dc-electrical conductivity as a method for monitoring radiation curing of unsaturated polyester...

DC-electrical conductivity as a method for monitoringradiation curing of unsaturated polyester resins III.

Evaluation of results

Irina PucicÂ *, Franjo Ranogajec

Rudjer BosÏkovicÂ Institute, Zagreb, Croatia

Received 22 October 1996; accepted 5 February 1998

Abstract

The results of DC-electrical conductivity monitoring of radiation and thermally initiated crosslinking ofunsaturated polyester resins are interpreted using conductivity data itself instead of commonly used logarithmic dataform. The main setbacks of logarithmic conductivity data were the shift toward longer reaction time compared to

non-logarithmic conductivity data and extraction analysis results and pronounced scattering at the end of thereaction so it was impossible to detect vitri®cation point. By revision of approach to analysis of results, fullsensitivity of the electrical conductivity method to structural changes in the reacting system was shown. Theapparent rate constants calculated from conductivity itself showed the in¯uence of upper liquid±liquid transition on

the rate of radiation induced reaction that could not be seen if the logarithm of conductivity was used. In¯uence ofdose rate e�ects and electrical ®eld e�ects on reaction rate were detected too and con®rmed by DSC measurements.All details of reaction can be detected using ®rst derivative of conductivity and in the case of thermally initiated

reaction two maxims of reaction rate were found that are probably caused by local increase of temperature due tohighly exothermic reaction. # 1999 Published by Elsevier Science Ltd. All rights reserved.

1. Introduction

In two previous papers (PucicÂ and Ranogajec, 1995,

1996) results of monitoring radiation and thermally

induced crosslinking of unsaturated polyester resin

with styrene by measurement of DC-electrical conduc-

tivity were presented. During the course of the reac-

tion, viscosity increased due to formation of three-

dimensional network, reducing the mobility of charge

carriers. Accompanying signi®cant decrease of electri-

cal conductivity was high enough to enable good sensi-

tivity. The advantages of this method are simplicity

and good reproducibility of measurements. Unlike the

case of most conventional kinetic methods, physical

changes of the system (changes of viscosity, vitri®ca-

tion) did not make the measurements impossible. The

determination of gel content and free styrene content

by extraction analysis, as a non-electrical method,

showed that the decrease of electrical conductivity is

directly related to the extent of crosslinking reaction.

Obtained results proved that the electrical conductivity

method is a very promising method for following the

course of polymerization and/or crosslinking reaction,

especially because it is suitable for the direct in-source

monitoring of radiation polymerization.

The electrical ®eld enhanced crosslinking of unsatu-

rated polyester resin, probably due to the favourable

orientation of polar resin chains. That in¯uence was

detected by conductivity measurement and con®rmed

by extraction analysis. On the other hand, lower ®eld

strengths were preferred when structural changes in

resin, such as liquid±liquid transition (Boyer 1987;

1992) were detected. It has to be pointed out that

upper liquid±liquid transition Tlr caused by breaking

of intramolecular interactions in the polyester coil, was

Radiation Physics and Chemistry 54 (1999) 95±108

0969-806X/99/$19.00 # 1999 Published by Elsevier Science Ltd. All rights reserved.

PII: S0969-806X(98 )00191-1

Radiation PhysicsandChemistry

PERGAMON

* Corresponding author.

detected in the same temperature range where radi-

ation induced reactions were conducted (PucicÂ and

Ranogajec, 1992).

To obtain kinetic information out of electrical con-

ductivity measurements, it is common practice based

on works of War®eld and Petree (1959) and Kagan et

al. (1968) to present the experimental data as the log-

arithm of conductivity versus the reaction time or radi-

ation dose. They proposed the expression for

calculation of reaction rate:

klns t � ln��lnst ÿ lns0�=�lns1 ÿ lns0�� 1�

where st is conductivity at time t, s0 is initial conduc-

tivity and s1 is ®nal value of conductivity at the end

of the reaction. It is not common practice to present

data collected by various experimental methods in the

logarithmic form. From the above-mentioned papers it

is not clear why logarithm of electrical conductivity

should be used instead of the conductivity itself.

Presumably the reason may be that before more than

25 years it was di�cult to handle a data range of

several orders of magnitude.

In this paper we will show that use of conductivity

data in logarithmic form may cause a partial loss of in-

formation about reaction. Therefore a di�erent

approach to conductivity data analysis for both the

radiation and thermally induced crosslinking of unsa-

turated polyester resin is presented. This correction

showed the sensitivity of the electrical conductivity

method to structural changes in the reaction system.

Fig. 1. The change of electrical conductivity of Chromoplast during radiation induced crosslinking at the dose rate B = 0.345 kGy/

h at di�erent temperatures.

I. PucicÂ, F. Ranogajec / Radiation Physics and Chemistry 54 (1999) 95±10896

2. Experimental

All the experiments were carried out using the com-

mercial unsaturated polyester resin, Chromoplast,

poly(propyleneglycol-maleate) with approximately 30%

styrene, supplied by Chromos, Zagreb. Experimental

details were described earlier (PucicÂ and Ranogajec,

1992, 1995) so here will be mentioned only those that

are necessary for a better understanding of this article.

All reactions were conducted isothermally at preset

temperature. The measurements were carried out at

three electrical ®eld strengths: 2.5, 25 and 250 kV/m.

Radiation initiated crosslinking was performed in

panoramic 60Co gamma source at three dose rates

A = 3.05 kGy/h, B = 0.354 kGy/h and C = 0,096

kGy/h, in the temperature range 290 to 345 K.

Thermally initiated crosslinking was started by

immersing the cell with the resin sample into the sili-

cone oil bath heated to a preset temperature high

enough to cause spontaneous crosslinking, between

380 to 423 K. No initiator was needed in this tempera-

ture range.

The electrical conductivity s was calculated from

measured current data I:

s � e0I=C0V �2�where e0 is permittivity of vacuum, C0 is capacity of

the empty cell, and V is the applied voltage.


h at 290 K and its ®rst derivative. The reaction stages could be easily detected using ®rst derivative of conductivity: 1 represents in-

hibition period, 2 normal propagation period and 3 di�usion controlled propagation period of crosslinking.

I. PucicÂ, F. Ranogajec / Radiation Physics and Chemistry 54 (1999) 95±108 97

The extraction analysis as a reference method for

verifying results of electrical conductivity measure-

ments was described in details in previous paper (PucicÂ

and Ranogajec, 1996). Free styrene content changes

proportionally to conductivity and can be determined

at any reaction step, while gel content can be deter-

mined only in a later part of the reaction and changes

inversely to conductivity. As another reference method

di�erential scanning calorimetry was used to con®rm

previously determined combined e�ect of electrical

®eld and dose rate. The residual reactivity of partially

radiation crosslinked samples was determined at four

samples irradiated to 1, 1.5, 2 and 3 kGy at each dose

rate A, B and C under electrical ®eld strength 0 and 25

kV/m at 290 K. Dynamic scans were performed atheating rate 5 K/min from 323 to 523 K.

3. Results and discussion

Under the action of ionizing radiation or due toheat, free radicals are formed in unsaturated polyester

resin. Three di�erent free radical reactions are possiblefollowing initiation step (Yang and Lee, 1988; Huangand Leu, 1993). One of them, styrene homopolymeri-

zation does not result in crosslinking, but usually it isnegligible and is of no signi®cance for cases discussedhere. The reaction between polyester unsaturations


h at 290 K in non-logarithmic (solid symbols) and logarithmic form (open symbols). The logarithm of conductivity is calculated

from the same data presented in non-logarithmic form. The changes of free styrene content after the extraction are shown too

(large solid squares).


themselves is relatively improbable due to steric hin-

drance. The third reaction, the copolymerizationbetween polyester unsaturation and styrene, is in factcrosslinking. Three-dimensional network is formed

only in case of intermolecular reaction while intramole-cular crosslinking results in shrinking of polyester coiland formation of microgels (Liu et al., 1994). Free-rad-

ical polymerization or crosslinking reactions of com-mercial monomers have three characteristic stages:induction period where there is no reaction due to in-

hibitor added, propagation period and vitri®cation. Incase of crosslinking, the formation of three-dimen-sional network reduces the possibility of bimolecular

termination that causes an increase of free radical con-centration and an enhancement of reaction rate whatresults in gel e�ect. The concentration of styrene

monomer is much greater than that of polyester unsa-

turations so the rate of crosslinking is considered to beof ®rst order.The conductivity change during radiation initiated

crosslinking at di�erent temperatures is plotted inFig. 1. The di�erence between values of conductivityat the start of the reaction is caused by its temperature

dependence and is about an order of magnitude if low-est and highest temperature is compared. The lastingof induction period was independent of temperature to

about 320 K. Previous experiments showed that, in thistemperature range, the rate of radiation initiation isonly dose rate and not temperature dependent but the

overall reaction rate increased with temperature.At ®rst glimpse it is rather di�cult to detect all men-

tioned stages of the crosslinking reaction from the con-

Fig. 4. The ®rst derivative of electrical conductivity from Fig. 2 (lower curve) and the ®rst derivative of the same data in logarith-

mic form (upper curve). The reaction maximum of logarithmic data is shifted to higher times and vitri®cation point of the system

could not be detected due to data scattering.


ductivity curve itself such as in Fig. 1, but they are all

easily seen on its ®rst derivative plot shown in Fig. 2.During the induction period (indicated by 1 in Fig. 2)

there is no crosslinking reaction and no signi®cantchange of conductivity so the ®rst derivative is ap-proximately zero. In the ®rst propagation stage (indi-

cated by 2 in Fig. 2) the rate is controlled by law ofmass and the ®rst derivative increases, it reaches maxi-

mum and decreases when di�usion limitations set in(indicated by 3 in Fig. 2). The highest reaction rate

period can be seen from conductivity itself by morecareful inspection. At the end of reaction the systemvitri®es, the conductivity becomes constant and its ®rst

derivative approaches zero.In our previous papers it was shown that electrical

conductivity is inversely related to formation of theproductÐthe network. Since it is common practice to

use lns instead of s itself, both approaches will be

compared in following text. The same reaction data,

both as pure conductivity and its logarithm, are

plotted in Fig. 3 together with changes of free styrene

content, determined on separate samples but in same

conditions. It can be easily seen that, while the conduc-

tivity data itself are in good agreement with the extrac-

tion results, there is considerable discrepancy between

extraction results and logarithmic data. Not only the

change of the lns is delayed compared to change of

free styrene content but there is no leveling o� at the

end of the reaction which can be seen in both pure

conductivity data and free styrene content. This

changes are brought in by logarithmic function and

similar delay can be seen between the extent of reac-

tion calculated from DSC and logarithm of conduc-

Fig. 5. The plot of two sets of conductivity data as (stÿs0)/(s1ÿs0) and (lnstÿlns0)/(lns1 ÿlns0) of radiation initiated crosslinking

at 310 K. In both cases the same st value was used for s1 and ln s1, respectively. Data smoothing was avoided to show the e�ect

of data analysis approach.


tivity in paper by Belucci et al. (1995) that is chosen as

an recent example.

The ®rst derivatives of the same conductivity data as

in Fig. 3 and its logarithmic form are shown in Fig. 4.

The scattering of data in both cases is caused by noise

and increased by the di�erentiation operation. The

data were not smoothed on purpose to show the e�ects

of logarithmic operation in full scale. The delay of log-

arithmic data compared to non-logarithmic can be

seen again from the positions of maxims. The scatter-

ing of logarithmic data in di�usion controlled period

of the reaction is so great that it makes it very di�cult,

in some cases impossible, to detect the vitri®cation

point.

By comparing the extraction results to the changes

of conductivity presented in logarithmic form it is

obvious that use of lns for kinetic analysis could

reduce sensitivity of the method and, in cases whereconductivity change is smaller, give completely false

results. Because of that, we chose to analyse the con-

ductivity data using pure conductivity data, presentedby Eq. (3):

klns t � ln��st ÿ s0�=�s1 ÿ s0�� 3�the symbols are the same as in Eq. (1)).

The rates of reaction were determined as follows:

the relations (stÿs0)/(s1ÿs0) and (lnstÿlns0)/(lns1ÿlns0) were plotted against the reaction time. The

choosing of ®nal conductivity value used for s1 wascomplicated due to signi®cant scattering in logarithmic

data at the end of the reaction due to logarithmic func-tion that modi®es data with low values more than the

Fig. 6. The Arrhenius plot of the logarithm of the apparent reaction rates calculated from the conductivity change itself (solid sym-

bols) and its logarithm (open symbols) during radiation crosslinking of Chromoplast. Change of reaction rate at Tlr transition

could be detected only from the apparent rate constants calculated from conductivity data itself.


data with high values. In Fig. 5, two sets of data are

shown, the same st was used for both s1 and lns1,the time delay of logarithmic data is again obvious in

both cases. The reaction extents were calculated from

slope of linear parts of those curves, that parts also

appeared at di�erent reaction times and had to be cho-

sen separately for logarithmic and non-logarithmic

data. The ends of linear parts of the logarithmic data

were shifted into intense scattering zone.

The same procedure was applied to data sets for

whole temperature range of radiation induced cross-

linking and the Arrhenius plot of the reaction rates

calculated using both Eqs. (1) and (3) are shown in

Fig. 6. It can be seen that reaction extents calculated

from logarithmic conductivity data, klns, (empty signs)

can be ®tted linearly giving one straight line but with

signi®cant scatter. On the contrary, reaction extents

calculated from the conductivity data itself, ks, fall on

two linear segments with much less scattering. Linear

segments intersect in same temperature region where

the upper liquid±liquid transition, Tlr was detected

(PucicÂ and Ranogajec, 1992). It was mentioned that at

Tlr transition temperature intramolecular interactions

were broken and the polyester coil becomes more

loose. This allowed styrene molecules to penetrate the

coil more easily so at temperatures above the upper

liquid±liquid transition more polyester double bonds

became available to crosslinking. That resulted in low-

ering of the activation energy of crosslinking what can

be seen as change of slope in Fig. 6. The temperature

of Tlr transition determined from the intersection

point of linear segments in Fig. 6 was 321 K and is in

Fig. 7. The change of electrical conductivity (open symbols) and its ®rst derivative (solid symbols) during thermally induced cross-

linking of Chromoplast at 393 K and at the ®eld strength 25 kV/m. The ®rst derivative revealed two reaction rate maxims that are

marked by dashed lines.


good agreement with Tlr temperature determined fromtemperature dependence of electrical conductivity

measurements, DSC and NIR spectrophotometry on

same samples (to be published).

Two major de®ciencies can be avoided using pure

conductivity data instead of logarithmic: the delay inthe reaction extent compared to other methods and

loss of information about structural changes, that

should in¯uence the reaction rate, particularly in cases

when such changes increase the accessibility of reaction

sites. If such a change cannot be detected, something

must be wrong with the data analysis procedure. The

error induced using the logarithmic data was signi®-cant and caused pronounced scattering at lower tem-

peratures that masked the changes of reaction rate due

to the structural transformations. In favour of use of

pure conductivity data is the fact that scattering of cal-culated reaction rates is signi®cantly less than in caseof logarithmic data, the structural changes are easily

detected and there is good agreement with the extrac-tion analysis. The sensitivity of electrical conductivitymethod can be seen in full scale only if the interpret-ation of the results does not reduce it.

3.1. The e�ect of the electrical ®eld on the rate ofthermally initiated crosslinking

The di�erences between the conductivity curves ofthermally and radiation induced reactions are caused

by the fact that the temperature range of radiationinduced reaction is below the range of spontaneousthermal crosslinking so the samples for radiation cross-

Fig. 8. The Arrhenius plot of the apparent reaction rates calculated from the conductivity change during thermally initiated cross-

linking of Chromoplast. Open symbols denote apparent rate constants of the ®rst and solid symbols denote apparent rate constants

of the second reaction period at electrical ®eld strengths 2.5, 25 and 250 kV/m. The second reaction rates are more sensitive to elec-

trical ®eld.


linking could have achieved thermal equilibrium prior

to reaction. During the induction period of thermallyinduced reaction the conductivity ®rst rose due to tem-

perature increase from room to reaction temperature.

The lasting of the induction period strongly depended

on temperature while induction period of radiationcrosslinking is almost independent of temperature.

Further di�erences cannot be seen from the conduc-

tivity curve itself, but its ®rst derivative revealed two

maxims corresponding to two separate rate maxims inthe propagation phase (Fig. 7). At temperatures about

370 K even the conductivity curve itself showed two

separate propagation slopes. The reason could be that

the heat released during the ®rst propagation periodand not transferred out of the sample mass enhanced

crosslinking and induced second rate increase.

Dielectric spectroscopy in similar reaction system

(Day, 1994) showed that there are di�erences betweenreaction conversion at surface and in deeper parts. At

surface the reaction began earlier but proceeded slower

than in the middle part of the sample where it beganlater but was faster due to released heat of the reaction

that could not be dissipated because of poor thermal

di�usivity. Day found this e�ect to be signi®cant for

samples thicker than 5 mm, his experiments were per-formed at single temperature, 423 K. It can be

expected at lower temperatures that heat released

during the reaction had more in¯uence on reaction

rate what is in fact evident from our experiments.

In case of radiation induced reaction the secondmaximum did not appear because the reaction was

conducted in the temperature range below the range of

Fig. 9. Residual heat determined after irradiation of Chromoplast to selected total doses at 290 K, at three dose rates and electrical

®elds strengths 0 (open symbols) and 25 kV/m (solid symbols). The residual heat con®rms delayed crosslinking at dose rate A.


thermal initiation and initiation depended only on

dose rate as it was shown before. The heat released

during reaction was not high enough to induce further

initiation reaction and cause the appearance of second

rate maximum.

The reaction rates were calculated for each rate

maximum of thermally initiated crosslinking. Fig. 8 is

the Arrhenius plot of apparent rate constants of ther-

mally initiated crosslinking calculated from conduc-

tivity data at three di�erent electrical ®eld strengths.

There was almost no in¯uence of electrical ®eld on the

reaction rate (ks)1 at the beginning of propagation

period, but signi®cant changes of reaction rate with

®eld strength were detected in later period of propa-

gation, as the increase of the second reaction rate

(ks)2. Electrical ®eld induced orientation of polar

polyester chains what was already detected in di�erent

types of experiments (PucicÂ and Ranogajec, 1995,

1996).

It is known that electrical ®eld can in¯uence poly-

merization and crosslinking reaction depending on po-larity of monomers and polymers and reaction

conditions. Dudek (1973) found that polymerization

rate of polar monomers increased under the in¯uence

of electrical ®eld. Orientation induced in unsaturated

polyester resins had more in¯uence at the second

propagation maximum. At the beginning of cross-

linking, in the ®rst stage of propagation, there were

enough double bonds available to the reaction, and the

system was liquid so di�usion of monomers was easy

and the orientation had no e�ect on the reaction. On

the contrary, in the second stage a great part of double

bonds had already reacted and the rest was less avail-

able to reaction. Also, the viscosity was much higher

Fig. 10. The Arrhenius plot of vitri®cation dose during radiation initiated crosslinking. In the temperature range vitri®cation dose

under liquid±liquid transition is constant and above liquid±liquid transition vitri®cation dose becomes lower.


and di�usion of monomers was greatly reduced. Insuch conditions, orientation that increased accessibilityof reaction sites had much more in¯uence on the reac-tion rate. That should be the reason why the (ks)2reaction rate increased at higher ®eld strengths. In thetemperature range of thermally initiated reaction therewas no structural change in resin (as shown in Fig. 6)

so no change of slope in the Arrhenius plot wasdetected.

3.2. The e�ect of the electrical ®eld and dose rate on

radiation initiated crosslinking

The increase of reaction rate of radiation initiated

crosslinking under the in¯uence of electrical ®eld wasgreatest at low dose rate, C, at medium dose rate, B, itwas still pronounced but at highest dose rate, A, the

e�ect of the ®eld was insigni®cant (PucicÂ and

Ranogajec, 1996). These results were obtained by elec-

trical measurements and extraction analysis. The doses

to which the samples for extraction analysis were irra-

diated were chosen according to changes of electrical

conductivity so the total doses were di�erent at each

dose rate. In the present work the resin samples were

irradiated to the same total dose at each dose rate and

residual reactivities were determined using di�erential

scanning calorimetry. The results are plotted in Fig. 9.

The residual reactivity was highest in samples irra-

diated at higher dose rate A because during the ir-

radiation the concentration of primary radicals was

high and termination was favoured over the propa-

gation that would lead to crosslinking. The remaining

double bonds reacted thermally and con®rmed that

extraction analysis results were not in¯uenced by

Fig. 11. The Arrhenius plot of vitri®cation times during thermally initiated crosslinking at electrical ®eld strengths 2.5, 25 and 250

kV/m. The vitri®cation times are shorter at higher temperatures, but there is no slope change because there is no structural change

in the temperature range of thermally initiated reaction.


choosing di�erent total doses at given dose rates. Thein¯uence of electrical ®eld at lower dose rates B and C

is also obvious from residual reactivity although thereis some scattering caused by lower sensitivity of calori-metric method compared to electrical measurements

and extraction analysis.

3.3. The extent of the reaction determined fromvitri®cation point of the reaction system

In order to determine the degree of conversion atdi�erent temperatures, the conductivity of all thereacted samples should be determined at the same tem-perature. It is very di�cult to choose such referent

temperature because at room temperature the conduc-tivity of crosslinked resin can be so low that its valuewould be determined with great uncertainty. If higher

temperature was chosen, there is possibility that heat-ing could induce further crosslinking reaction insamples reacted at lower temperatures. Increasing of

®eld strength could induce various undesired e�ectsand even change conduction mechanism. Structuralchanges in the resin between reaction and referent tem-perature can also in¯uence the results. Because of this,

the conversion of crosslinking from electrical conduc-tivity can be compared only for reactions conducted atsame temperature. The widespread practice to compare

the extent of reactions performed at di�erent tempera-tures using logarithmic data without measurement atreference temperature is misleading. Such a problem

can be avoided using characteristic reaction times suchas time of vitri®cation, at which point it is presumedthat the isothermal reaction is completed at that tem-

perature.Under the assumption that reaction rate depended

only on the degree of crosslinking, Batch andMacosko (1994) have shown linear relationship

between the reaction time and degree of crosslinking.From this it can be deduced that vitri®cation time ordose was related to certain extent of crosslinking and

by comparing the vitri®cation times it is possible to in-vestigate the in¯uences of di�erent reaction conditions.In cases of direct monitoring of crosslinking the vitri®-

cation times and doses for given reaction temperaturewere determined as the point at which ®rst derivativeof conductivity became zero at the end of the reaction.The vitri®cation doses determined by in-source moni-

toring of crosslinking by electrical conductivity methodat di�erent temperatures showed changes related toliquid±liquid transition (Fig. 10). In the temperature

range below the transition temperature, they were ap-proximately constant and at temperatures above thetransition vitri®cation dose was getting smaller. Their

temperature dependence is similar to dependence of kswhich led to the conclusion that it depended on degreeof order in the resin as well.

The vitri®cation doses have already been estimatedby the di�erent type of electrical conductivity measure-

ments described earlier (PucicÂ and Ranogajec, 1992).The main di�erence between the two methods is thatthe measurements described in present paper were per-

formed directly during the radiation crosslinking. Inthe previous case, a di�erent kind of polyester, poly-(hexanediol-maleate) resins, were irradiated prior to

the measurement, then the temperature dependence ofthe DC-conductivity was measured and this wasrepeated after another irradiation step. The apparent

activation energy of the electrical conductivity (not tobe confused with the activation energy of crosslinking)was then calculated for each step and plotted againstthe dose. The apparent activation energy of the electri-

cal conductivity increased with increase of dose andthen leveled o�. The vitri®cation dose of the systemwas the dose at which leveling o� was detected, it var-

ied between 4 and 5 kGy and changed according tochanges of reactivity. Reactivity of poly(hexanediol-maleate) resins increased with increase of fumarate

content in the resin which resulted in a decrease of thevitri®cation dose. On the other hand the vitri®cationdose of commercial resin Chromoplast determined in

the same manner was about 1.6 kGy. That di�erencein reactivity could be caused by di�erent chemicalstructure of resins. The number of carbon atomsbetween two double bonds in poly(hexanediol-maleate)

was greater and the network was more loose than inthe case of poly(propyleneglycol-maleate), so a higherdose was needed to achieve vitri®cation and ®nal con-

ductivity. These facts show that vitri®cation time ordose can give valuable information about reaction sys-tem.

The in¯uence of electrical ®eld on the vitri®cationtime was tested on thermally initiated crosslinking. Itcan be seen that the stronger the electrical ®eld was,the system reached vitri®cation earlier. In Fig. 11

Arrhenius plots of vitri®cation times are shown atthree di�erent electrical ®eld strengths. As wasobserved, the vitri®cation times were getting shorter as

electrical ®eld strength increased. There is no structuralchange in the temperature range of thermally initiatedreaction so the slopes at di�erent ®eld strengths were

identical. Such behaviour was expected and is similarto changes of apparent rate constants that are greaterabove the Tlr temperature than below it.

4. Conclusions

The DC-electrical conductivity data collected duringradiation and thermally initiated crosslinking of unsa-

turated polyester resins were interpreted using data innon-logarithmic form while the basis for calculation ofkinetic parameters in the older model (War®eld and


Retree, 1959; Kagan, et al., 1968) was logarithm of theconductivity. By comparing the logarithmic and pure

conductivity data to extraction analysis results it wasshown that using the logarithmic data induced inac-curacies: the shift of reaction parameters to higher

reaction times and increased scattering of the lowerdata values at the end of the reaction.Use of the pure conductivity data made it possible

to show full sensitivity of the method. The valuable in-formation of the e�ect of structural changes on cross-linking could not have been detected from logarithmic

data. The agreement with reaction parameters deter-mined by other experimental methods (extraction,DSC) was also better when conductivity data itselfwere used.

The ®rst derivative of electrical conductivity made iteasier to determine di�erent reaction periods.Thermally initiated reaction had two reaction rate

maxims, the second being due to rate increase causedby heat release in the ®rst part of the reaction. Thesecond maximum was more sensitive to changes in

electrical ®eld strength because favourable orientationof polyester chains had greater importance in partiallycrosslinked system. The combined in¯uence of electri-

cal ®eld and dose rate on crosslinking reaction wascon®rmed by di�erential scanning calorimetry. Thevitri®cation point of the reacting system could be easilydetected from the point where the ®rst derivative of

electrical conductivity reached zero. It re¯ected the in-¯uences of reaction conditions and reactivity of polye-ster.

Acknowledgements

The ®nancial support by the Ministry of Science,Technology and Informatics of the Republic ofCroatia and by the International Atomic Energy

Agency, Vienna, under Research Contract No. 6128/RB is gratefully acknowledged.

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