towards a molecular approach to physical ageing in poly(methyl methacrylate)

Polymer International 47 (1998) 65È71

Towards a Molecular Approach toPhysical Ageing in Poly(methyl

methacrylate)

Richard A. Pethrick* & William J. Davis

Department of Pure and Applied Chemistry, University of Strathclyde, Thomas Graham Building, 295 Cathedral Street, GlasgowG1 1XL, UK

(Received 15 October 1997 ; revised version received 12 January 1998 ; accepted 29 January 1998)

Abstract : Physical ageing studies are reported on poly(methyl methacrylate)(PMMA) using positron annihilation lifetime spectroscopy (PALS), dielectricrelaxation spectroscopy (DRS) and dynamic mechanical thermal analysis(DMTA). A comparison of the results obtained from these di†erent techniquesindicates that the assumption of thermorheological simplicity for physical ageingis most probably questionable. Physical ageing appears to be primarily con-cerned with a loss in the relaxation strength in the region below the glass tran-sition temperature as monitored isothermally using DRS. Analysis of the “ageingratesÏ obtained from these three very di†erent types of observation indicates thepossibility of a common molecular origin to the processes observed. 1998(Society of Chemical Industry

Polym. Int. 47, 65È71 (1998)

Key words : positron annihilation lifetime spectroscopy ; dielectric relaxationspectroscopy ; dynamic mechanical thermal analysis ; physical ageing studies ;poly(methyl methacrylate)

INTRODUCTION

Physical ageing is a phenomenon which has been inves-tigated extensively over the last 25 years.1,2 The pheno-menon is associated with the slow approach toequilibrium of a system quenched to below its glasstransition temperature.3 The quenching process freezesinto the system disorder (entropy), which reÑects thethermal history of the sample. Physical ageing leads tocreep, an increase in tensile modulus, a decrease in lossmodulus, an increase in the glass transition tem-perature, shrinkage and densiÐcation in the polymermatrix.

A variety of di†erent phenomenological models havebeen developed to describe these processes.1,2,4h6Unfortunately, it is found that model or analytical

* To whom all correspondence should be addressed.Contract/grant sponsor : EPSRC.Contract/grant sponsor : Ford Corporation.

approaches suited for the interpretation of one type ofexperiment are often inadequate when applied toanother. In this paper an attempt will be made to probethe molecular origins of the process occurring duringphysical ageing by the use of three di†erent types ofrelaxation techniques. Positron annihilation lifetimespectroscopy (PALS) has been developed over the last10 years as a tool for probing the free volumeÈvoidstructure of amorphous materials.7 Developments inreal-time dielectric relaxation spectroscopy (DRS) havesimilarly allowed isothermal real-time access to a broadrange of dipole motions. The dynamic mechanicalthermal analysis (DMTA) technique complements moreconventional mechanical test methods and has theadvantage of allowing a thermal characterization of thedistribution of relaxation processes within a material bythermal scanning. Establishment of a correlationbetween the nature of the observations from these threevery di†erent techniques will be used as an indicator ofthe way in which various processes may be coupled and

651998 Society of Chemical Industry. Polymer International 0959È8103/98/$17.50 Printed in Great Britain(

66 R. A. Pethrick, W . J. Davis

allow the development of a universal model for physicalageing in amorphous materials.

EXPERIMENTAL

Materials

Commercial PMMA (Diakon) (ICI), 136 000,Mw Tg105¡C, was annealed at 120¡C and quenched in icewater to room temperature. “Dog bonesÏ (120 mm ]10 mm] 3É25 mm), square plaques (60 mm] 60 mm]3É25 mm) and creep bars (15 mm] 20 mm] 3É25 mm)were compression moulded. Isothermal ageing wasperformed on samples previously equilibrated at120¡C, followed by rapid quenching to room tem-perature (about 298 K) and reheating to the ageing tem-perature Tc .

Dielectric relaxation spectroscopy

The dielectric measurements were performed using adielectric relaxation spectrometer constructed at theUniversity of Strathclyde that has been described pre-viously.8 The instrument allows measurements to beperformed on samples with thickness varying between10 lm and 10 cm, and isothermal and isochronousageing studies were carried out over a frequency rangefrom 10~2 to 6É5 ] 105Hz at 10¡C temperature inter-vals between 30 and 120¡C.8 The samples were ther-mostated in an Oxford Instruments cryostat, capable ofcontrolling the temperature to ^0É1¡C. The referencecapacitance of the sample was calculated from itsdimensions.

Dynamic mechanical analysis

A Rheometrics dynamic mechanical thermal analyser(DMTA) Mk III was used in a single cantilever arrange-ment. Both E@ and tan d were measured as a function oftemperature at a frequency of 1 Hz over the temperaturerange [145 to ]150¡C and a heating rate of20¡Cmin~1 for the isochronous experiments.

Positron annihilation lifetime spectroscopy

A fastÈfast PALS system using cylindrical (40 mmdiameter] 15 mm thick) scintillators9 arranged atBaF290¡ to each other to avoid pulse pile-up problems wasemployed. A count rate of 150È300 counts s~1 wasachieved with a 22Na source and an instrumentresolution of 220È240 ps FWHM for a 50lCi source.Benzophenone and 60Co were used to determine theresolution and source correction. The spectrum wasanalysed using POSITRONFIT10 with a “ÐxedanalysisÏ, assuming (p-Ps),q1\ 0É125 ns q2\ 0É400 ns(free e`) and at 3 : 1. Isochronous experimentsI3/I1involved the samples being aged for various times at a

deÐned temperature before being thermally scanned.Isothermal experiments involved the sample being mea-sured continuously as a function of ageing time at aparticular temperature. PALS were collected at 10¡Cintervals from 30 to 100¡C in 60 min corresponding to5 ] 105È6 ] 105 counts.

Comparison between POSITRONFIT andCONTIN11,12 analysis indicated that only for 106counts or greater could the results of the analysis bedi†erentiated. Spectra with approximately 5] 105counts were used as optimum in this study.

RESULTS AND DISCUSSION

Positron annihilation lifetime spectroscopy

Both isochronous and isothermal experiments havebeen performed using PALS. In addition, a set ofexperiments was performed on a sample surrounded bya light aluminium foil in an attempt to determinewhether or not charging e†ects might be having a sig-niÐcant e†ect on the time dependence of either the life-time or intensity of ortho-positron annihilation (o-Ps) inthis material. The issue of charging e†ects on the posi-tron annihilation characteristics of polymeric materialshas been identiÐed previously in the case of poly-styrene.13 It was found that the lifetime intensity datadid not signiÐcantly vary when the location of thesource was varied within the sample and betweenexperiments in which the poly(methyl methacrylate)sandwich was surrounded by aluminium foil which hadbeen earthed. These observations supported the earlierreports14 that in poly(methyl methacrylate) electric Ðelde†ects are minimal.

Estimation of the ideal equilibrium lifetimes forPMMA

In order to assess the values of the lifetimes and inten-sities for the ideal completely aged sample, measure-ments of the temperature dependence of an unagedsample of poly(methyl methacrylate) were performed(Fig. 1). Below the glass transition temperature, the life-time is higher than the value obtained by taking thelifetime variation as a function of temperature above Tgand extrapolating it to below The di†erence betweenTg .the observed values and those extrapolated from theliquid phase represent the theoretical maximum devi-ation of the free volume from its ideal value. This typeof behaviour parallel very closely that seen in volumerelaxation studies and exempliÐed in the work ofKovacs and Hutchinson.15,16

Isothermal ageing at temperatures between 70 and120¡C was performed for poly(methyl methacrylate) andare shown in Fig. 2. A compromise between the numberof data points collected in a particular lifetime spectrumand the number of individual measurements taken in a

POLYMER INTERNATIONAL VOL. 47, NO. 1, 1998

Physical ageing in PMMA 67

Fig. 1. Plot of versus temperature data for PMMA, includ-q3ing extrapolation of equilibrium “liquidÏ line below Tg .

particular time period was adopted. Ideally one wouldlike to use the CONTIN program for analysis of thelifetime data and to attempt to determine the distribu-tion of lifetimes ; however, this program requires inexcess of 106 counts to be measured for the statistics tojustify such an analysis, and the time required to collectsuch a large number of points would mean that thesample had aged signiÐcantly during the periodrequired for data collection. Therefore a compromisehas to be made between long collection times leading togood statistics with the possibility of the lifetime dis-tribution having changed within period of the measure-ment, and using shorter collection times where thechange in the distribution will be minimal. Thisproblem is a manifestation of the Heisenberg uncer-tainty principle, and we have chosen to use the shortercollection times in this study. The curve for 120¡C doesnot change with time because the sample is relaxedcompletely in the instrument before the experimentstarts. As the temperature is lowered so the ageing ratedecreases, and at 70¡C only a very small part of thetotal curve is available within the 1000 h dedicated toobserving the ageing. The data points show a scatterwhich is not completely random and deÑects theunavoidable drifts which occur in the instrument over a

Fig. 2. Exponential Ðts to isothermal data for PMMA overq3the temperature range 70È120¡C. The 120¡C data are Ðttedwith the equation of a straight line. Data are in order ofincreasing temperature from the bottom of the plot upwards :

70¡C, 80¡C, 90¡C, 100¡C, 110¡C, 120¡C.= |, È, + %, …

very long period of time. In these experiments it isimpossible to recalibrate the instrument by re-measurement of the benzophenone standard sample, aswould be normally carried out for good practice. Thedata obtained are presented without any attempt tosmooth the data. Isothermal measurements at 30, 70,80, 90, 100, 110 and 120¡C, rather than isochronousexperiments, were carried out to reduce any errors dueto uncertainty in the thermal history. A variety of di†er-ent equations17 were applied to the data and includelogarithmic regression

q3\ a ] log(t)] b

single exponential

q3\ a ] exp([t/q) ] b

double additive exponential

q3\ a ] exp([t/q1)] b ] exp([t/q2) ] c

the Narayanaswamy equation [6], and

q3\ exp([t/q)b

A simple exponential decay was adopted and representsthe simplest application of OccumÏs Razor. Followingthe approach of Struik for analysis of creep data,1,2 wehave taken the initial slope of the lifetime against timedata and derived an “ageing rateÏ, which is presented inTable 1. This “ageing rateÏ parameter when plottedagainst temperature gives a pseudolinear plot, the slopeof which can be used to calculate an “activationÏ energy,and the value obtained from the experiments is84 ^ 7 kJmol~1.

Dielectric relaxation spectroscopy

Dipole relaxation of poly(methyl methacrylate) belowits glass transition temperature is well known to containat least two features at very low frequencies : a featurewhich can be associated with the dipole process corre-sponding to the glass transition temperature, and thesecond feature located in the kilohertz region corre-sponding to the side-chain dipole reorientation.18 Thelatter process is not inÑuenced by application of pres-sure to a sample, whereas the former glass transitiontemperature is known to be sensitive to pressure, andhence is volume-controlled. Examples of the dielectricrelaxation of poly(methyl methacrylate) is shown in Fig.3. The processes of physical ageing leads to a reductionin the loss in the region between 10~2 and approx-imately 103Hz and in diminution in the permittivity ofthe material. It is very clear from this spectrum that theprocess of physical ageing does not signiÐcantly inÑu-ence the distribution in relaxation times associated withthe b process and is primarily associated with areduction in amplitude of those relaxation modes whichlie between the a and b process. At higher temperaturesthere is the possibility of ionic conduction contributing



TABLE 1. Summary of fitting parameters for isothermal ageing data overs3

the temperature range 70–120ÄC

Ageing Single exponential fit Log fit

temp. (¡C)

t3

(t ¼ Æ)(ns) t3

(h) (relaxation Dt3

ns Rate dt3/d log t

(fixed) time constant) (extent of (gradient)

ageing)

70 1·820 6 339 0·165 É0·005 0

80 1·888 2 478 0·131 É0·008 5

90 1·956 1 240 0·092 É0·014 0

100 2·024 610 0·049 É0·011 7

110 2·050 324 0·062 É0·024 2

120 – – – É0·007 4

to the observed dielectric loss ; however, at temperaturesbelow there is no evidence of signiÐcant contributionTgdue to this process. Once more the Heisenberg uncer-tainty principle operates and a compromise has to bechosen between accessing very low frequencies of about10~5Hz which would require data collection times ofseveral days, and limiting the frequency range to thatindicated in Fig. 3 with a total data collection time ofthe order of 4 h. For this set of experiments the compro-mise chosen was to limit the low frequency range to10~3Hz. In order to assess the e†ects of physicalageing, the di†erence between the sum of the dielectricloss (SDL) of the completely aged dielectric spectrumand that of the unaged sample was determined by inte-grating the di†erence between the loss curves. Thisparameter was then investigated as a function of timeand the rate of change of this parameter with time usedto calculate an ageing rate. The SDL, deÐned as thearea below the plot of eA against log frequency is relatedto the relaxation strength *eA by :

Pf1

f2eAd log f \ *en/2 (1)

where and are, respectively, the upper and lowerf1 f2limits of the frequency interval used for the integration.3

Fig. 3. Frequency dependence of e@ and eA for aged/unagedPMMA at 90¡C.

The decrease in the SDL due to ageing is thereforeequal to the decrease in relaxation strength deA

deA \ *eaged [ *eunaged (2)

Because the SDL is a direct measure of the e†ectivedipole activity over the frequency range at the chosentest temperature, it is a useful parameter for relatingdipole activity to ageing time. All mathematical Ðttingwas carried out using the computer package Fig-P(V6.0). The loss processes observed may be attributedto, respectively, at low frequency the process, and atTghigher frequency the b process. As indicated previously,no conductivity contribution is observed within thefrequencyÈtemperature range of these measurements attemperatures below The SDL for ageing tem-Tg .peratures 70È120¡C does not exhibit a simple exponen-tial dependence upon ageing time, anddouble-exponential, stretched-exponential or logarith-mic models were also used to curve-Ðt these sets of data(Table 2). However, the concept of a “rateÏ of ageingdetermined as the gradient of log Ðts to ageing data iscommonly employed. No values are given for stretched-exponential Ðts, the solutions for which were veryunstable. Also no values are given for exponential Ðtsfor ageing at 120¡C, because at this temperature SDLwas independent of ageing above the of the material.TgIn the case of double-exponential models, an improve-

TABLE 2. Summary of fitting parameters for

various fits to isothermal SDL data for PMMA over

the temperature range 70–120ÄC

Ageing temp. 1 Éexp. fit 2 Éexp. fit Log fit

(¡C) t (h) (gradient)

t1

(h) t2

(h)

70 47 8·5 157 É0·633

80 57 0·2 56 É0·652

90 106 3·0 98 É0·702

100 145 1·5 181 É0·988

110 23 1·3 29 É1·572

120 – – – 0



ment in the quality of the Ðt to this data is observed atshort times ; however, there is a lack of a deÐned patternto the temperature variation for the lifetime obtainedfrom this Ðt which emerges. The pattern of behaviourobtained using logarithmic regression of the rate,increasing as is approached and then apparentlyTgdropping to zero, is remarkably similar to StruikÏs1ageing “rateÏ versus temperature plot derived fromsmall-strain creep experiments. The dielectric relaxationdata raise the question about the validity of theassumption implicit in thermorheological models. Theprimary assumption in the model is that the nature ofthe process stays independent of the temperature usedin physical ageing, and changes in rate are associatedprimarily with a shift of the relaxation process on thetimeÈtemperature axis. Because the dielectric data pointto the fact that physical ageing leads to a loss of ampli-tude of the relaxation processes rather than any shift inthe distribution, we have to question the validity of thethermorheological simplicity assumption.

Dynamic mechanical analysis

Two approaches can be adopted from the point of viewof the analysis of the mechanical properties of thesample : isochronous or isothermal.

Isochronous The dynamic mechanical spectrum of asample quenched was measured and is shown in Fig. 4.The sample was now aged and the dynamic mechanicalspectrum remeasured. The principal changes which areobserved are a diminution in the mechanical loss proÐlebelow the glass transition temperature, an increase inthe modulus and also an increase in the grass transitiontemperature as measured by DMTA. These obser-vations are consistent with those of previous workers.18

Isothermal ageing The alternative approach of isother-mal ageing was also performed by selecting a frequency

and observing the tan d as a function of time (Fig. 5).Comparison of the shapes of the curves at two di†erenttemperatures, 70¡C and 90¡C illustrates the nature ofthe problem with analysis previously identiÐed with thePALS and DRS experiments. The data for 70¡C mightbe Ðtted to a sum of two exponentials, there beingapparently a short-time fast relaxation process followedby a long-time slow process. However, at 90¡C we seethat this approach is not valid, there clearly being morethan two features, and the curve now takes on asigmoidal form.

Following the approach proposed by Struik1,2 wehave calculated the ageing rates for the dominant relax-ation process (Table 3). Once more the curve for theageing rate shown in Fig. 6 has the familiar formobserved for both PALS and DRS data.

Correlation of PALS, DRS and DMTA data

In view of the apparent di†erences in approach adoptedfor the analysis of physical ageing data obtained by dif-ferent techniques, it seemed appropriate to see whethercorrelations existed between the three techniques

TABLE 3. Fitting parameters for mechanical data

Ageing temp. 1 Éexp. fit 2 Éexp. fit Log fit

(¡C) t (h) (gradient)

t1

(h) t2

(h)

70 –a 1·4 40 É0·005 28

80 – 1·1 30 É0·007 67

90 – 0·8 62 É0·008 41

100 – 1·5 33 É0·027 6

110 2·3 – – É0·065 4

120 0·6 – – –

a Where no values are given it was found to be impossible

to fit the data.

Fig. 4. Dynamic mechanical spectra showing both E@ and tan d of unaged (]) and aged (]) PMMA over the temperature range[145 to ]150¡C at 1 Hz frequency.



Fig. 5. Isothermal tan d data for PMMA aged at (a) 70¡C andat (b) 90¡C.

reported in this paper by plotting the ageing ratesobtained from the various techniques against oneanother. If these processes have a common molecularorigin then ideally the rates obtained by various tech-niques would show a one-to-one correlation. However,in view of the fact that the approach adopted in thispaper has been phenomenological, we would expectthere to be an undeÐned correlation factor giving rise toa non-ideal slope for such plots. Plots obtained for the

Fig. 6. Ageing “rateÏ versus temperature for PMMA over thetemperature range 70È120¡C. The “rateÏ was calculated as the

slopes of log Ðts to tan d data.

Fig. 7. Correlation between ageing “ratesÏ determined by (a)DRS and PALS experiments, (b) DRS and DMA experiments,(c) DMA and PALS experiments. Ageing “ratesÏ in each case

are determined from gradients of log Ðts to data.

data presented in this paper (Fig. 7) show that ingeneral there is connectivity between the data obtainedpointing to a common molecular origin for physicalageing.

Similar studies on other polymer systems will bereported in future publications.

CONCLUSIONS

The data reported in this paper point to the essentialmolecular features of physical ageing and show thatthese can be associated with loss in the relaxation



amplitude for processes with activity lying between theglass transition temperature and a sub-glass transitiontemperature. No single form of relaxation function isable to describe the data obtained at di†erent tem-peratures and this illustrates the problem of formulationfrom a single simple phenomenological model which isable to describe the data obtained with di†erent ageingtimes and temperatures.

ACKNOWLEDGEMENTS

The authors wish to thank the EPSRC and Ford Cor-poration for support of this work.

REFERENCES

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towards a molecular approach to physical ageing in poly(methyl methacrylate)

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