Lowfrequency ac conduction and dielectric relaxation in vinyl chloride:vinylacetate copolymersRamadhar Singh, V. S. Panwar, R. P. Tandon, N. P. Gupta, and Subhas Chandra Citation: Journal of Applied Physics 72, 3410 (1992); doi: 10.1063/1.351413 View online: http://dx.doi.org/10.1063/1.351413 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/72/8?ver=pdfcov Published by the AIP Publishing

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

Low-frequency ac conduction and- dielectric relaxation in vinyl chioride:vinyl acetate copolymers

Ramadhar Singh, V. S. Panwar, R. P. Tandon, N. P. Gupta,‘) and Subhas Chandra National Physical Laboratory, Dr. K. S Krishnan Road, New Delhi 110012, India I _ (Received 4 March 1992; accepted for publication 15 June 1992)

ac conductivity a(o), dielectric constant E’, and loss E” of vinyl chloride:vinyl acetate, (VC:VAc) copolymers having 3%, lo%, and 17% VAc content (by weight) have been measured in the- temperature range 77-410 K and in the frequency range 50 Hz-100 kHz. 4t low temperatures up to 250 K, the ac conductivity can be expressed by a(w) =Ad, where the slope s is close to unity and its value decreases with the increase in temperature. The dielectric constant in this temperature region shows a very weak frequency and temperature dependence. At temperatures above *300 IS, the ac conductivity shows a strong temperature dependence; however, in this temperature region the dielectric constant shows a strong frequency dispersion. The measured dielectric loss as a function of temperature reveals the &, the & and the a relaxations. The & relaxation is associated with the movement of the more flexible side group dipoles and the & relaxation is due to the movement of rigidly attached side group dipol~es; whereas the a relaxation is attributed to the segmental motion of the main chain of the copolymer. Both the latter relaxations seem to be long range in nature with distribution of relaxation times associated with the cooperative motion. The mechanism of conduction in the low- and high-temperature regions have been discussed in light of existing theoretical models.

1. INTRODUCTION The molecular mechanism responsible for the relax-

ations in polymers continues to be a subject of great inter- est. The emergence of amorphous polymers in recent years with their practical importance has given a great stimulus to the studies of their electrical properties. There have been a large number of studieslm5 concerning the long chain lin- ear polymers but the interpretation of their relaxational behavior remains uncertain. Studies of electrical and di- electric properties of polymers having a small or a large number of polar groups in the same monomer unit have been made earlier.5-‘0 The analysis of dielectric constant E’ and loss en as a function of frequency and temperature has revealed two types of relaxation processes,8 termed a and fi relaxations, above and below the glass transition tempera- ture Tg respectively. The a and the 0 relaxations have been observed in polyvinyl alcohol (PVA),8 polyvinyl chloride (PVC) ,8,9 polyvinyl acetate (PVAc),’ the copol- ymer of vinyl chloride and vinyl acetate (VC:VAc),” and the terpolymer of vinyl chloride, vinyl acetate, and vinyl alcohol (VC:VAc:VA) .‘>14 However, no detailed studies of the dielectric relaxation and ac conduction of VC:VAc copolymers have been reported in the literature so far. As such we have studied the dielectric behavior of VC:VAc copolymers having 3%, lo%, and 17% VAc content in the frequency range 50 Hz-100 kHz and in the temperature range 77-410 K, and the results of these studies are re- ported in the present-paper.

II. EXPERlMENT The VC:VAc copolymers having 3%, lo%, and 17%

VAc content (by weight) and designated here as P 1, P2,

‘IPermanent address: Department of Physics, J. V. Jain College, Sahar- anpur 247 00 1, India.

and P3 were obtained from M/s. Polysciences, U.S.A. Films of Pl, P2, and P3 having a thickness of - 100 ,um were prepared by the solution evaporation technique de- scribed earlier.15 The films were kept in vacuum. ( 10B5 Torr) for 48 h prior to deposition of electrodes. Silver electrodes were vacuum deposited on both sides of these samples thus making an Ag-P-Ag structure. After the dep- osition of electrodes these samples were transferred to a specially designed three-terminal cell which included a de- hydrant (fused calcium chloride 9 to minimize the absorp- tion of water by the samples during the course of measure- ment. The dielectric measurements were made by using a GR 1615-A capacitance bridge in the frequency range 50 Hz-100 kHz and in the temperature range 77-410 K. The temperature of the cell was measured with an accuracy of f 0.1 K with a Keithley 150B microvoltammeter by using a copper constantan thermocouple. The dc conductivity was measured by asing a Keithley 610C electrometer.

III. RESULTS

As a representative result, the measured ac conductiv- ity a( o 9 ,,, and the dielectric constant E’ (09 of the copol- ymer Pl as a function of temperature in the range 77-410 K at four fixed frequencies 0.1, 1, 10, and 100 kHz are shown in Figs. 1 and 2, respectively. Similar results have been obtained for P2 and P3. For a good electrode, l6 E’ (w ) shows a peak when it is measured as a function of temper- ature. The possibility of a large barrier width, giving rise to a small surface capacitance and a reasonable dielectric con- stant value cannot be completely ruled out.17 It is evident from Fig. 2 that E’(W) shows a saturation region and then a decrease with increasing temperature; however, after that it increases suddenly with increasing temperature. The in- crease in E’(W) after the saturation region will be ignored

3410 J. Appl. Phys. 72 (8), 15 October 1992 0021-8979/92/20341 O-07504.00 @ 1992 American Institute of Physics 3410

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

6 7 0 77K

I4 I I I I

0 2 4 6 8 IO I2 14

103/T (K-l)

FIG. 1.. Total measured conductivity a(o), of copolymer Pl as a func- tion of reciprocal temperature for four fixed frequencies.

in further discussion since it may be due to electrode po- larization or ionic conduction14 and does not necessarily represent the true bulk property of the material as has been discussed earlier.16 A decrease of static dielectric constant with increasing temperature clearly indicates that the mea- sured value of E’(W) represents the true bulk phenomenon and the electrode polarization or other spurious effects have a negligible effect. It is seen from Fig. 1 that at low temperatures the measured ac conductivity a(o), is con- siderably higher than the dc conductivity od, and increases with increasing frequency; however, it shows a very weak dependence on temperature in the low-temperature region.

15

IO

"3 w

5

0 0.1 KHz l I KHz

A IO KHz

A 100KHz

01 I I I

50 150 250 350 450

TEMPERATURE(K)

FIG. 2. Variation of dielectric constant with temperature for four fixed frequencies of copolymer PI.

8-

TE o 9-

is

,E $ IO-

8 J 1 II-

I 2 3

Logf (Hz)

4 5 6

l?IG. 3. Variation of total measured conductivity ~(0)~ as a function of frequency at different fixed temperatures for copolymer Pl.

At high temperatures, a(o), becomes equal to cd, and the temperature at which the a(w), becomes equal to od, in- creases with increasing frequency.

The behavior of the variation of E’(W) with tempera- ture is similar for all the frequencies. At low temperatures, E’ (w ) shows little dependence on temperature; however, at higher temperature E’(W) shows a strong temperature de- pendence and increases rapidly with increasing tempera- ture at a given frequency. This rapid increase is followed by a slow decrease, thus giving a peak. The temperature at which the rapid increase in E’(W) starts with temperature and a peak in E’ (0) is observed increases with increasing frequency, and the peak value of E’(O) is lower for higher frequencies (Fig. 2).

Figure 3 shows the variation of a( w ) m as a function of frequency in the range 100 Hz-100 kHz at five different temperatures, namely 77, 125, 250, 300, and 330 K for copolymer Pl. Similar results were obtained for P2 and P3. It is observed that the value of slope s at 77 K is -0.94- 0.95 which is independent of temperature up to 250 K for all the copolymers and beyond this it decreases with in- creasing temperatures. It may be noted that at 77 K, the conductivity shows an increase with increasing frequency and this trend is noticed even at 330 K. As a representative result the variation of E”(W) with temperature for the four fixed frequencies in the range 77-410 K for copolymer Pl is shown in Fig. 4. It is evident from this figure that the higher-temperature side of the (r relaxation is masked by the dc conductivity and its magnitude decreases with in- creasing frequencies. The /3t and the /3z relaxations (smaller in magnitude) appear as kinks in the lower- temperature side of the spectrum around 150 and 225 K. Figure 5 shows the variation of E”(W) as a function of temperature indicating the pt. and the pZ relaxations men- tioned above on a magnified scale. The activation energies for these relaxations have been evaluated by the Fuoss ap- proach,’ in which a variable x is defined as

3411 J. Appl. Phys., Vol. 72, No. 8, 15 October 1992 Singh et al. 3411 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

2.5 0 0.1 KHz

2.0

I.5

zi = 1.0 w

0. 5

0.0 i

. I KHz h IO KHz I IOOKHz

100 150 200 250 300 350 400

TEMPERATURE (K)

FIG. 4. Variation of dielectric loss as a function of temperature for four fixed frequencies for copolymer Pl.

x=[l+(l-K2)1’2]/K, (1)

where K = E”/E:,,. A plot of log x vs l/T gives a straight line given by the empirical relation

Iogx=a+b/T, (2)

where a is the intercept of the straight line on the x axis and b is the slope which gives the energy of activation U as

U=bk (eV>,

where k is the Boltzmann constant.

(3)

The activation energy has been evaluated from the slopes of log x vs l/T curves and are summarized in Table I. The plot of log x vs l/T is shown for only the a relax- ation of copolymer Pl in Fig. 6. These observed values of activation energies are in good agreement with the values reported earlier.8 The E’(O) and E”(O) as a function of frequency in the range 50 Hz-100 kHz at 340 K are given for Pl, P2, and P3 in Figs. 7 and 8, respectively.

0 0.1 KHz . I KHz

8 h IO KHz A IOOKHz

0 100 150 200 250 300 350

TEMPERATURE (K)

FIG. 5. Variation of dielectric loss as a function of temperature for four tixed frequencies for copolymer Pl.

TABLE I. Activation energy U for different relaxations of copolymers PI, P2, and P3 calculated by the Fuoss approach.

Activation energy U (eV)

Samples 8, relaxation & relaxation a relaxation

Pl 0.36 0.72 1.02 P2 0.32 0.70 0.96 P3 0.30 0.68 0.94

IV. DISCUSSION

A. Low-temperature region where &&,$w~~

The ac conductivity U(O) at low temperature is fre quency dependent and can be expressed as18

a( w ) =Aw: (4)

where s (0.7 <s < 1) is independent of frequency. The value of conductivity at 100 Hz and 100 kHz and the values of slope s for different temperatures are reported in Table II. At 77 K where (T(w),su~~ the variation of a(w), with frequency can be expressed in terms of Eq. (4), where the values of parameters is -0.94-0.95 for Pl, P2, and P3 and is independent of temperature up to 250 K, however, beyond this temperature region it decreases with increasing temperatures. The activation energy of the car- riers calculated at 77 K for the copolymers are given in Table II which indicates the evidence of electronic hopping conduction” in these materials at low temperature.

The number of pair centers responsible for ac conduc- tivity can be estimated from Pollak and Geballe,20 which can be expressed for the frequency range 100 Hz to 100 kHz in the following form:

o - 0.1 KHz l - I KHz n- IO KHz q - IOOKHz

2.0

1.5

G 1.0 4

0.5

0.C I I

2.7 2.8 2.9 3.0 3.1 3.2 103/T (K-l)

FIG. 6. Plot of log x vs l/T for copolymer Pl for a relaxation.

3412 J. Appl. Phys., Vol. 72, No. 8, 15 October 1992 Singh et al. 3412

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

25 , 5

20

15

3 -w IO

5

I 2 3 4 5 6 I 2 3 4 5 6

Logf (Hz) Log f (Hz)

FIG. 7. Variation of dielectric constant as a function of frequency at 340 FIG. 8. Variation of dielectric loss as a function of frequency at 340 K, K, for Pl, P2, and P3. for Pl, P2, and P3.

dw) =iFJj kT a “ivAN$(;)r( 1-i)

11 5 x (OTW-’ a-’ .

( 1 (5)

The average valueZ1 of 7 in the frequency range 100 Hz- 100 kHz has been taken and a value of a-l as 4 8, with the known value of slope s and the measured value of a( o ) m at 77 K and at 100 kHz can be used to calculate NAND from Eq. (5). The estimated value of NY (NAND) 1’2 is of the order of 1 X 10” cmm3 indicating a large number of donor and acceptor levels. The estimated value of iVJVD seems to be reasonable and in good, agreement with the estimated values reported by several workers for amorphous semi- conductors.‘*

An estimate of the density of states near the Fermi level N(Ef) can be made from the measured ac conduc- tivity at low temperatures where hopping near the Fermi level is expected to dominate. The equation suggested by Pollak22S23 is similar to that proposed by Austin and Mott24 but differs in the values of the constant. According to,Aus- tin and Mott,24

~(~)=frre~kT[N(E~)]~a-‘w[ln(l/ph/W)14. (6) The values of N(Ef) calculated from Eq. (6) assuming Itph”1012 Hz and (r--l as 4 8, and using the measured

values of ac conductivity a(w), at 100 kHz, are also re- ported in Table II. The estimated values of N(Ef) are of the order of 1021 cmm3 eV-’ depending on the choice of the numerical values of a-’ in Eq. (6). The reasonable estimate of N(Ef) from Eq. (6) suggests that hopping near the Fermi level is between the nearest-neighbor sites. In spite of the fact that Eq. (6) gives reasonable estimate of iV(E’), it fails to explain the temperature dependence of a(w). Equation (6) predicts a linear temperature depen- dence of a(w), however, the measured values show very weak temperature dependence of a(w) in the low- temperature region while E!q. (5) predicts a very weak temperature dependence of a(w) which is in good agree- ment with the observed behavior: Pollak22,23 has argued that the temperature dependence is due to multiple hops but Mansingh, Tandon, and Vaid25 have shown that mul- tiple hops cannot give strong temperature dependence of a(w) as observed in V205-P205 glasses.

B. Temperature region where a(w), approaches ad,

The measurement of total measured ac conductivity a(w), as a function of temperature (Fig. 1) shows that the temperature at which the dc conductivity ad, becomes equal to (T(O), for a given frequency increases with in- creasing frequency . The dc conductivity shows an expo- nential dependence on temperature while the ac conduc-

TABLE II. The value of slope s, activation energy U at 77 K, total measured conductivity u(o),, and density of states iV(EJ for copolymers Pl, P2, and P3.

Samples 77

Value of slope s at different temperatures (K)

125 250 300 330

a(o), (lo-” Cl-’ cm-‘)

at 100 Hz and at 77 K

U(~), ( 10m9 W’ cm-‘) at lOC,kHz and

at 77 K NW/)

(10” cmM3 eV-‘)

Pl 0.95 0.95 0.95 0.86 0.80 0.012 1.38 1.04 1.03 P2 0.94 0.94 0.94 0.85 0.80 0.011 1.44 1.00, 2.14 P3 0.94 0.94 0.94 0.90 0.70 0.011 3.81 2.51 4.08

3413 J. Appl. Phys., Vol. 72, No. 8, 15 October 1992 Singh et al. 3413 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

tivity shows comparatively weak dependence on temperature. Hence, at some temperatures, the measured ac conductivity o(o), for a given frequency and the dc conductivity od, will appear equal because the dc conduc- tivity may be very much larger than a(o) and so a(o), would appear equal to ad, within the accuracy of measure- ment.” A similar argument will hold good for the varia- tion of conductivity as a function of frequency at fixed temperatures. Thus, en (0) can be derived from the follow- ing relation: L.

E”(W) = (+(@),--ucj, da> =- 40 40 ’

(7)

which may be real or due to the different temperature de- pendencies of ac and dc conductivities.25 In the low- temperature region, carrier hopping occurs within a system in which a characteristic relaxation frequency f. is difficult to define; however, at high temperatures, where (TV approaches o,+, the ac component of conductivity c(w) may show clear evidence for f,-,. In particular, E”(W) de- rived from Pq. (7) may show a Debye-type peak at f =fw A difficulty in this approach is that both a(.&), and cd, are comparable and the error in a(w) is-large.” It is therefore necessary to examine both E’(W) and E”(W) to justify an analysis in terms of Debye-type dispersion.

1.5 2 2.5 3

103/ T ( K-‘1

FIG. 9. Variation of static dielectric constant as a function of reciprocal temperature for Pl, P2, and P3.

The dielectric constant e’(w) for a Debye-type disper- sion is -given as .

E’(W) -Em 1

E0-ECO =l+(f/foy’ .: (8)

where e. and E, are the static and the infinite frequency dielectric constants, f is the measuring frequency, and f. is the relaxation frequency at which a peak in E”(W) is ob- served. It is seen from Fig. 2 that in the low-temperature region the change in E’(O) with temperature is negligible and then it has a sharp rise at the temperature at which f=fo; IfJbfo, the measured value of E’(O) represents coo and if f eo, the measured value of E)‘(W) represents the value of Q. It can be observed that a strong temperature dependence starts at higher temperatures for higher fre- quencies or at lower temperatures for lower frequencies indicating thereby that f. increases ‘with the increase in temperature. It is seen that the region where there is a strong~ temperature dependence of E’(W) at a given fre- quency (Fig. 2) is the same at which a(w), approaches a,, (Fig. 1). Thus the variation of E’(O) with temperature confirms the existence of Debygtype loss peaks indicated in Fig. 1. The measured values of E’ (0) at a given fre- quency will give an estimate of e. at temperatures higher than the temperature region where E’(W) shows a strong temperature dependence. The measured values of E’ (0) at 0.1, I, 10, and 100 kHz clearly show a saturation region at the higher-temperature end and this may be.taken as an estimate of e& The increase in E’ (w > beyond this saturation region (Fig. 2) may be due to the electrode polarization or ionic conduction. l4

Debye-type dispersion and suggests that ‘the loss peaks de- picted in Fig. l,.are real. The existence of well-defined loss peaks has also been observed in silicate glasses26-28 and amorphous films&of Moo3 (Ref. 29) and WOs.30 The vari- ation of E’(W) with frequency (Fig. 7) is also consistent with a Debye-type dispersion.

A plot of log a(w) vs log f at a fixed temperature of 340 K,. where a(w), is close-to o& at low frequencies, is shown in Fig. 10 for Pl, P2, and P3. It may be noted that

.--i 7 P3

P2 PI

‘. ?; g s -I I

I6 :2 -.

II 1 I I I I 2 3 4 5 6

Logf (Hz)

It is also evident from Fig. 9 that e. decreases with the increase in temperature. .Figure-2. is consistent with the

RG. 10. Variation of ac conductivity o(o) as a function of frequency at 340 K for Pl, P2, and P3.

P3

3414 J. Appl. Phys., Vol. 72, No. 8, 15 October 1992 Singh et al. 3414

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

a change in slope occurs at a fixed frequency, which cor- responds to the relaxation frequency fw For an asymmetric distribution a slope of 2 below f. and a nonzero slope above f. is expected. This suggests that there is a distribu- tion of relaxation times. This is very much consistent with the observed data. The evaluation off0 from conductivity measurements becomes difficult especially where the mea- surements have been made as a function of temperature. However, the distribution of relaxation times appears to be asymmetric. The alternative method to determine f. from the measured E’ (0) as a function of temperature (Fig. 2) seems to be unrealistic; however, it does not have ambigu- ity caused by the closeness of (T(W) m and o& (Fig. 1). It can be seen from Eq. (8) that the temperature at which [E’(O) --E,] at a given frequency is equal to (eO-em)/2, the measuring frequency becomes equal to the relaxation frequency. The relaxation frequency f. can be represented by the relation f. = f ie- U’kT, where f. is a constant having dimensions of frequency and U is the activation energy.

The above discussions show that the well-defined di- electric loss peaks are observed in the temperature region where measured ac conductivity a(w), approaches the dc conductivity o&. The static dielectric constant e. can be determined from the measured frequency variation of E’ (0) or the temperature variation of E’(W) at fixed fre- quencies. The relaxation frequency f. can also be estimated from the measured dielectric constant E’ (w ) as a function of temperature or frequency. The estimated value of e. can at best be accurate within 10%.

It has already been observed’ that the development of the crystalline part makes the structure of the amorphous part more complicated and the curve of the distribution of relaxation become broader. If this assumption is true then in these copolymers with an increase31 in the ratio of amor- phousity to crystallinity from Pl to P3 the loss peaks shift to the higher-frequency side. This is very much consistent with the observations (Fig. 8).

It is evident from Fig. 7 that the dielectric constant E’(W) increases with the increase in VAc content, and it is at minimum in the copolymer Pl and maximum in the copolymer P3. The temperature of 340 K falls in the glass transition region where the materials perhaps turn into a rubbery state and in which the side group dipoles, whether rigidly or flexibly attached to the main chain of the copol- ymer, contribute to the polarization. Further, when VAc content increases the polar character of the materials in- creases due to the addition of strong polar groups, so the atomic polarizability increases and the effective field in the material medium reduces, which renders an increase in the dielectric constant. Studies of E’(O) as a function of fre- quency indicate that the dipoles in the materials P2 or P3 respond more than that in the case of Pl to the external alternating dielectric stress of varying frequency at a par- ticular temperature.

C. Relaxation in copolymers

The observed activation energies are attributed to the molecular motion involving the main chain or the large

segments of the main chain’ and is of the same order as has beeen reported earlier.8132 The loss peaks are very broad, and in conventional bridge measurements, the distribution of the relaxation is contemplated by its width on the fre- quency scale. Therefore, the marked broadness of the peak (Figs. 5 -and 8) is understood to be a consequence of the superposition of the multirelaxations and can be explained as follows. The polymer chain possesses a variety of inter- nal Brownian motion in which segments of the main chain diffuse from one relative configuration, to another with changing .dipole moments. Each segment of the chain should correspond to a characteristic relaxation time, when a reference polar group rotates or oscillates perpen- dicular to the chain axis, the motion induces the successive rotation or oscillation of the neighboring polar groups like the propogation of the waves, which indicates that the chain motion involved in the loss mechanism in this copol- ymer is apparently long range in nature and as such the mechanism of distribution of relaxation can be associated with a cooperative mechanism which exists in the relax- ation process of the copolymer chain having multiple/ different types of polar groups.

V. CONCLUSION

The ac conductivity in the low-temperature region can be described by o(w) =Ad, where s is close to unity, which decreases with the increase in temperature. The ac- tivation energy of the carriers at 77 K indicates the evi- dence of electronic hopping conduction at low tempera- tures. Three relaxations have been observed having activation energies (i) -0.36-0.30 eV for & relaxation; (ii) w-0.72-0.68 eV for & relaxation; and (iii) - 1.02-0.94 eV for a relaxation. The & relaxation is associated with the movement of flexible side group dipoles whereas the p2 relaxation with the rigidly attached side group dipoles and the a relaxation is due to the segmental motion of the main chain of the copolymer. Both the latter relaxations seem to be long range in nature with the distribution of relaxation times associated with the cooperative interaction.

ACKNOWLEDGMENTS

The authors are grateful to the Director, National Physical Laboratory, New Delhi, India for his interest in this work.

‘R. M. Fuoss, J. Am. Chem. Sot. 63, 369 (1941). *D. J. Mead and R. M. Fuoss, J. Am. Chem. Sot. 63, 2832 (1941). 3K. Yamafuji, J. Phys. Sot. Jpn. 15, 2295 (1960). 4K. Yamafuji and Y. Ishida, Kolloid 2. 175, 27 ( 1960). 5Y%hida, Kolloid Z. 168, 29 (1960). 6Y. Ishida, M. Matsuo, and K. Yamafuji, Kolloid Z. 180, 108 (1962). ‘Y. Ishida, J. Polym. Sci. Polym. Phys. Pd., Part A-2 7, 1835 (1969). ‘N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric

Effects in Polymeric Solids (Wiley, London, 1967). ‘A. C. Rastogi and K. L. Chopra, Thin Solid Films 27, 311 ( 1975).

‘OS. Saito, H. Sasabe and T. Nakajima, J. Polym. Sci. Polym. Phys. Ed. 6, 1297 (1968).

“P C Mehendru, N. P. Gupta, and S. Chand, J. Macromol. Sci. Phys. . . B 20, 571 (1981).

‘*P. C. Mehendru, R. Singh, V. S. Panwar, and N. P. Gupta, J. Phys. D 17, L61 (1984).

3415 J. Appl. Phys., Vol. 72, No. 8, 15 October 1992 Singh et al. 3415 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57

“P. C. Mehendru, R. Singh, V. S. Panwar, and N. P. Gupta, Thin Solid Films 120, L83 (1984).

t4P. C. Mehendru, R. Singh, V. S. Panwar, and N. P. Gupta, IEEE Trans. Electr. Insul. EI-21, 297 (1986).

‘sR Singh V. S. Panwar, P. C. Mehendru, and N. P. Gupta, J. Mater. si L&t.’ 9, 932 ( 1990).

t6R Singh, R. P. Tandon, V. S. Panwar, and S. Chandra, J. Appl. Phys. 6;,2504 (1991).

“J G. Simmons, G. S. Nadkami, and M. C. Lancaster, J. Appl. Phys. 41, 538 (1970).

‘*N. F. Mott and E. A. Davis, Electronic Processes in Non-Ctystalline Materials (Oxford University Press, London, 1971).

t9A. K. Jonscher, Thin Solid Films 1, 213 (1967). “M. Pollak and T. H. Geballe, Phys. Rev. 122, 1742 (1961). “A. Mansingh, J. K. Vaid, and R. P. Tandon, J. Phys. C 8, 1023 (1975). 22M. Pollak, Phys. Rev. 133, A564 (1964).

23M. Pollak, Philos. Mag. 23, 519 (1971). “I. G. Austin and N. F. Mott, Adv. Phys. 18, 41 (1969). *‘A Mansingh, R. P. Tandon, and J. K. Vaid, J. Phys. Chem. Solids 36,

l267 (1975). 26R. J. Charles, J. Appl. Phys. 32, 1115 (1961). 27B. S. Rawal and R. K. MacCrone, J. Non-Cryst. Solids 28, 347 (1978). **R. A. Anderson and R. K. MacCrone, J. Non-Cryst. Solids 14, 112

(1974). 29M. Sayer, A. Mansingh, J. B. Webb, and J. Noad, J. Phys. C 11, 3 15

(1978). 30A. Mansingh, M. Sayer, and J. B. Webb, J. Non-Cryst. Solids 28, 123

(1978). 3’V. S. Panwar, R. Singh, G. L. Malhotra, S. K. Sharma, P. C. Mehen-

dru, and N. P. Gupta, I. Mater. Sci. Lett. 7, 572 (1988). 32N. P. Gupta, K. Jain, and P. C. Mehendru, Thin Solid Films 61, 297

(1979).

3416 J. Appl. Phys., Vol. 72, No. 8, 15 October 1992 Singh et al. 3416

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

195.19.233.81 On: Mon, 03 Feb 2014 09:39:57