Thermally Stimulated Discharge Current Analysis of Polymers

ELECTRICAL PROPERTIES OF POLYMERS

Chapter

5

Thermally Stimulated Discharge Current Analysis of Polymers Stephen H. Can DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING NORTHWESTERN UNIVERSITY EVANSTON, ILLINOIS I. II.

Thermally Stimulated Discharge Current Technique (TSDC) Characterization of Molecular Relaxation Processes References

I.

THERMALLY STIMULATED DISCHARGE CURRENT TECHNIQUE (TSDC)

215 222 236

T S D C analysis of polymer solids is rapidly becoming recognized as a very rich source of information from polymeric materials. T h e kinds of insight being gained from T S D C analysis include quantitative m e a s u r e ­ ment of the following: impurity concentrations, the wide varieties of pos­ sible molecular motions, characterization of the states of m a c r o m o l e c u l e s and their local environments, chemical effects (state of c u r e , degradation chemistry), and anisotropy in m i c r o s t r u c t u r e . T h e T S D C analysis involves a thermoelectric schedule as follows. T h e c o m m o n situation is to start with any dielectric (this includes virtually all polymers) in a parallel plate capacitor configuration, elevate its t e m p e r a ­ t u r e , apply an electrical field across the electrodes, cool the material to some reduced value, and then r e m o v e t h e external electrical field. T h e specimen now possesses an electrical polarization that will persist for a very long time. This polarized state induces in adjacent electrodes charges equal in magnitude and opposite in sign to that at the specimen surface; these are called image c h a r g e s . T h e s e external electrodes are then shortcircuited to each other through a device that can m e a s u r e electrical cur­ rents with great sensitivity. T h e T S D C p h a s e of this schedule then com­ mences with the establishment of a uniform, slow (about l°C/min) heating 215 C o p y r i g h t © 1982 by Academic Press, Inc. A l l rights of reproduction in any f o r m reserved. I S B N 0-12-633680-6

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rate. As the t e m p e r a t u r e rises, the persistent polarization induced during the initial phase begins to d e c a y , and w h e n e v e r a t e m p e r a t u r e range is encountered over which the decay rate m a t c h e s the time scale of the experiment, there follows a release of some of these image charges. A s a result, one then sees some current flowing in the external circuit through the current-measuring device. A plot of this current as a function of tem­ perature is a thermally stimulated discharge current t h e r m o g r a m . Figure 1 shows this schematically. Samples used during T S D C experiments are commonly in the form of films. This permits the externally applied electrical potentials (volts) to be reasonably small, while still giving strong electrical fields (volts p e r cen­ timeter). Samples may have acquired a polarization prior to the T S D C experiment, in which case the starting materials are considered electrets t h e m s e l v e s . H o w e v e r , one may still expect to see T S D C currents gener­ ated even from nonpolarized polymers, at least in some c a s e s . T h u s , the T S D C method may also serve to evaluate the magnitude of the electrical polarization on which such characteristics as piezoelectricity and pyroelectricity are b a s e d . C o m m o n l y , the electrodes used are actually very thin (approximately 100 A) layers of metal deposited either by sput­ tering or v a c u u m evaporation. This configuration prevents the existence of an air gap between the dielectric material to be tested and the elec­ trodes used to do the testing. As will be detailed later in this c h a p t e r , variations on this physical configuration may be justified. T h e reason that T S D C is a thermal analysis technique being used in­ creasingly relates to t w o factors: high sensitivity and high resolution. T h e sensitivity arises b e c a u s e electrical techniques can yield signals derived from exceedingly subtle effects, and the resolution effect arises from the fact that relaxation half-widths a r e intrinsically foreshortened in the c a s e Fig. 1. Sequence of events during a T S D C experiment. The temperature schedule fol­ lowed is shown at the top. The first stage (pol.) involves application o f external voltage £p across the specimen at an elevated tem­ perature, and the second stage, T S D C , in­ v o l v e s measurement of the current flowing between the short-circuited electrodes as the specimen is heated at a constant rate. In the example depicted here, the polarization Ρ developed during the polarizing stage is shown to decay arbitrarily in t w o stages and, as a direct c o n s e q u e n c e , a peak in discharge current i(T) is seen coincident with each decay process.

5.

Thermally

Stimulated

Discharge Current Analysis

Fig. 2. T S D C thermograms from poly­ ethylene terephthalate) film polarized at 120°C under fields Ev of (a) - 4 4 . 4 k V / c m , (b) - 8 3 . 3 k V / c m , and (c) - 1 6 6 . 7 k V / c m . [Adapted from Asano and Suzuki (1972, Fig. 2), reprinted with permission.]

of

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Temperature (°C)

of very slow test frequencies ω. In fact, the relationship that d e t e r m i n e s the effective test frequency of a T S D C analysis test is shown by ω = A/bkTl.

(1)

H e r e A is the apparent activation energy, b is the reciprocal of the heating rate, A is B o l t z m a n n ' s constant, and Tm is the t e m p e r a t u r e at which T S D C reaches its m a x i m u m . A s the test frequency diminishes, the characteristic half-widths of any relaxation peak likewise decline. Similarly, the shifting of a peak to lower t e m p e r a t u r e s as a result of the m e a s u r e m e n t s being m a d e at lower frequencies tends naturally to increase the separation of individual p e a k s along the t e m p e r a t u r e axis. T h u s , closely spaced dis­ charge p e a k s will b e c o m e m o r e distinct in the t h e r m o g r a m as the test frequency goes d o w n . C o m m o n l y , relaxation p r o c e s s e s , which o c c u r on the same time scale as a T S D C experiment in the cryogenic t e m p e r a t u r e 5 ranges, c o r r e s p o n d to frequencies of 10" H z or lower, while highert e m p e r a t u r e peaks (with their concomitantly higher activation energies) 3 may h a v e corresponding test frequencies of 10" H z . A typical T S D C t h e r m o g r a m is shown in Fig. 2. H e r e it can b e seen that increasing the polarizing voltage likewise increases the magnitude of the currents released. T h e s e currents arise from charges in the electrodes t h e m s e l v e s , which are images of the polarization charge possessed b y the dielectric (the test material itself) - T h u s , the surface of the dielectric, which has a positive c h a r g e , will induce in its contacting electrode a negative charge of equal magnitude; the o t h e r side of the dielectric will h a v e a nega­ tive charge and will, in turn, induce an equal charge of opposite sign in its contacting electrode. When the dielectric is heated into t e m p e r a t u r e ranges where the origins of the polarization relax and t h e r e b y disappear,

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the image charges are released from their electrodes and flow t o w a r d each other via the external circuit. It is the current flowing in this external circuit that provides the output signal for the T S D C t h e r m o g r a m . Unfor­ tunately, in the case w h e r e some of the polarization in the dielectric arises from charged species that possess some mobility, it is possible for t h e s e charges to diffuse during the T S D C experiment, either toward each other through the dielectric itself or alternatively away from the dielectric into the electrode materials, thereby annihilating their charging effects. It will be discussed subsequently how these effects can be identified and c h a r a c ­ terized. Persistent electrical polarization, from which the discharging currents are usually a reflection, is commonly thought to arise from a variety of contributions. T h e first distinction among t h e s e contributions is divided between heterocharge and h o m o c h a r g e (Adams, 1927; G e m a n t , 1935; Gross and Denad, 1945; Perlman, 1971; Natarajan, 1972). A heterocharge is a polarization (coulombs p e r square centimeter) at a surface whose sign is opposite that of the polarizing electrode adjacent to it. A h o m o c h a r g e , conversely, is a polarization w h o s e sign on a given surface is the s a m e as that of the polarizing electrode next to it. O n e m a y think of a heterocharge as being the result of the dielectric reaction of a material to an impressed external electrical field, while a h o m o c h a r g e can be envisioned as result­ ing from charges being transferred directly from a polarizing electrode to the surface of the dielectric adjacent to it. Another way of viewing total polarization is to apportion it between contributions arising from dipolar moieties in the solid having a preferred orientation and real charged mo­ lecular species that have b e c o m e displaced such that the centroid of posi­ tive charges does not coincide along the thickness direction with that of the negative charges. The physical situation is summarized in Fig. 3. Most polymeric materials contain chains along which are spaced groups of atoms possessing a permanent dipole moment. E x a m p l e s are ester

Fig. 3 . Schematic representation of a polarized slab of a dielectric of thickness d and surface area A. Real charges are represented by circles containing either a plus or a minus sign; dipolar moieties are represented by arrows. The net polarization Ρ on the surface c o m e s from the sum of internal electric fields arising from preferential orientation of the dipoles and net displacement of real charges.

5. Thermally Stimulated Discharge Current Analysis of Polymers

219

linkages, amide linkages, carbonyl g r o u p s , and nitrile g r o u p s . If any frac­ tion of these dipolar moieties has a physical orientation in which as m a n y groups, on a v e r a g e , point up as point d o w n , then no polarization will result from t h e m . H o w e v e r , if these dipoles are, on bulk a v e r a g e , dis­ posed in space such that a few m o r e of them point in one direction than in the opposite direction, then one will e x p e c t to obtain a finite a m o u n t of permanent polarization Páiv. This relationship is shown quantitatively by (Hille* eil., 1969) P d i p = (/coo + 2 ) A ^ o ( c o s 0 > / 3 ,

(2)

w h e r e K«, is the permittivity of the medium m e a s u r e d at infinite frequency, Ν is the n u m b e r of dipoles having p e r m a n e n t dipole m o m e n t μ 0 per unit volume, and (cos Θ) results from bulk-averaging o v e r all orientation angles θ b e t w e e n t h e dipolar a x e s a n d t h e electrical polarization direction. T h u s , it is seen that, as the n u m b e r of dipoles per unit volume increases or as the average degree to which the dipoles are aligned parallel with the field direction increases, the depolarization resulting from dipoles will correspondingly increase. Polymer electrets c o m m o n l y have this dipolar polarization generated by heating to elevated t e m p e r a t u r e s and then applying a strong external elec­ tric field E. Although the electrical field inside the dielectric / may not be exactly the same as E, it nonetheless has a finite value which in turn imposes a t o r q u e θ on the dipoles and tends to orient t h e m in a parallel alignment: θ = [ 3 κ 0 / ( 2 κ 0 + U K £ sin 0,

(3)

where κ0 is the permittivity of the medium at zero frequency. After t h e electret has been formed a n d the t e m p e r a t u r e has been d r o p p e d , this orientation of the dipoles is largely retained b e c a u s e thermally activated motions necessary t o permit a return of the orientation distribution in these dipoles t o w a r d r a n d o m b e c o m e exceedingly sluggish. In fact, it may require y e a r s or even centuries before an appreciable fraction of this orientation is lost. Only by returning the t e m p e r a t u r e once again t o w a r d that at which the dipolar orientations w e r e created is it possible to foreshorten this depolarization time. In the c a s e of p o l y m e r s , this de­ polarization process o c c u r s at a rate having a characteristic t e m p e r a t u r e dependent time constant r, and this fact b e c o m e s t h e very basis of the use of T S D C in analyzing polymeric materials. F o r e x a m p l e , it is now possible to o b s e r v e what are called secondary and primary dispersion effects ( L a c a b a n n e and Chatain, 1973) in p o l y m e r s . Secondary dispersion effects are c o m m o n l y ascribed to molecular motions involving very small por­ tions of a polymer chain, typically those involving a single chemical repeat unit or a side g r o u p .

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Primary dispersions involve motions of whole segments of b a c k b o n e s , possibly represented by tens of repeat units. T h u s , t h e motional freedom imparted to a given dipole once secondary motions b e c o m e possible is sufficient to permit the onset of some randomization motions, but the complete disorientation process will require the mobility of whole polymer chain segments, which b e c o m e s possible only when primary dis­ persion effects are possible. T h u s , T S D C m e a s u r e m e n t s on polarized polymer solids should be e x p e c t e d to reveal the t e m p e r a t u r e ranges o v e r which each of these individual relaxation p r o c e s s e s o c c u r s . T h e o t h e r source of polarization, that arising from real charges, is re­ sponsible for heterocharging a n d / o r homocharging. E x a m p l e s of real charged species are ions injected from the exterior of the sample, electrons implanted by irradiation, ionic species indigenous to the material before any thermoelectric t r e a t m e n t s w e r e i m p o s e d , a n d counterions b o u n d to ionic sites along the p o l y m e r chains. Such charges may be concentrated with equal quantities of opposite signs on opposite sides of the film, or they m a y be of unequal concentration, giving rise to an a s y m m e t r i c electret condi­ tion . T h e e x t r e m e example of this latter situation is what is called a monopole electret, and it is characterized by simply having an excess of charges of one sign located asymmetrically across the thickness of the electret. A monopole electret is opposed to a dipole electret, which is the case w h e r e the dielectric has the same n u m b e r of oppositely charged species on op­ posite sides of the film. Injected ions or electrons can be c r e a t e d by e x p o s u r e of the sample to ion or electron accelerators prior to insertion in T S D C measuring devices (Sessler and West, 1975; Legrand et al., 1977; H a s e g a w a and M o r i m o t o , 1974; Marconi C o . , 1974; Gross et ai, 1973). Ions can also b e injected by electromigration (Osaki and Ishida, 1973) or by photoinjection (Sapieha and Wintle, 1977; Takai et al., 1976; Pillai et ai, 1977). L i k e w i s e , e x p o s u r e of electrets t o a corona (as m a y be c r e a t e d , for e x a m p l e , by radio-frequency excitation of a gas at reduced pressure) will probably h a v e a combination of effects on an electret, including ion injection and chemical reaction of the surfaces leading to some d e v e l o p ­ ment of ionic species in the electret itself (Creswell and Perlman, 1970a; Moreno and G r o s s , 1976; J o r d a n , 1975; F u k u n a g a and Y a m a m o t o , 1973; K o d e r a , 1975). Subsequently, during T S D C experiments, the redistribu­ tion of these ions is usually o b s e r v e d in a r a t h e r discrete t e m p e r a t u r e range, usually 20-40°C above the primary dispersion t e m p e r a t u r e (Tg). T h e discharge current peak corresponding to the onset of this redistribu­ tion depends on actual electrical conductivity in the dielectric, and it is, therefore, a m e a s u r e of the bulk redistributing as a result of t r a n s p o r t of charged ionic species themselves (Seytre et al., 1973; Borisova et al., 1975; Mehendru et al., 1976a). Such discharge peaks are often labeled ρ

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Paper •log

Punched tape

Fig. 4. Circuit and components schematic diagram for a typical fully automated T S D C apparatus. The input to the electrometer Ε is a small current in the picoampere range. [From van Turnhout (1975, Fig. 9-1), published with permission.]

peaks and a r e , therefore, indicative of the amount of polarization pos­ sessed by a p o l y m e r electret that was not d u e to dipolar orientation. O n e needs to bear in mind that the discharging of polarization resulting from ionic species can o c c u r by drifting of these charges either into electrodes (therefore, out of the sample) or t o w a r d each o t h e r within t h e sample under the influence of the internal electrical field /. Equipment for conducting T S D C experiments is historically tailorm a d e for each individual investigator's p u r p o s e s (van Turnhout, 1975, C h a p t e r 9). H o w e v e r , at least one commercial a p p a r a t u s is currently available through the Toyo-Seiki C o m p a n y . * O t h e r a p p a r a t u s h a s been described by Yalof and Hedvig (1975). Figure 4 is a c o m m o n configuration for such pieces of equipment. Voltages c o m m o n l y supplied are in t h e 14 range 0 - 1 0 kV, and the currents often m e a s u r e d lie in t h e range 1 0 ~ 5 10~ A. T e m p e r a t u r e stability and control is highly important, the most critical environmental control factor being the linearity of t h e heating r a t e , h~\ This rate n e e d s to be held within 0 . 1 % of the selected value; oth­ erwise, noticeable artifacts will be developed in the discharge current t h e r m o g r a m . T h e a t m o s p h e r e in t h e s e instruments is best maintained at a reduced p r e s s u r e , although a high vacuum is u n n e c e s s a r y and may actu­ ally interfere with the best thermal control. L i k e w i s e , very low p r e s s u r e s may induce a corona to form in the gas space of the sample c h a m b e r . Continuously flowing purges are often u n d e s i r a b l e , as they may introduce static charging on various dielectric c o m p o n e n t s of the sample-holding

* This equipment is fashioned after the design developed by E . Fukada of the Japanese Institute of Physical and Chemical Research. Currently, the Toyo-Seiki electret thermal analyzer is distributed in the United States by Atlas Electric D e v i c e s Company, Chicago, Illinois.

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fixture itself. T S D C m e a s u r e m e n t s at elevated hydrostatic pressures are being m a d e in the a u t h o r ' s laboratory and elsewhere (Ai et al., 1979). II.

CHARACTERIZATION OF MOLECULAR RELAXATION PROCESSES

Imagining for a moment that p o l y m e r s are h o m o g e n e o u s solids throughout which are dispersed dipolar moieties, one can calculate [Eq. (2)] a polarization Páw knowing the entire distribution of orientations p o s ­ sessed by t h e s e dipoles. N o t e that ( c o s 0) is a function that ranges from + 1 to - 1 and, therefore, can take into account orientations projecting by some amount parallel with the imposed electrical field or by a m o u n t s projecting in opposition to the impressed electrical field. In t h e c a s e w h e r e these dipoles do not interact with each o t h e r , the value of (cos 0) is found to be a function of t e m p e r a t u r e Τ and polarizing voltage, as given by ( c o s 0) = ε 0 μ ο £ / 3 £ Γ .

(4)

In such dielectrics, t h e rate at which polarization g r o w s or d e c a y s is given by a D e b y e equation: dP(t)/dt

= -aP(t)

+ ε 0( κ 0 - Κοο)α£,

(5)

w h e r e P(t) is the time polarization of the dielectric as a function of time and a = \/τ(Τ). As mentioned in the previous section, the heating of electrets will eventually bring the t e m p e r a t u r e to levels at which a. b e c o m e s large (r, the relaxation time, b e c o m e s very small) and, conse­ quently, the derivative b e c o m e s large. A s polarization is lost from elec­ trets in a T S D C a p p a r a t u s , the corresponding image charges in the elec­ trodes are released and permitted to flow through the external circuit to cancel each other. T h u s , the time derivative b e c o m e s exactly equal to the discharge current /. In T S D C e x p e r i m e n t s , Ε is typically 0, so one may then write from Eq. (5) an expression for the discharge current: /(/) = -dP(t)/dt

= aPif).

(6)

This expression permits calculation of P(t) as a function of time: P(t) = P 0 e x p ( -

(?)

w h e r e P0 is the polarization present at time 0. Combining E q s . (6) and (7), and using the chain rule to change the integration from time to t e m p e r a t u r e , permits one to express the discharge current as a function of t e m p e r a t u r e i(T): i(T) = - a P 0 e x p ( - b jja

dT),

(8)

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w h e r e the inverse heating rate b = dt/dT. T h u s , the discharge current i(T) l depends on both t h e heating rate b~ a n d t h e relaxation frequency a. In the case of polymers in which some dipolar motions relate simply to isolated dipoles, it is found that the Arrhenius relationship can b e used t o express t h e t e m p e r a t u r e d e p e n d e n c e of a\ α{Τ)λΐΤ

= A0exp(-AAT),

(9)

w h e r e a0 is t h e natural relaxation frequency of the dipole in question. H o w e v e r , certain relaxation processes a r e o b s e r v e d to b e dependent not upon absolute t e m p e r a t u r e Τ but rather the difference in t e m p e r a t u r e be­ tween some nonzero value T' and t h e prevailing t e m p e r a t u r e T. In these cases, an Eyring-type process m a t c h e s m o r e closely that which is o b ­ served: A(DE

YR

= a0exp[-A(T)/k(T

-

T')].

(10)

For long-chain macromolecular materials, some relaxation p r o c e s s e s a r e dependent upon t h e cooperative effects necessarily involved in chain segment mobility. In these c a s e s , t h e empirical relationship c o m m o n l y designated W L F seems most appropriate: « ( A V L F = OG Β Χ Ρ Ι Γ Λ Γ -

7G)/(C2 + Τ -

Tg)l

(11)

w h e r e ag is t h e relaxation frequency in t h e glassy state, Tg is t h e liquidglass transition t e m p e r a t u r e , a n d C\ and C 2 are c o n s t a n t s . From the a b o v e , one has the basis for calculating an analytical e x p r e s ­ sion for the discharge current obtained during a continuous heating exper­ iment, specifically a T S D C experiment. Insertion of Eq. ( 9 ) o r ( 1 0 ) or ( 1 1 ) into E q . ( 8 ) should give the desired result. H o w e v e r , this is a m a t h e m a t ­ ically difficult task, a n d resort is m a d e to approximations. T h e primary problem is that the integration leads t o a convergent infinite series, and so an approximation needs t o b e invoked in o r d e r to obtain a tractable result (Cowell and Woods, 1 9 6 7 ; van Turnhout, 1 9 7 1 ) : i(T) = C 3 exp

A kT

2

C4(kT) 2 A "

( e

Xp

V

A kT

(12)

This relationship involves t w o adjustable p a r a m e t e r s , C 3 a n d C 4 , b u t it d o e s faithfully r e p r o d u c e experimentally obtained T S D C p e a k s a s well a s peaks obtained from such different experiments a s t h e r m o l u m i n e s c e n c e . An example of such curve fitting to actual T S D C m e a s u r e m e n t s is shown in Fig. 5 . H e r e , o n e sees t w o distinctly different discharging p r o c e s s e s each of which exhibits t h e characteristic skewed shape predicted by E q . ( 1 2 ) . T h u s , the thermally stimulated discharge of polarization o c c u r s b y a process that starts out slowly, rises exponentially a s the t e m p e r a t u r e con-

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80

100

120

Can

140

Temperature (°C) (a)

160

180

Temperature (°C) (b)

Fig. 5. T S D C thermogram (circles) obtained from polyacrylonitrile polarized at under a field of 56 kV/cm. Solid lines and triangles represent a fitting of Eq. (12) to centered at (a) 90°C and (b) 180°C. The squares in Fig. 5a show the low-temperature the 180°C peak by subtracting the fitted curve from the actual data. S e e Comstock (1977).

130°C peaks toe of et al.

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tinues to increase, r e a c h e s a m a x i m u m , and then d r o p s sharply as the randomization of preferentially oriented dipoles b e c o m e s c o m p l e t e . O n e notes from E q . (12) that activation energy Λ for the relaxation process a p p e a r s in the equation. It is not possible to obtain a good fit b e t w e e n theoretical prediction and experimental data unless the p r o p e r value of A has b e e n , in fact, selected. T h u s , c u r v e fitting can be regarded as a m e a n s for experimental determination of the activation energy. F u r t h e r m o r e , E q . (12) is intended to apply only to c a s e s w h e r e the depolarization pro­ cess o c c u r s uniformly across the thickness dimension of a specimen. Inspection of E q . (12) also reveals that t h e r e should be a linear relation­ ship between In i(T) and 1/Γ, at least in the early stages of depolarization. T h e slope of such plots, at t e m p e r a t u r e s considerably below the location of the peak m a x i m u m r m ax should be approximately given by d In /(Γ) d\/T

=

~

τ< r m ax

4

"

.

(13)

k

Plots such as are suggested by this treatment are t e r m e d the initial rise method (van Turnhout, 1971; Nicholas and Woods, 1964). D a t a from Fig. 5 are plotted thusly in Fig. 6, w h e r e it is seen that, for the first approximately 30% of the charge lost, this relationship holds fairly well (Sessler and West, 1976). A p p r o p r i a t e agreement b e t w e e n activation energies obtained by the initial rise method and by curve-fitting tech­ niques, as mentioned a b o v e , is good. Differentiating Eq. (8) and solving for the condition at the peak m a x i m u m results in the relationship given by dl/a dT

= -b.

(14)

What this relationship says is that when the change in relaxation time of the dipoles with respect to t e m p e r a t u r e b e c o m e s identical with the recip­ rocal of the heating r a t e , then the rate at which the charge remaining in t h e sample is being lost likewise r e a c h e s a m a x i m u m . Taking E q . (9) (the Arrhenius relationship) as one plausible expression for a , one can rewrite Eq. (14) as 2

a(Tmax)bkT max/A

= 1.

(15)

Alternatively, as one recalls from t r e a t m e n t s of dielectric dispersion data, there are o b s e r v e d m a x i m a at various frequencies ω ^ 3 Χ in the imaginary component κ" of the c o m p l e x permittivity κ*, which o c c u r when the con­ dition WmaxT(r) =

1

(16)

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-8r

Fig. 6. T S D C data plotted according to Eq. (13). Circles and triangles are data from two different preparations of polyacrylonitrile films. Straight lines yield slopes from which acti­ vation energies of 27.7 and 31.7 kcal/mole, respectively, were obtained. [From M . S . thesis of R. J. Comstock, Northwestern University, Evanston, IL. (1974).]

is met. By inspection, one can o b s e r v e that combining E q s . (15) and (16) explains the origin of E q . (1). Reconciliation between dielectric dispersion data and m e a s u r e d T S D C t h e r m o g r a m s has been accomplished with good success (Sessler and West, 1976). It follows from what is contained in the preceding paragraph that a complex T S D C t h e r m o g r a m , comprised of m a n y overlapping p e a k s , can be analyzed incrementally to obtain activation energies for the discharging process at successively higher t e m p e r a t u r e s . An example of the d e c o m ­ posing of a T S D C maximum is found in Berticat et al. (1978). Plots of the initial rise of each successively higher discharge increment on a log cur­ rent versus reciprocal t e m p e r a t u r e yields t h e c u r v e in Fig. 7. F r o m the slopes of each line, it is possible to determine activation energies that

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Polymers

\ o X

o

l

Í

hi

'

I 0 0 0

\

o

/ Τ

(Κ"' )

Fig. 7. T S D C data plotted according to Eq. (13) from a partial heating experiment on poly(bisphenol A carbonate). [From Aoki and Brittain (1976, Fig. 6), reprinted with permis­ sion.]

prevail for the discharge in each small t e m p e r a t u r e range. Figure 8 shows a plot of these activation energies as a function of the t e m p e r a t u r e at which each datum was d e t e r m i n e d , and such a relationship essentially represents the activation energy spectrum throughout a specified range of t e m p e r a t u r e s . It is seen that the activation energy is larger for higher t e m p e r a t u r e s , as one would e x p e c t . H o w e v e r , there are certain tempera­ ture ranges over which a c o m m o n value of activation energy prevails, and so it b e c o m e s plausible to s u p p o s e that a c o m m o n molecular event is responsible for the discharge effects throughout any particular t e m p e r a ­ t u r e interval. T h u s , t h e s e t e m p e r a t u r e intervals provide evidence for t h e existence of multiple molecular events associated with a broad T S D C peak (Gobrecht and Hofman, 1966; Creswell and Perlman, 1970b; Vand e r s c h u e r e n , 1972; Aoki and Brittain, 1976; Suzuoki, 1978). The interest­ ing thing to note here is that correlations are being d i s c o v e r e d b e t w e e n these individual values of activation energies and such mechanical c h a r a c ­ teristics as yield stress (Aoki and Brittain, 1977) and c r e e p ( B e r t i c a t ^ al., 1978). T S D C analyses of m a n y other commercial polymers h a v e been reported and give support to the notions that a significant contribution to polymerization arises from the relaxation of dipoles that had acquired a preferential orientation during the electrical polarization s t e p . E x a m p l e s of these studies are contained in Table I. An alternative way to m a k e a direct determination of activation energy for the discharge p r o c e s s e s occurring at different t e m p e r a t u r e s is called

228

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Can

0.8

100

150

200

Τ (Κ ) Fig. 8. Activation energy distribution through the cryogenic temperature range for poly(bisphenol A carbonate). The two runs correspond to t w o successive partial heating exper­ iments on the same specimen. Θ , first run; χ , second run. [From Aoki and Brittain (1976, Fig. 8), reprinted with permission.]

fractional polarization. It is a method in which the specimen is polarized intermittently as it is being cooled, rather than having polarization start at some high t e m p e r a t u r e and be maintained continuously while being cooled to the beginning of a T S D C experiment. What fractional polariza­ tion means is that only portions of the total dielectric reaction to im­ pressed electrical fields are developed. A subsequent T S D C determina­ tion will sequentially release these increments in polarization without polarization being released in a given t e m p e r a t u r e range having a tail that superposes on polarization that will release at some higher t e m p e r a t u r e range. Since the discharge t h e r m o g r a m will be c o m p o s e d of a series of individual p e a k s , it is then possible to plot these p e a k s as shown in Fig. 7. Consequently, one then obtains activation energies throughout that s a m e t e m p e r a t u r e range. Unfortunately, experience (Vanderschueren and Linkens, 1977) with this method has revealed that it shows rather less resolu­ tion of individual processes a n d , further, that the values of activation energy obtained from it lie below those commonly obtained by T S D C analysis or by dielectric dispersion a n a l y s e s . Persistent electrical polarization can be developed in p o l y m e r solids by techniques other than the thermal polarization method referred to a b o v e . T h e s e include mechanical m e a n s , e x p o s u r e to electrical c o r o n a s , direct

5.

Thermally TABLE I

Stimulated

Discharge Current

Partial Bibliography

Analysis

of TSDC Analyses

of Polymers of Common

229 Polymers

Polymer

References"

Polyvinyl chloride) Polyvinyl acetate) Polystyrene Polypropylene Polyethylene terephthalate) Polyvinyl alcohol) Poly(methyl methacylate) Poly(vinylidene Polyethylene Polyvinyl Poly(bisphenol A carbonate) Polycaproamide (nylon 6) Poly-/7-chlorostyrene Poly-4-vinylpyridine Cellulose (regenerated) Polyacrylonitrile Polyoxymethylene Polyvinylbutyral Polytetrafluoroethylene

1 2 3 4 5 6 7 fluoride) fluoride)

8 9 10 11 12 13 14 15 16 17 18 19

Thiourea formaldehyde resins Phenolic resins Polyester urethanes E p o x y resins Poly(2,6-dimethyl-l,4-phenylene oxide) Copolymer of ethylene and vinyl acetate Copolymer of styrene and p-chlorostyrene Copolymer of vinyl chloride and vinyl acetate

20 21 22 23 24 25 26 27

Copolymer o f chlorinated ethylene and acrylonitrile-styrene Blends of polyethylene and polyacrylonitrile Blend of poly(2,6-dimethyl-l,4-phenylene oxide) either polystyrene, poly-p-chlorostyrene, or poly(/?-chlorostyrene-cY;-styrene) Hemoglobin Poly-L-proline

28 29

a

30 31 32

References:

(1) Pillai et al. (1969, 1972a,b, 1973); Talwar and Sharma (1978). (2) Pillai et al. (1972b); Mehendru et al. (1975, 1977). (3) Marchai et al. (1978); Bui et al. (1974); Alexandrovich et al. (1976); Bhargava and Srivastava (1979); Draconu and Dumitrescu (1978). (4) Matsui and Murasaki (1973); Takamatsu and Fukada (1972).

(5) A s a n o and Suzuki (1972); Marchai et al. (1978); Takai et al. (1976); Lushchelkin and Voiteshanak (1975); Kojima et al. (1976); Borisova et al. (1975); Vanderschueren and Linkens (1978b). (6) Jain et al. (1975); Sharma et al. (1980). (7) Creswell and Perlman (1970b); Solunov and Vasilev (1974); Gubkin and Ogloblin (1972); van Turnhout (1977); {continued)

230

Stephen Η. TABLE I Vanderschueren (1974); Vanderschueren and Linkens (1977); Lamarre et al. (1980).

(8) Murayama and Hashizume (1976); Tamura et al. (1977); Sharp and Garn (1976). (9) Takamatsu and Fukada (1972); Fischer and Roehl (1974); Hashimoto et al. (1975, 1978): leda et al. (1979): Perret and Fournie (1975). (10) Reardon and Waters (1976). (11) Aoki and Brittain (1976, 1977): Kryszewski and Ulanski (1976); Wissler and Crist (1980). (12) Ikeda and Matsuda (1976). (13) Marconi Co. (1974). (14) Gable etat. (1973). (15) Baum (1973); Pillai and Mollah (1980). (16) Comstock et al. (1977); Stupp and Carr (1975).

Can

(Continued) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32)

Goel and Pillai (1979). Jain et al. (1979). Gross et al. (1976). N a l w a et al. (1979). Goel et al. (1978). Baturin et al. (1976). Tanaka et al. (1977); Woodard (1977); Pillai and Goel (1973); Su et al. (1980). Alexandrovich et al. (1976). Linkens et al. (1976). Alexandrovich et al. (1976). Gupta et al. (1977, 1979). Takamatsu and Nakajima (1974). Kartalov (1973). Alexandrovich et al. (1976). Rechle et al. (1970). Guillet et al. (1977).

injection of electrons, and implantation a n d / o r incorporation of ionic species. Studies by Sacher (1973) have revealed w a y s in which molecular orientation induced during the manufacture of poly(ethylene terephthal­ ate) film can p r o d u c e an electrical anisotropy detectable by T S D C analy­ sis. Similar studies h a v e been reported e l s e w h e r e (Tsygel'nyi, 1975). E x ­ posure of films to excited gas p l a s m a s , especially those p r o d u c e d in the electrical b r e a k d o w n of air, are widely exploited in the preparation of permanently polarized p o l y m e r s . In some cases, large electrical fields are established between the plasma and the grounded side of the p o l y m e r film in question ( M c K i n n e y and Davis, 1977). E x a m p l e s of other studies on corona-charged polymers are found in Creswell and Perlman (1970), F u k u n a g a and Y a m a m o t o (1973), J o r d a n (1975), Creswell et al. (1972), and Kodera(1975). The problem with corona charging of polymers from a scientific standpoint is that a collection of individual events may o c c u r for any given combination of corona-charging conditions and the polymeric material in question (Moreno and G r o s s , 1976). For e x a m p l e , ionized gas molecules accelerate in the corona and e m b e d themselves with various binding ener­ gies in the polymeric material. L i k e w i s e , electrons that are released in the corona and can travel into the specimen (provided the polarity of the charging field is suitable) can develop the desired polarized state. In some cases, it is plausible to imagine these trapping events involving a chemical reaction with the polymer molecules t h e m s e l v e s . This may be due to the

5.

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Stimulated

Discharge Current Analysis

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231

ion itself bonding to the chain. It may alternatively be that the energy of the ion c a n , in turn, be transferred to parts of p o l y m e r chains, and these ionized species then may proceed to react e l s e w h e r e in the polymer solid itself. In cases w h e r e the polymer chains b e c o m e so chemically modified, it is even possible that ionizable g r o u p s , such as carboxylic acid g r o u p s , can be formed if oxygen is present during the corona-poling s t e p . Simi­ larly, injection of charge directly by e x p o s u r e of polymeric films to elec­ tron b e a m s (Marconi C o . , 1974; H a s e g a w a and M o r i m o t o , 1974; L e g r a n d et al., 1977; Sessler and West, 1975; Gross et al., 1973; Borisova et ai, 1975) and χ rays (Suzuoki, 1978) has been performed. T S D C analysis of polymers, which have been charged by e x p o s u r e to electron b e a m s or to coronas, can permit evaluation of both dipolar effects and charge trans­ port effects. B e c a u s e of the electrical gradients and local electrical fields created when t h e s e polarization m e t h o d s are u s e d , dipoles may adopt some pre­ ferred orientation. T h u s , a subsequent T S D C t h e r m o g r a m often reveals discharge maxima coincident with t e m p e r a t u r e ranges over which dipolar relaxation effects are e x p e c t e d . O t h e r discharge current m a x i m a are also o b s e r v e d , and these are usually attributed to the motion of real charges implanted during the polarization steps (Creswell and P e r l m a n , 1970; Moreno and Gross, 1976). What can b e determined here is the magnitude of charge released as a result of implanted and mobile ionic species. Unfortunately, some of the charged species are generated internally to the film after it has been irradiated. F u r t h e r m o r e , any induced dipolar orienta­ tion is of a heterocharge n a t u r e , while implanted charge is usually of a homocharge n a t u r e . T h u s , overlapping peaks of opposite polarity may be o b s e r v e d and thus imperfectly d e t e r m i n e d b e c a u s e of the difficulty in decomposing such a t h e r m o g r a m . F u r t h e r m o r e , the stability of charges trapped inside such polymer solids is often dependent upon the physical or chemical nature of the trapping site and, as a result, the release of such charges occurs in a stagewise m a n n e r . Finally, real charged sites gener­ ated during the initial polarization irradiation can also be b o u n d to the chain as pendant and ionizable side g r o u p s . T h e s e charged species cannot drift at all, and as a result the polarization they represent cannot be mea­ sured by T S D C analysis. Recent work by Collins (1975) and others (DeReggie et al., 1978) has described w a y s of making direct m e a s u r e m e n t of the distribution (Natarajan, 1975) of charges across the thickness of a polarized polymer film. Discrimination b e t w e e n electronic and ionic con­ ductivity in the discharge of implanted species has been studied (Seanor, 1968). Ionic species can also be incorporated into polymers either at the time the solid is itself being prepared or while it is being polarized. It is possible to p r e p a r e " d o p e d " p o l y m e r s (Jain et al., 1975; Wissbrun and H a n n o n ,

232

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1975; M e h e n d r u et al.y 1976b; L a t o u r and Donnet, 1976) by dissolving ionic species directly into p o l y m e r solutions from which subsequently dried films are cast. T h e s e materials usually exhibit s p o n t a n e o u s polariza­ tion due simply to the anisotropic distribution of charges that result during the final stages of evaporation (Stupp and Carr, 1975; M e h e n d r u et ai, 1976b). F u r t h e r m o r e , the injection of ions from electrodes is also ob­ served to o c c u r ( K o j i m a ^ r at., 1976; Osaki and Ishida, 1973), depending upon the metal ions that can be liberated from t h e m . It has b e c o m e com­ mon practice for gold to be the material of choice for electrodes, since it is the least frequently implicated as being a source of ionic impurities im­ planted in dielectric solids. Alternatively, ions can be deliberately intro­ duced from electrodes if the electrodes a r e , in fact, electrolyte solutions (Turyshev et al., 1977). T h e u s e of solutions as conducting electrodes has employed w a t e r , dioxane, methanol, and amyl acetate as solvents. Al­ though these polymers are capable of storing a considerable a m o u n t of charge by simple displacement of the ionic species they contain, films prepared from polyelectrolytes store an even greater charge b e c a u s e of the counterions they naturally contain (Seytre et al., 1973; Bornzin and Miller, 1978). A quantitative treatment of the transport such ionic species represents has been r e p o r t e d by S a i t o h al. (1974). Activation energies for charge transport w e r e in the range of 2 eV, strongly suggesting that a cooperative motion of chain segments w a s required for the passage of charge from point to point. P r e s u m a b l y , activation energies that require such motions involve ionic species that exist as individual, and therefore dissolved, entities inside the polymer solid p h a s e itself (Linder and Miller, 1973). The a m o u n t by which ionizing radiation can c a u s e discharging (or charging, for that matter) of polymer films can also be studied by T S D C analysis. In a sense, electrets can serve as very useful dosimeters for ionizing radiation, although in t h e s e cases the m e a s u r e m e n t of surface charge alone can suffice to detect the irreversible d a m a g e d o n e during e x p o s u r e to some form or forms of ionizing radiation. Research related to this subject is found in Pineri et al. (1976), Bowlt (1976), Perret and Fournie (1975), and Vanderschueren and Linkens (1978a). What is ob­ served in many cases is a very pronounced increase in the magnitude of the ρ peak (see below), indicating the creation of charged species, at least some fraction of which are mobile at a suitably high t e m p e r a t u r e (specifi­ cally, t h e one at which space charges are released in a large quantity). O n e of the current challenges in T S D C analysis is establishing exactly w h e r e in a t h e r m o g r a m t h e role of ionic species is manifested. In m a n y c a s e s , one is able to correlate discharge p e a k s with dielectric loss m a x i m a o b s e r v e d dielectrically, and in this way it is c o m m o n for the assignment of

5.

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Discharge Current Analysis

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233

dipolar motions to be extended from dielectric studies to the T S D C analy­ sis. Such a p r o c e d u r e , h o w e v e r , b e c o m e s m o r e tenuous when the relaxa­ tion process in question coincides with the major dispersion, the glass transition. Observations of T S D C m a x i m a that coincide with Tg lend con­ fidence to the proposition that it is the dipolar n a t u r e of t h e side g r o u p s on the chains or portions of the main chain t h e m s e l v e s that acquire mobility. H o w e v e r , activation energies for the glass transition are often calculated to be in the range 1-3 eV, a n d , as such, it is also possible that the dielectric effect might actually be due to t h e t r a n s p o r t of real charge. T h e ambiguity in this assignment still needs to b e resolved. In only one c a s e (Stupp and Carr, 1978) has direct m e a s u r e m e n t of dipolar orientation been followed through the simultaneous depolarization of the p o l y m e r . In this w o r k , the slight preference in orientation of nitrile side groups in polyacrylonitrile w a s o b s e r v e d to decay o v e r exactly the s a m e t e m p e r a t u r e range as the major relaxation p r o c e s s . T S D C analysis of a large n u m b e r of polymers reveals, h o w e v e r , that at a t e m p e r a t u r e about 30-50°C a b o v e Tg a second discharge peak is ob­ served. This is normally called the ρ peak, so designated b e c a u s e it im­ plies resistivity and is related to the t r a n s p o r t of charge (van Turnhout, 1975; V a n d e r s c h u e r e n , 1972). An e x a m p l e of j u s t how c o m m o n the ρ peak is can be seen in Fig. 9, which s h o w s T S D C t h e r m o g r a m s for a homolo­ gous series of acrylate p o l y m e r s (Vanderschueren and L i n k e n s , 1977). T h e thermal activation of the ρ peak conforms most closely to the W L F rela­ tionship, while, as implied by the previous p a r a g r a p h , the main discharge

Τ (°C)

Fig. 9. T S D C thermograms of a series of acrylate polymers showing the ρ peak at a temperature about 30°C a b o v e the primary dispersion (a peak). [From Vanderschueren and Linkens (1977, Fig. 3b), reprinted with permission.]

234

Stephen Η.

Can

peak assigned to the glass transition in fact o b e y s the Arrhenius relation­ ship (Bui et ai, 1974). In an earlier study by Stupp and Carr (1975), it was shown that the dipolar p e a k s d e c a y e d after a single t e m p e r a t u r e s c a n , but that the ρ peak recurred in slightly diminished form upon a repeated t e m p e r a t u r e scan. This is characteristic of a peak arising from space charges and is p r e s u m a b l y due to the fact that ions that had been dis­ placed macroscopic distances during the initial polarization d e t r a p and drift at retarded rates, even though the specimen is in t e m p e r a t u r e range where their discharge can o c c u r (Pillai et al., 1975). F u r t h e r m o r e , ρ p e a k s are not seen in dielectric dispersion m e a s u r e m e n t s , but they are seen in T S D C t h e r m o g r a m s (van Turnhout, 1977). Even if the concentration of mobile anions and cations is u n e q u a l , ρ peaks will be o b s e r v e d . Further­ m o r e , ρ p e a k s will be seen if one type or another of the anions or cations is not mobile, as would be the case for ionic sites b o u n d to the p o l y m e r chains t h e m s e l v e s . T h e coincidence of the observation of a major relaxation, the ρ p e a k , at t e m p e r a t u r e s 30-50°C a b o v e Tg and the proposition of a liquid-liquid transition (Tü) (Gillham and B o y e r , 1977) must be noted ( L a c a b a n n e et al., 1980). The exact molecular nature of the Tu transition is still the subject of some controversy ( N e u m a n n and M a c K n i g h t , 1981), but it is attributed, at least in part, to a distinct change in the nature of molecular mobility. F u r t h e r work needs to be done to establish j u s t how plausible the proposition is that ρ peaks in T S D C t h e r m o g r a m s a r e , in fact, manifes­ tations of the same effect reported from studies that o b s e r v e a Ttl transi­ tion. W h a t e v e r the situation actually is, at least, can be regarded as in­ volving either a new m o d e of chain segmental motions that permit rapid transport of ions or motions that abolish trapping sites at which ions w e r e localized in their initially polarized condition. The primary variant of the T S D C method of polymer analysis is the thermally stimulated polarizing current (TSPC) t e c h n i q u e . This technique has been reported in some detail by von Turnhout (1978) and others (Wieder and Kaufman, 1953; Vanderschueren and Linkens, 1978b). O n e of the primary advantages of the T S P C method is that one can scan the relaxation spectrum without using an experiment that requires previous heating of the specimen to an elevated t e m p e r a t u r e . This t e c h n i q u e has been exploited effectively by Vandershueren and Linkens (1978b). In their study, it was possible to distinguish clearly between polarization contribu­ tions arising from space-charge drifting and from dipolar orientation. Other studies have emphasized how this method can give information on the relaxation times of polarizable chain segments (Vanderschueren and Linkens, 1978b). It is also possible to m a k e instructive variations on the T S D C method

5.

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Discharge Current Analysis

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235

Polymers

itself. T h e s e have been s u m m a r i z e d by van Turnhout (1978) and are shown in Fig. 10. Figure 10a illustrates the standard T S D C analysis con­ figuration. T h e overall electrical field in this configuration is z e r o , since the internal polarization gives rise to an internal electrical field equal in magnitude but opposite in sign to that imposed externally by the image charges in the electrodes. T h u s , integrating in the thickness direction χ from the b o t t o m surface to the top surface located at d yields a null value for the overall electrical potential of this three-layered s t r u c t u r e . One m e a s u r e s , as has been stated previously in this article, the current that flows in this external circuit when the sample is h e a t e d , following the stagewise decay of polarization through the concomitant release of image charges from the contracting e l e c t r o d e s . An alternative configuration is shown in Fig. 10b, in which a finite air gap of thickness s exists between the top of the dielectric (nonmetallized surface) and the u p p e r e l e c t r o d e . In this c a s e , it is possible to o b s e r v e the neutralization of space charges inside a polarized dielectric b e c a u s e of their subsequent drift upon heat­ ing. This o c c u r s b e c a u s e the electrical potential across the dielectric is not z e r o . T h e fact that the upper electrode is placed some distance from the upper surface m e a n s that part of the image charge it should have is in the lower, contacting electrode. T h u s , integrating the electrical fields due to both the internal polarization and the external charges contained in the electrodes results in a nonzero internal electrical field. It is this nonzero internal electrical field that causes space charges to drift when polariza(a) Current

(b) TSDC

(c)

Current T S D C w i t h air g a p

Charge

Fixed air gap s

Variable air gap

TSDC

:

Configuration Shorted electrodes Field: Ε dx = 0

/ o

Current

:

Fig. 10. Three test configurations for performing thermally stimulated measurements on polarized dielectrics. S e e text for detailed description. [From van Turnhout (1975, Fig. 9-1), reprinted with permission.]

Stephen Η. Carr

236

tion o c c u r s . T h e primary advantage is that a homocharge possessed by the film will usually decay at higher t e m p e r a t u r e s than t r a p p e d space c h a r g e s . The third configuration, shown in Fig. 10c, illustrates a method essentially for measuring surface potential by a vibrating electrode m e t h o d . In this kind of experiment, a backing voltage is applied to the u p p e r e l e c t r o d e , as it is physically oscillated up and d o w n in the space j u s t a b o v e the electret. An electronic feedback system regulates the applied potential such that the overall bias on the configuration is always nullified. The backing volt­ age applied, then, is the experimental variable detected while the entire specimen is heated. Although a very wide variety of physical aspects of polymers can be characterized via their relaxation characteristics a n d , therefore, via T S D C analysis, there are a few general areas that are also worthy of mention. T h e first involves the physical aging of p o l y m e r s . In some c a s e s , the T S D C method can simply be used as a screening method for determin­ ing the service life of an electret material (Sharp and G a r n , 1976). S o m e ­ times these aging effects are simply due to the u p t a k e of w a t e r from the surrounding a t m o s p h e r e , and if this is in fact the c a s e , then they can also be characterized via T S D C analysis (Pillai et al., 1972b; V a n d e r s c h u e r e n , 1974). The primary area in which T S D C analysis provides information on aging relates to the role relaxation p r o c e s s e s have in strength, stress re­ laxation, and c r e e p . T h e s e effects involve various combinations of the vari­ ous kinds of relaxation effects, including those of side groups and those involving the main p o l y m e r chain b a c k b o n e s t h e m s e l v e s . Consistent with this picture is the fact that some thermally activated p r o c e s s e s detected by T S D C analysis obey the Arrhenius rate law, while others obey the W L F kind of rate law. Direct correlation has been m a d e recently (Pillai et al., 1972b) between yield stress and activation energy of one part of the ß-relaxation process in poly(bisphenol A carbonate). T h e s e data suggest that the rate-limiting step in the yielding event is one that can be detected by T S D C analysis. O t h e r studies (Berticat et al., 1978; L a m a r r e et al., 1980) have m a d e direct m e a s u r e m e n t s of c r e e p and correlated t h e m di­ rectly with T S D C data. A detailed study of the long-term relaxation ef­ fects in p o l y v i n y l chloride) has emphasized how T S D C analysis can pro­ d u c e the information n e e d e d to predict effects related to long-chain r e a r r a n g e m e n t s . This study spans the range of mechanical properties from bulk-level stress-strain relationships to microscopical strain such as that e n c o u n t e r e d in c r e e p (van Turnhout et al., 1977; Struik, 1978). REFERENCES Adams, E. P. (1927). J. Franklin Inst. 204, 469. Ai, B . , Stoka, C. P., Giam, Η. T., and Destruel, P. (1979). Appl. Phys. Lett. 34, 821. Alexandrovich, P., Karasz, F. E . , and MacKnight, W. J. (1976). J. Appl. Phys. 47, 425. Aoki, Y., and Brittain, J. O. (1976). J. Appl. Polym. Sei. 20, 2879.

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Thermally

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Analysis

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