STUDY OF THE MULTIPLICITY OF DIELECTRIC RELAXATION TIMES IN ICE AT LOW TEMPERATURES

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STUDY OF THE MULTIPLICITY OF DIELECTRIC RELAXATION TIMES IN ICE AT LOW

TEMPERATURES

L. Apekis, Polycarpos Pissis

To cite this version:

L. Apekis, Polycarpos Pissis. STUDY OF THE MULTIPLICITY OF DIELECTRIC RELAXATION

TIMES IN ICE AT LOW TEMPERATURES. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-

127-C1-133. �10.1051/jphyscol:1987119�. �jpa-00226263�

JOURNAL DE PHYSIQUE

Colloque C1, supplkment au no 3, Tome 48, m a r s 1 9 8 7

STUDY OF THE MULTIPLICITY OF DIELECTRIC RELAXATION TIMES IN I C E A T LOW TEMPERATURES

L. APEKIS and P. PISSIS

National Technical University of Athens, Physics Department, Zografou Campus, GR-157 73 Athens, Greece

R6se.-En utilisant les possibilitgs experimentales de la mgthodedes thermocourants de dgpolarisation (T.C.D.),on a montr5 que le pic de T.C.D. basse tempgrature de la glace polycristalline,dCi 5 la relaxation diglectrique dipolaire de la glace dans ce domaine de temp6rature,peut 8tre dicomposgen un pic secondaire I 108K,avec une Snergie d'activation W=0,24eV,un facteur prgexponentiel dans la relation d'Arrhenius

-4% de celle du pic entier et B un pic principal B 119K qui peut Stre attribug un mscanisme de relaxation caract6risg par une distribution con- tinue de temps de relaxation dillectrique dont les deux paramStres,l7gnergie d'acti- vation et le facteur prEexponentie1,sont distribuSs,avec des valeurs moyennes 0,31eV et 5,0x10-12s respectivement. On a aussi essay6 d'interprgter les rgsultats au ni- veau molCculaire.

Abstract.-By the use of several experimental

of thermally stimulated depolarization (TSD),it was demonstrated that the low tempera- ture TSD peak of polycrystalline ice Ih,which is due to the dipolar polarization me- chanism of ice in this temperature range,consists of a secondary component at 108K and a main peak at 119K. The characteristics of the secondary component are:activa- tion energy W=O.24eV,pre-exponential factor in the Arrhenius equation T O = ~ . ~ X . O - ~ S and dielectric strength -4% of the whole peak. The main peak can be described by a dielectric relaxation mechanism characterised by a continuous distribution of rela- xation times,with both W and To being distributed parameters,with mean values of 0.31eV and 5x10-12s respectively. An attempt has been made to interpret the results at the molecular level.

1. Introduction.- The study of the dielectric behaviour of ice by the AC method has shown the existence of a dipolar polarization mechanism which at the relatively high temperatures can be described by a single Debye-type dielectric relaxation mechanism

11-61 ,while at lower temperatures a departure from the single Debye-type mechanism is observed C7-111 ,the change in behaviour occurring at a temperature which depends on the quality of the crystal 112-161 . The dipolar polarization mechanism of ice is attributed to the orientational polarization of water dipoles in the ice crystal

a-163. The change in behaviour is attributed to the transition from one polariza- tion mechanismJnwhichthe changeoforientation of the water dipoles is effected through the motion by intramolecular jumps of intrinsic D and L (Bjerrum) defects, to another in which extrinsic D and L defects predominate 02-16]

The dipolar polarization mechanism of ice exhibits itself in Thermally Stimula- ted Depolarization (TSD) current measurements by the presence of a depolarization current peak in the plot of thermocurrent vs temperature,at about 120K,and is also attributed to orientational polarization of the water dipoles,which is effected through the motion of extrinsic orientational D and L defects [17-211 . ^{This cur-}

rent peak does not conform to the Debye depolarization mechanism r17-213 .

The multiplicity of the dielectric relaxation mechanism which is due to the re- orientation of water molecules was studied by Johari and Jones [17,221 and was attri- buted to three discrete mechanisms with slightly different dielectric relaxation

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987119

C1-128

JOURNAL DE PHYSIQUE

times. Pissis et al. L18] reported of strong indications that the TSD peak of ice may be better represented by a continuous distribution of relaxation times rather than by a sum of discrete relaxation processes.

In the present work,use was made of several experimental techniques offered by the TSD method,such as the variation of polarization conditions,partial heating and thermal sampling,which make possible the experimental resolution of a complex dielec- tric mechanism something which is not possible in measurements by the AC method rely- ing on computational techniques for this resolution. It was examined whether the low-temperature dielectric relaxation mechanism of polycrystalline ice Ih consists of a combination of a small number of discrete processes,or is characterized by a continuous distribution of relaxation times. Also studied were the characteristics of this relaxation mechanism and their changes,and an attempt was made to relate the- se results to the existing theoretical models for the dielectric behaviour of ice.

2. Experimental.- The TSD method may be briefly described as follows C23]: The sam- ple is polarized by an applied electric field Ep at a temperature Tp. This polariza- tion is subsequently frozen in by cooling the sample down to a temperature To suffi- ciently low to prevent depolarization by thermal energy. The field is then removed and the sample heated at a constant rate b while the depolarization current is dete- cted by an electrometer.

In the case of a single relaxation process having relaxation time given by the Arrhenius expression ~(T)=r,exp(W/kT),the depolarization

J(T)=

P, exp(-W/kT) exp exp(-w/~T')~T'

-

"

where W is the activation energy of the relaxation,To the pre-exponential factor,T the absolute temperature,k is Boltzmann's constant and Po the initial polarization.

Analysis of the shape of the

vs T curve makes it possible to obtain W , T ~ and the contribution AE-of a peak to the static permittivity [23,24] .

The polycrystalline ice samples,which were cylinders of approximately 8mm diame- ter and 0.5 to lmm height,were grown in the measuring capacitor. The water used was

Fig.1.- a:the low temperature TSD peak of Fig.2.- Enhancement of the secondary

b:thermal component by a suitable choice of pola- sampling responses of the TSD peak. The rizing conditions: T -98.5K,tp=2min, experimental conditions are given in the P-

Ep=9. 6kV/crn,b=3.7K/mln.

text.

doubly-distilled and deionized,with a DC conductivity of U=l

~-'cm-'. The apparatus used has been described elsewhere C251 . The measuring capacitor was made of brass. The measurements were performed in the temperature region of 77 to 150K.

3. Results.- In Fig.la the continuous line shows the TSD peak of ice,which is due to the dipolar polarization of the water molecules (polarization temperature T -135K, polarization time tp=imin,polarizing field Ep=8. 5kV/cm,heating rate b=2.~~/minPT The broken line shows the single Debye-type peak with peak temperature Tpl17.6K,W=0.23eV and- Eo=1.8 10-8s which was found by the least-squares method to have the best fit to the experimental peak.

By suitable choice of the polarization conditions,it is possible to show that there is a contribution to the main peak from a second TSD peak. In Fig.2,the low- temperature peak is the secondary peak and the main peak is at higher temperatures.

The characteristics of the secondary peak are:Tr108K,height -4% of that of the main

Fig.3.- Variation of TM,W,and %nTo of the thermal sampling responses,as functions of Different symbols correspond to different samples.

Fig.4.- Variation of EnTo as function of W. Different symbols correspond to different samples.

Fig.5.- W versus cut-off temperature

. ^{Tc in PH} experiments. Different sym-

bols correspond to different samples.

CI-130

peak,mean value of activation energy as calculated by the initial rise method C23-24 W=0.24eV,with corresponding pre-exponential factor t0=7. 4 10-9s.

The caracteristics of the main peak determined after the elimination of the se- condary peak using the thermal sampling technique [26-27J (with Tp=143K,depolariza- tion temperature Td=llOK t =lOmin,E =8.5kV/cm),were TM=117K,W=0.24eV and to=5.6 10-~s

'.P P

by least-squares curve -fitting and W=0.30eV and To=lxl~-lls by the initial-rise me- thod. In other words,the values obtained by curve-fitting were only slightly affe- cted by the elimination of the secondry peak,while there were drastic changes in tho- se obtained by the initial rise method. We consider the initial rise values to be more representative of the real peak parameters as we have found that in multiple peaks the curve-fitting values (which represent the depolarization mechanism as a whole,giving little weight to the weaker components at the rising or falling tails of the peak) are systematically lower than the actua1,while the initial rise method

(which takes into account mainly the faster components of the distribution) gives va- lues which are nearer to the actual values. In what follows,the W values given were determined by the initial rise method.

In order to investigate the multiplicity of the main TSD peak of ice,use was made of the techniques of varying the polarization temperature Tp(i8] ,of thermal sampling [26J and of partial heating [29] .

For a multiple peak consisting of discrete components,the change of polarization temperature will cause a shift of the peak maximum and a noticeable change in the

Tp

133

100K,TM

120

117K with the shape of the peak remaining practically unchanged apart from the relative enhancement of the secondary peak mentioned above.

The thermal sampling technique (~~),[26,27] ,consists of "sampling" the relaxa- tion process within a narrow temperature range by means of polarization at Tp,follow- ed by depolarization at Td,a few degrees K below Tp,in order to isolate some of the relaxation components. By this method,the main (complex) TSD peak of ice has been analysed into simpler components,(Fig.lb). The thermal sampling conditions were usually as follows:cooling rate of 3K/min and application of the field for about 40 sec,polarization window Tp-Td=2K. The polarization temperature was varied in steps of 3K. Thermal sampling analysis resulted in the resolution of the complex peak into components which are not single Debye-type peaks. Shown in Fig.3a,b and c are the peak temperature TM,the activation energy W and Entoof the thermal sampling respon- ses,as functions of the polarization temperature Tp. In Fig.3a a~ld b the strong in- fluence of the secondary peak is evident for points with Tp<108K. It follows that TM varies continuously with Tp(Fig.3a). W increases continuously with Tp(Fig.3b), with a mean value of 0.31 eV. In addition,RnTo,as calculated from TM and W C231 ,de-

creases with increasing Tp (Fig.3~) ,with a mean value of T0=5 10-12s. The values of W and To obtained by TS analysis are strongly correlated,as shown in Fig.4,with a li- near correlation coefficient between EnTo and W of 0.98.

In the partial heating technique (PH),the sample,after being polarized as usual, was then partially depolarized by partial heatings (separated by rapid cooling) up

to a series of temperatures that spanned the whole temperature range of the TSD peak [29] . ^{The PH} analysis of the low temperature TSD peak of ice does not indicate the presence of discrete components,apart from the secondary component mentioned above.

The activation energy W increases continuously with increasing "cut-off" temperature Tc at which each cycle of depolarization of the sample is terminated (Fig.5). The values of W corresponding to the three points of Fig.5 for Tc<108K are due to the secondary peak and the sudden jump in W observed at about 108K is due to the fact that for Tc>108K the contribution of the secondary peak is negligible.

4. Discussion.- As we have shown in previous studies [18-211,the low temperature peak in TSD measurements on ice (Fig.la solid line) is due to the reorientation of water molecule dipoles in the ice crysta1,an observation which is in agreement with those of other researchers [17] and corresponds to the mechanism of dipolar polariza- tion of ice given by AC measurements in the same temperature range [9-11,161 .

Attempts to fit a single Debye-type peak. (Fig.la,broken line) to the low tempe- rature TSD peak of ice (Fig.la-solid line) by least-squares fitting,indicates that the mechanism causing this peak is not of the simple Debye type,a result which agre- es with those of other researchers c9-221 .

The TSD techniques of varying Tp,of thermal sampling and of partial heating are

complementary to each other in the study of multiple peaks. In varying the

polarization temperature Tp we enhance each time different components of a complex mechanism,in thermal sampl~ng analysis we select each time different groups of com- ponents (with neighbouring relaxation times),while in partial heating analysis we isolate in each cycle the faster components of the complex mechanism (i.e.those with smaller relaxation tines). The results of the study of ice using these three techni- ques of analysis constitute very strong indications that the main TSD peak does not consist of discrete components,but should be attributed to a mechanism of dielectric relaxation characterized by a continuous distribution of relaxation times. This re- sult is in agreement with previous results reported by one of the authors [18] but disagrees with the resolution into two distinct mechanisms by JOHARI and JONES[S~,Z~~.

As shown in Fig.3b,the activation energy W of the thermal sampling responses varies continuously between 0.29 and 0.37eV. Values of W obtained by partial heat-- ing analysis vary practically within the same limits. The pre-exponential factor

in the Arrhenius equation is computed indirectly for each component peak of TS ana- lysis from the corresponding TM and W values. The variation of To shown in Fig.3~

is such that leads to a linear relation between LnTo and W,as shown in Fig.4,having a correlation coefficient of 0.98. These results for W and To given by TS analysis constitute a very strong indication of the presence of a dielectric relaxation mecha- nism which is characterised by continuous distributions of both W and To.

The relation between LnTo and W shown in Fig.4,for which some researchers use the term 'compensation effectl,should be attributed to the fact that the continuous distribution which constitutes the mechanism of dipolar polarization of ice in the low temperature region is very narrow. This view is reinforced not only by the nar- row range of variation of TM,W and LnTo of TS analysis (Fig.3a,b,c) and of W from PH analysis (Fig.5),but also by the smallness of the temperature shift of the compo- site peak (TM from 120 to 117K) that was caused by the variation of the polarization temperature Tp. The overall behaviour could be explained by a distribution of rela- xation times corresponding to

narrow distribution of W about the value of 0.31eV and of To about 5 10-~'s. The combined effect of these is a relatively narrow com- posite TSD peak with T ~ 1 1 9 K and a strong correlation between W and RnTo.

If the activation energies W of the thermal sampling responses are determined by curve-fitting,the variations of the characteristic parameters of the polarization mechanism as functions of T are of the same form as those shown in Fig.3a,b, and c, with mean values of ~=0.28ef and to=lxlO-lOs. In addition,although the values of W from initial rise measurements are nearer to the actual values,they must be conside- red as lower than these,since both the thermal sampling responses and the partial heating components are only approximately of the Debye-type. Consequently,foracor- rect comparison of activation energy values with others reported in the literature, it is essential that the method used for their determination be known,since the pre- sence of the secondary peak affects strongly the values obtained by the initial ri- se method,while the least-squares fitting method and its equivalent whole-curve me- thod based on the plot of Ln(P/J) vs 1/T r231 ,give consistently lower values for w.

Reported values from AC measurements in the low temperature region are for monocry- .talline ice 0.28eV 191 and 0.235e3 r10,lll and for polycrystalline ice 0.34eV [13-151

and 0.45eV C163 .

The values of activation energy W and peak temperature TM and consequently of the relaxation time,as well as of the contribution of the peak to the static permit- tivity,Ac=174 [i~l,allows us to attribute the main TSD peak of ice to the reorienta- tion of the water molecule dipoles through the motion of extrinsic D and L defects, in agreement with Hippel et al. C13-ld,spectrum 3 for polycrystal . Sources of D and

defects are mainly the physical defects of the crystal El91 . The experimen- tal evidence that the dielectric relaxation mechanism in both monocrystalline and polycrystalline ice is of the single Debye type at relatively high temperatures whe- re intrinsic D and L defects predominate,allows us to correlate the multiplicity with the dominance of the extrinsic defects in the polarization mechanism of ice.

The values of W are found to be higher than the activation energy for ordinary motion of D and L defects in the ice crysta1,0.235eV@],0.28e~[30]. The higher values of energy may mean motion hampered by the physical defects of the crysta1,or contribu- tion in the production of D and L defects by the physical defectsr161. However,in dispersions of ice microcrystals,where owing to supercooling there are available high concentrations of physical defects,higher values of W occur (0.33-0.40eV by TSD

E311 and 0.5eV by AC measurements 1321) than those of macroscopic polycrystalline

ice. This difference disappears after thermal annealing of the samples (which lowers

C1-132 JOURNAL

DE PHYSIQUE

the concentration of physical defects) [31] . It appears therefore that we should ra- ther attribute the higher W value to the fact that the motion of D and L defects is made more difficult than ordinary motion by the presence of physical defects in the crystal. The continuous nature of the distributions of W and ro (and therefore of relaxation times) may be attributed to the great variety of configurations ofthecom- plexes formed by the normal water molecules and the physical defects. According to this interpretation the mean values (and widths) of the continuous distributions of W and -co should depend on the quality of the crystal. This is compatible with the fact that in the low temperature region activation energies were reported from measu- rements on monocrystalline ice (with low concentration of physical defects)of0.235eV [lo, 112 and 0.28eV C 93,which are lower that those for polycrystalline ice,of 0.34eV C13-153,0.45eV C16J and 0.31eV of the present work. It is also compatible with the high values of W from measurements on dispersions of ice microcrystals mentioned abo- ve,where the high concentrations of physical defects in the microcrystals result in high concentrations of extrinsic D and L defects,something which is also verified

(within the framework of the Jaccard model C4J) by the values of

for dispersions of ice microcrystals which are lower than those for macroscopic ice [31] .

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COMMENTS

V.F.

Which theory do you use for comparison of experimental data and calculated curves of

Answer

We extended Jaccard's theory to non isothermal TSD measurements at low temperature .

Then I have a comment

In the use of TSD, electrical field strength is very small and the main moving force for charge carriers is configurational vector . ^{But is}

not considered in a classical theory of TSD

Answer

We are going to have a look at the theory that you just presented.

L. Apekis et al. Nuovo Cimento,