)

W(eV)

f o r H30+-xerogel .',~

,

5.3

0

1.8xi0-12(*)

230

1.4xi0 -11

H30+

213 198

2.7xi0 -11 4xi0 -11

0.14

6 7

296

4x!O -11

16

0.23

Domain 3

258

1.3xi0 -I0

24

0.23

X-H20

230

3.2xi0 "10

27

0.22

213

8x10 -lO

33

0.24

39

0.28

4C 43

D.28 C.28

52

0.27

'""I

~

and parameters

Domain 4

y-

1o .

~

Relaxation times

198

2.4xi0 -9

Domain 2

296 258

| . I x i 0 -9 8.8xi0 -9

Y-H20

230

2xi0 -8

0,21

" E'

Fig. 7. Cole-Cole plots (e" vs e') for Na+-xerogel at 296K. Numbers indicate frequency in MHz.

= 11; (*) extraoolated value

3.27

147

J.C. Badot, N. Baffler / Rf-microwave dielectric relaxation

2 corresponding to a frequency dependence of the permittivity e*(o~) et (ko) n-I with n=0.3. - Domain 1': this domain occurs in middle frequency range and is represented by semi-circle arcs characterizing (quasi)Debye dielectric relaxation (or---O).We notice that the relaxation time "~1 (see table l-a and figure 8) is strongly lowered with increasing temperature. The temperature dependence of '~1 follows an Arrhenius law, i.e. xt exp(Wl/kT), with an activation energy W l=0.48eV. Domains 2, 3 and 4: : these domains exist in high and microwave frequencies and are represented by semi-circles (domain 3) and circular arcs (domains 2 and 4) characterizing respectively Debye and non-Debye type relaxations. The temperature dependence of the relaxation times x2 (domain 2), "c3 (domain 3) follows an Arrhenius law with activation energies W2=0.25eV and W3=O.28eV. In otherwords, temperature dependence of the relaxation time 't4 exhibits a more complex behaviour: i) a non-actived behaviour for temperatures above T=220K. ii) an Arrhenius behaviour with activation energy W4=0. leV for temperatures below T=220K. The figure 9 and table l-a compare the variation of dielectric susceptibility, i.e. A~: = es -eoo , for each relaxation domain versus the temperature. We observe that: i) the susceptibility of domain 1' is a decreasing function of the temperature. ii) the susceptibilities of domains 2, 3 and 4 are constant with the temperature.

,oI/i. '°

,~60...--

. . . .

2

2o{ IIIZ22_...3 /, 3

'

4 i

|

3

5

107T( K )

-

11

4

10

:

= ,

,\

I

6. Assignement of the relaxations 61. Short-range charge transfer

In Na÷-xerogel, activation energies of the dcconductivity o(0) and the relaxation time Xl corresponding to domain I' have the same value W=0.48eV (cf.fig.8 and table I-a). The relaxation time 'tl is approximatively 108s at room temperature. These values are in good agreement with those corresponding to Na + jumps in the hydrates N a U P (W=0.43eV and x=10"8s,18]) and Na-vermiculite (W--0.44eV and "c=10-Ss, [15]). These results support the assignement of the relaxation of domain 1' to Na + jumps with characteristic time x=10-Ss. It is possible to explain it by the existence o f " bounced-back effect " [ 161 due to high repulsive coulombic interaction (see also [171) between Na + cations. This phenomenon is negligible in H30+-xerogel [7} because the coulombic interactions between H30 ÷ ions are lower than Na ÷ ions [8]. Otherwise, we can determine the diffusion coefficient of Na ÷ ions from our experimental data: DNa+ =

2\

o

Fig. 9. Temperature dependence of the susceptibility Ae corresponding to different domains.

12 2't

where I is the jump distance (1=3.6,~) and "~the jump time ('~=10-8s). At room temperature, DNa+= 5.7 x 10-8cm2.s "1. This value is in good agreement with the diffusion coefficient, D= 5 x 10-Scm2.s -1, obtained by pH measurements during ionic exchange [181.

7

62. Water reorientations

2

3

4

5 i0~'T

Fig. 8. Temperature dependence of relaxation frequency fp corresponding to different domains. Domain 1': Na ÷ jump. Domains 2 and 3: water reorientations. Domain4: intrasite motion of Na ÷ cation.

Generally, in V205 xerogels (Na +, H30 ÷) three types of motions may be considered: i) diffusion of Na ÷ and H30 + as discussed previously. ii) reorientation of the H30 ÷ dipolar ion as discussed in a previous paper (7). iii) reorientation of the water molecules 17]. We notice that the domains 2 and 3 of the two xerogels

148

J.C. Badot, N. Baffler / Rf-microwave dielectric relaxation

(cf.table I and [7]) are similar as far as activation energies and relaxation times are concerned. It seems thus reasonable to assign the relaxations 2 and 3 to stronglybonded water (low mobility or Y water) and weaklybonded water (high mobility or X water) respectively. Generally when the interaction of water molecules (dipoles) with their environment (V205 ribbons, counterions) is stronger, their rotational motion is slower and thus the relaxation time 17(i.e. 172,173) is higher. The increase of the relaxation times "t3 of X-water (173=4x10lls and 10-10s for H3 O t and Na ÷ xerogels respectively at T=295K) and 172 of Y-water ('t2=10-9s at T=295K) in comparison with the relaxation time of the free liquid water (cf.table I-b), can be explained by the "slowing-down" of the molecular motion due to the electrostatic field induced by the negatively charged ribbon and counter-ions Na t, H3 O÷. It is assumed that the activation energy for the reorientation of the free liquid water is connected to the breaking and reforming energy of H-bonds (W=0.2eV, cf.table I-b). Moreover, the activation energies relative to the reorientation of water molecules are stronger in the case of Nat-xerogel. This difference is probably due to the higher electrostatic field intensity induced by Na ÷ cations (electrostriction effect). The temperature independent dielectric su~eptibilities Ae corresponding to the domains 2 and 3 are characteristic of a strong dielectric saturation due to the existence of high ion-dipole interaction (Nat-H20) and of intensive local electric field. The same phenomenon has been observed also in NaUP 18]. On the otherhand, in the case of H3Ot-xerogel, Ae is proportional to T-I (no saturation effect). 63. Domain 4

We have defined previously two types of behaviours in Nat-xerogel: i) the jump of Na + cation from one site to the other (domain 1'). ii) the reorientation of X and Y water (domains 2 and 3). However we have experienced another type of behaviour (domain 4) characterized by a fast motion in microwave frequencies. Assuming that the Na t cation is localized in the center M of the square plane constitued by four water molecules (X-water) (cf.fig.2-b), the distance M-H20 equal to 2.5A is higher than the sum of Na t and H20 radii, i.e. 2A. Consequently the Na t cation is free to move inside the squa/'e. This motion would correspond to a fast motion described by the domain 4 whose characteristic time is "t4=10 -I Is. The distinctive feature of the behaviour lies in fact that the characteristic time x4 is constant for temperatures above T=220K. The first results of QNS would confirm that this type of motion is not due to protonic species [ 19]. This fact supports one part of our assumption on Na t motion because Na t and the protonic species are the only mobile species. No phase transition at 220K has been observed by thermal analysis which supports the dynamic nature for the transition from tunneling to activated state.

7. Conclusion With the dielectric relaxation study of Na+-xerogel Na0.33V205-1.6H20, we have demonstrated the influence of the ion exchange on electrical properties and mobility of water molecules. Three different types of motions have been identified: i) Nat jumps whose characteristic time is 10-8s. ii) Reorientation of water molecules whose characteristic times are 10-9-10-10s. iii) "Intrasite" motion of Na t whose characteristic time is 10-1Is. The comprehension and the confirmation of this later behaviour necessites complementary Na-NMR studies.

Acknowledgement The authors wish to thank Professor A.FOURRIERL A M E R (Laboratoire de Dispositifs lnfrarouges et Microondes,UA836-CNRS, Universit6 P. et M.Curie,Paris, France) for fruitful discussions and experimental facilities.

References [1] J.J. Legendre and J. Livage, J. Coll. Int. Sci. 94(1) (1983) 75. [2] P. Aldebert, N. Baffier, N. Gharbi and J, Livage, Mat. Res. Bull. 16 (1981) 669. [3] P. Barboux, Thesis, Paris VI (1987). 14] J.C. Badot, J.J. Bitemo and N. Baffler, to be published, [5] P. Barboux, N. Baffler, R. Morineau and J. Livage, Solid State lonics 9- I0 (1983) 1073. [61 P. Barboux, R. Morineau and J. Livage, Solid State Ionics,27 (1988) 211. [7] J.C. Badot, A. Fourrier-Lamer and N. Baffler, J. Physique 46 (1985) 2107. I81 J.C. Badot,A. Four'tier-Lamer, N, Baffier and P. Colomban, J. Physique 48 (1987) 1325. [91 J.C. Badot, A. Fourrier-Lamer, N. Baffier and P. Colomban, Solid State lonics 28-30 (1988) 1617. 1101 A. Bouhaouss, P. Aldebert, N. Baffler and J. Livage, Rev. Chim. Min. 22 (1985) 417. [111 L. Znai'di, Thesis, Paris VI (1989). [ 121 A. Hardy, J. Galy, A. Casalot and M. Pouchard, Bull. Soc. Chim. Fr. 4 (1965) 1056. [13] W.J. Getsinger, I.E.E.E. Trans. Microwave Theory Tech. M'I'I'-I4 (1966) 58. [ 141 H. Kolodziej and L. Sobzcyk, Acta Phys. Pol. A39 (1971) 59. [151 J. Hougardy, W.E.E. Stone and J.J. Fripiat, J. Chem. Phys. 64 (1976) 3840. [16] P.M. Richards, Phys. Rev. BI6 (1977) 1393. 1171 K. Funke, Solid State lonics 28-30 (1988) 1130. [ 18] L. Znaidi, D. Lemordant and N. Baffler, Solid State lonics 28-30 (1988) 1750. [ 191 C. Poinsignon, private communication.