Kinetics of hardness evolution during annealing of gamma-irradiatedpolycarbonateS. H. Yeh, P. Y. Chen, Julie Harmon, and Sanboh Lee Citation: J. Appl. Phys. 112, 113509 (2012); doi: 10.1063/1.4768277 View online: http://dx.doi.org/10.1063/1.4768277 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v112/i11 Published by the American Institute of Physics. Related ArticlesPiezoresistance behaviors of ultra-strained SiC nanowires Appl. Phys. Lett. 101, 233109 (2012) Stable fracture of a malleable Zr-based bulk metallic glass J. Appl. Phys. 112, 103533 (2012) Raman spectroscopic calibrations of phonon deformation potentials in wurtzitic AlN J. Appl. Phys. 112, 103526 (2012) Carbon nanotube film interlayer for strain and damage sensing in composites during dynamic compressiveloading Appl. Phys. Lett. 101, 221909 (2012) Tensile and fatigue behaviors of printed Ag thin films on flexible substrates Appl. Phys. Lett. 101, 191907 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

Kinetics of hardness evolution during annealing of gamma-irradiatedpolycarbonate

S. H. Yeh,1 P. Y. Chen,1 Julie Harmon,2 and Sanboh Lee1,a)

1Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan2Department of Chemistry, University of South Florida, Tampa, Florida 33620-5250, USA

(Received 31 May 2012; accepted 1 November 2012; published online 6 December 2012)

This study focuses on the evolution in microhardness values that accompany isothermal annealing

in gamma-irradiated polycarbonate (PC). Hardness increases with increasing annealing time,

temperature, and gamma radiation dose. A model composed of a mixture of first and zero order

structure relaxation is proposed to interpret the hardness data. The rate constant data fit the

Arrhenius equation, and the corresponding activation energy decreases with increasing dose. The

extent of structural relaxation that controls the hardness in post-annealed PC increases with

increasing annealing temperature and dose. The model demonstrates that hardness evolution in PC

is an endothermic process. By contrast, when the model is applied to irradiated poly(methyl

methacrylate) and hydroxyethyl methacrylate copolymer, hardness evolution is an exothermic

process. VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4768277]

I. INTRODUCTION

Polycarbonate (PC) has optimum mechanical properties

(e.g., high tensile strength, impact strength, and toughness),

excellent optical transparency in the visible wavelength

range, and is resistant to acids and bases.1 These properties

render PC, an ideal material for demanding applications.

Applications requiring exposure to gamma radiation necessi-

tate a thorough understanding of radiation effects on PC

properties, and this has been studied by a host of researchers.

Ara�ujo et al.2 used Fourier transform infrared spectroscopy

(FTIR) to analyze radiation induced chemical changes in PC

and found that the concentration of carbonyl groups

decreases with increasing radiation dose. Seguchi et al.3

determined that Rockwell hardness and wear resistance of

PC improve with small doses of gamma-ray or electron

beam irradiation at high temperatures. Wang et al.4 observed

a modification in chemical structure of PC irradiated by

1.4 GeV Ar ions by FTIR and UV/Vis absorption spectros-

copies. Specifically, bond breaking was noted at methyl, phe-

nyl, carbonyl, and ether groups in PC. The authors note that

this suggests that molecular weight decreases accompany

bond breaking. Indeed, Singh and Prasher5 analyzed the

chemical and spectral response of gamma irradiated Lexan

PC and documented cleavage of the carbonate linkages.

Neerja et al.6 investigated the effect of gamma radiation on

track detectors designed to determine pathway of charged

heavy ions travelling in PC. These particles are accompanied

by gamma radiation, and it is important to characterize the

influence of gamma radiation on particle tracking efficiency.

The energetic ions form linear damaged tracks in the PC.

Etching removes the damaged materials and reveals the

tracks of the particles. The authors tested the effect of

gamma irradiation on NaOH etching of LexanVR

PC. The etch

rate increased with gamma radiation dose, and this was

attributed to chain scission of carbonate linkages in the poly-

mer. Another study examined Makrofol-KGVR

PC and

researchers found that activation energies for etching

decreased as the radiation dose increased.7 Sapkal et al.8

studied the chemical etching of gamma irradiated TuffakVR

PC and confirmed above results finding activation energies

for etching that decrease with gamma radiation dose. This

was thought to be due to production of free radicals and ions

as a result of chain scission. Nouh and Naby9 found that

gamma irradiation affected the thermal stability of PC and

greatly depended on the dose administered. Samples under-

went scission at doses from 0–130 kGy, and the onset tem-

perature of thermal degradation decreased. At higher doses,

there was an increase in onset temperature and this was

attributed to cross-linking. At even higher doses (>350

kGy), the onset temperature decreased. Vujisic et al.10 exam-

ined the influence of gamma and neutron irradiation on the

dissipation factor and capacitance of capacitors filled with

PC dielectrics. They found that exposure to a mixed neutron

and gamma source causes a decrease of capacitance, while

the dissipation factor is unchanged. Weber et al.11 realized

that gamma irradiation did not change the mechanical behav-

ior of PC at high strain rates; however, low strain rates pro-

duced large changes in mechanical behavior. Of course, low

strain rates result in more ductile responses in which flow is

enhanced by radiation induced decreases in molar mass.

While much work has focused on amassing data charac-

terizing the effects of ionizing radiation on polycarbonate,

additional studies have been conducted on a host of other

polymers as well.12 From all of these data, the mechanisms

behind radiation induced changes in properties are being

unraveled. Color centers have been used to explain the UV/

Vis spectra of gamma irradiated polymers.13,14 Permanent

color centers form as a result of radiation induced reactions

producing unsaturated moieties that act as chromophores.

Transient color centers are due to the presence of trapped

free radicals caused by radiation induced bond scission.

These radicals are color centers that often fluoresce and

a)Author to whom correspondence should be addressed. Email address:

sblee@mx.nthu.edu.tw. Fax/Tel: 886-3-5719677.

0021-8979/2012/112(11)/113509/6/$30.00 VC 2012 American Institute of Physics112, 113509-1

JOURNAL OF APPLIED PHYSICS 112, 113509 (2012)

gradually disappear due to quenching by oxygen that slowly

diffuses into the polymer matrix. Alternatively, the free radi-

cals may recombine, especially if the matrix is warmed to

enhance molecular mobility. Radicals were also used to

interpret the EPR spectra of polymers exposed to gamma ray

irradiation.15,16 Earlier our laboratory characterized the evo-

lution of hardness of irradiated PMMA17 and HEMA copoly-

mer18 and postulated that unstable chemical and physical

structural changes induced by ionizing radiation anneal out

and produce stable structures. This article focuses on micro-

hardness related to unstable structures induced in PC by

gamma ray irradiation. A model is proposed that relates

annealing of unstable structures to hardness changes in post

irradiated PC. This model is also used to further explain the

mechanism behind hardness evolution in PMMA and HEMA

copolymer from our earlier studies.

II. EXPERIMENTAL

Lexan 8010 type polycarbonate sheets were obtained

from the General Electric Company (Compton, California,

USA). The glass transition temperature of the polymer is

418 K. Specimens of 15� 10� 1 mm3 were cut from the

sheets, ground with 800, 1200, and 400 grid Carbimet papers

and finally polished with 1 lm and 0.05 lm alumina slurries.

In order to release residual stresses caused by machining, the

samples were annealed in air at 373 K for 24 h and furnace

cooled to 298 K.

The samples were sealed in glass tubes and then irradi-

ated by a 30 K Curie Co-60 gamma ray source at the Radioi-

sotope Division, National Tsing Hua University, at a dose

rate of 11.69 kGy/h at 298 K. The accumulated doses are

400, 800, 1200, 1600, and 2000 kGy.

The microhardness measurements were carried out with

an Akashi MVK-E microhardness tester (Mitutoyo Corpora-

tion, Minato-Ku, Tokyo, Japan) with a load of 100 g and a

dwell period of 5 s. The irradiated PC samples and control

samples not exposed to radiation were annealed at 363, 373,

383, 393, and 403 K. These temperatures are near to, but

below the glass transition temperature which is 418 K. The

samples were removed from the furnace, tested at room tem-

perature within 30 s, and then returned immediately to the

furnace for the next measurement. The microhardness data

of irradiated and control samples were recorded as a function

of annealing time. The data were the average of three sam-

ples under the same conditions.

III. RESULTS AND DISCUSSION

The time dependence of hardness of polycarbonate con-

trols and samples irradiated with doses of 0, 400, and 2000

kGy is plotted in Figs. 1(a)–1(c), respectively. Other doses

of 800, 1200, and 1600 kGy yield similar results. As shown

in Fig. 1, for a given time, the hardness increases with

annealing temperature and gamma-ray dose. For a given

dose and temperature, hardness also increases with annealing

time. The control samples exhibited the lowest hardness val-

ues. The hardness of materials varies with both the molecular

structure and the microstructure. For a given single crystal-

line inorganic material, the atomic arrangement is con-

structed by repetition of a unit cell. Defects in an inorganic

crystalline material are due to deviations from a perfect sin-

gle crystal that arise due to the formation of a surface, vacan-

cies, voids, impurities, and grain boundaries. It is difficult if

not impossible to define perfect microstructure in polymeric

materials due to irregularities in molecular structure, chain

packing, and in the distribution of molecular weights. Here

we use as a reference the hardness of the control, non-

FIG. 1. The evolution of hardness of PC irradiated with (a) 0 kGy, (b) 400

kGy, and (c) 2000 kGy, at annealing temperatures 363–403 K.

113509-2 Yeh et al. J. Appl. Phys. 112, 113509 (2012)

irradiated samples designated by Hi. The defects are defined

as the microstructure of irradiated and/or aged samples as

they deviate from that of controlled samples. Different types

of defect will result in changes in physical, mechanical, and

chemical properties of polymeric materials. Additionally, we

note that the reference microstructure might also be a per-

fectly ordered microstructure. It is practical herein to use the

non-irradiated material as reference material.

As in a previous analysis of the hardness evolution in

irradiated PMMA and HEMA copolymer,17,18 we assume

the increment of hardness DH(¼H-Hi) is linearly propor-

tional to the concentration, n, of defects that affect control

hardness where Hi varies with temperature.

That is

DH ¼ H-Hi ¼ bn; (1)

where b is a constant. The annealing of defects affecting the

hardness is shown to follow a mixture of zeroith order and

first order kinetic processes, i.e.,

dn=dt ¼ -aðn-nfÞ=s; (2)

where a and nf are the rate constant and the concentration of

defects affecting the hardness at infinite annealing time. The

solution of Eq. (2) is

n ¼ nf þ ðn0-nfÞ e-at; (3)

where n0 is the concentration of defects that affect the hard-

ness at the initial time. Substituting Eq. (1) into Eq. (3), one

obtains

H ¼ Hf þ ðH0-HfÞ e-at; (4)

where H0 and Hf are the hardness of PC at the initial anneal-

ing time and infinite time, respectively. It is worthwhile to

note that for the controlled samples, H0 is equal to Hi.

The solid lines in Fig. 1 are obtained by Eq. (4) using

least squares curve-fitting. Note that this implies that defects

are possibly created in the non-irradiated PC during anneal-

ing as well. Radiation enhances the number of defects that

are at equilibrium. The corresponding a, H0, and Hf are

shown in Figs. 2–4, respectively. The experimental data indi-

cated by symbols in Fig. 1 are in good agreement with the

theoretical predictions.

Generally speaking, the increment of hardness and

defect kinetics follows Eqs. (5) and (6), respectively,

DH ¼ H-Hi ¼ bmnm; (5)

and

dn=dt ¼ �X

jdjn

j=sj; (6)

where m is the positive real number and j is an integer. If the

defect distribution is dilute, m is equal to unity. bm, dj, and sj

are constant. We vary m in Eq. (5) and j, sj, and dj in Eq. (6)

to fit the hardness data shown in Fig. 1. We found that,

only Eq. (5) with m¼ 1, and Eq. (6) with d1 ¼ �d0 ¼ a,

FIG. 2. The plot of Log(a) vs. 1/T with different doses where the units of aare h�1 and �K, respectively.

FIG. 3. The plot of H0 of PC irradiated with different doses at five

temperatures.

FIG. 4. The plot of log(Hf) of PC vs. 1/T with different doses where the unit

of hardness is MPa.

113509-3 Yeh et al. J. Appl. Phys. 112, 113509 (2012)

s0 ¼ s1 ¼ s can match the experimental data shown in Fig.

1. Because the hardness is proportional to the concentration

of defects that affects the hardness, we can infer from Fig. 1

that the concentration of these moieties that affect the hard-

ness approaches equilibrium at given annealing temperature.

The rate of concentration of defects that affect the hardness

increases slowly with annealing time until it reaches equilib-

rium (or a plateau) as shown in Eq. (4). That is, the defects

that influence the hardness are created during annealing. It

can be seen from Fig. 2 that the rate constant increases with

gamma ray dose for a given temperature. It is also found that

for a given gamma ray dose, the rate constant is linearly pro-

portional to the reciprocal of temperature. That is, according

to Fig. 2, the rate constant satisfies Arrhenius equation,

a ¼ a0e-Q=RT; (7)

where a0, R, and Q are the pre-exponent factor, gas constant,

and activation energy, respectively. T is the absolute temper-

ature in Kelvin. The activation energy for the evolution of

defects that influence the hardness in PC is calculated from

the slope of straight line in Fig. 2 and listed in Table I. The

activation energy decreases with increasing dose. This

implies that gamma rays enhance defect evolution by lower-

ing the activation energy barrier for defect generation.

Similar results were observed for PMMA,17 but it is in-

dependent in HEMA copolymer.18 According to Fig. 3, for a

given dose, the initial hardness increases with annealing tem-

perature. For a given annealing temperature, the initial hard-

ness is linearly proportional to the dose, and its proportional

constant (or slope) increases with increasing annealing

temperature.

Fig. 4 shows the hardness of PC annealed at infinite

time at different temperatures and doses. Based on Eq. (1),

the hardness is linearly proportional to the concentration of

the defects that change hardness. The system is similar to

polymer in solvent where the molar fraction, X, follows the

van’t Hoff equation19

X ¼ e-DE=RT; (8)

where DE is the enthalpy change or heat of mixing. Note that

DE> 0 and DE< 0 are endothermic and exothermic proc-

esses, respectively. Using Eq. (8), we obtain the straight lines

in Fig. 4 based on the least squares curve-fitting. The experi-

mental data are in good agreement with model predictions.

From the slopes, we calculate the enthalpy changes and

listed in Table II. The enthalpy change increases with

increasing dose. Because DE is greater than zero, this is an

endothermic process. Such a phenomenon was also observed

in PMMA and HEMA copolymer. The hardness of irradiated

PMMA and HEMA copolymer extrapolated to annealing at

infinite times were obtained from Fig. 3 in Refs. 17 and 18

and are reported in Figs. 5 and 6, respectively. Using Eq. (8)

with least squares curve-fitting, we obtain straight lines in

Figs. 5 and 6. Again the experimental data are in good agree-

ment with the theoretical predictions. From the slopes in

Figs. 5 and 6, we calculate the enthalpy changes for hardness

evolution in PMMA and HEMA copolymer. These are listed

in Tables II and III, respectively. Their processes are exo-

thermic as noted in the negative sign of enthalpy changes.

The magnitude of enthalpy change decreases with increasing

dose for PMMA, but an opposite trend is noted in HEMA

copolymer.

It is found, then, that Eq. (8) is valid for PC, PMMA,17

and HEMA copolymer.18 That is, the evolutions of hardness

values in PC, PMMA, and HEMA copolymer at elevated

TABLE I. The activation energies accompanying structural rearrangements

that affect the hardness in control PC and PC irradiated at different doses.

U (kGy) 0 400 800 1200 1600 2000

Q (kJ/mol) 16.39 11.46 10.00 9.10 8.29 6.73

TABLE II. The enthalpy change DE (kJ/mol) accompanying structural rear-

rangements that affect the hardness in control PC and PC irradiated at differ-

ent doses.

U (kGy) 0 400 800 1200 1600 2000

DE (kJ/mol) 2.07 2.24 2.80 3.52 3.58 3.60

FIG. 5. The plot of log(Hf) of PMMA vs. 1/T with different doses where the

unit of hardness is MPa.

FIG. 6. The plot of log(Hf) of HEMA copolymer vs. 1/T with different doses

where the unit of hardness is MPa.

113509-4 Yeh et al. J. Appl. Phys. 112, 113509 (2012)

temperatures can be explained by a mixture of zeroith order

and first kinetic processes that increase the defects that deter-

mine the hardness. This phenomenon is different from that

observed in LiF single crystals where the hardness decreases

with increasing annealing time until it returns to its original

value.20

Gamma irradiation causes scission and crosslinking in

PC. This results in the generation of free radicals, unsatura-

tion and various other side reactions. Wu et al.21 studied ace-

tone absorption in irradiated polycarbonate and found that

the molecular weight and glass transition temperature of PC

decrease with increasing gamma ray dose. This means that

chain scission is more severe at higher doses. In order to

understand the effect of gamma rays on hardness, the plot of

hardness versus gamma ray dose with different temperatures

is shown in Fig. 7 where the annealing time is 1.5 h. Similar

results are also observed for different annealing times. It can

be seen from Fig. 7 that the hardness is linearly proportional

to the gamma ray does and the slope increases with the

annealing temperature. At a given annealing temperature, the

slope of hardness versus dose increases with increasing

annealing time. In addition, for a given annealing time and

gamma ray dose, the hardness is linearly proportional to the

annealing temperature. The slope of hardness versus anneal-

ing temperature increases with gamma ray dose and anneal-

ing time. This implies that both gamma ray irradiation and

annealing temperature enhance the hardness evolution.

The discussion above focuses on the results of the radia-

tion study as they influence the evolution of hardness and on

developing a model to determine Hf, the activation energy

for evolution of defects that influences the hardness and the

corresponding enthalpy changes. Now, possible alterations

in the PC matrix that explain the above results are presented.

First, it is important to consider annealing induced micro-

hardness changes in non-irradiated samples. It is well known

that physical aging occurs in glassy matrices when samples

are annealed below their glass transition temperatures. This

phenomenon has been extensively studied by Struik.22,23

Physical aging is due to the non-equilibrium nature of glassy

polymers. The increase in viscosity that accompanies the

cooling process increases molecular relaxations times and

the molecules slowly seek their equilibrium structures during

extended aging times. This gradual approach to equilibrium

is accompanied by a decrease in free volume and is accom-

panied by increases in microhardness. The effect of aging on

microhardness had been reviewed by Flores et al.24 Thus,

nonequilibrium structures relax to produce more stable struc-

tures during annealing. A rapid increase in hardness is noted

during the initial healing period and this tapers off with time.

Herein, we demonstrate this behavior in non-irradiated con-

trol PC and note that it is enhanced in irradiated samples.

This implies that the nonequilibrium structure content

increases with irradiation. It is now appropriate to probe the

molecular nature of these rearrangements. Soloukhin et al.studied physical aging in PC through a variety of techniques

including moduli and hardness measurements.24 The elastic

moduli and hardness increased during aging at room temper-

ature, and they believe that this is a result of densification

during aging. FTIR experiments prompted the authors to

suggest that during aging at elevated temperatures trans-cis

to trans-trans conformational changes take place allowing

closer chain packing. Additionally, they note that any scis-

sion and/or crosslinking alter the molecular weight distribu-

tion and the free volume distribution. Finally, they realize

that gas release during annealing results in changes in free

volume distributions in the PC matrix that relax during fur-

ther annealing.

Seguchi et al. conducted a very interesting set of experi-

ments aimed at using gamma and electron beam irradiation

to improve the mechanical properties of PC and polysulfone

(PSF).3 They irradiated samples at room temperature and at

glass transition temperatures and above. Samples irradiated

at Tg and above exhibited maximum Rockwell Hardness val-

ues at doses as low as 3–5 kGy. Increases in the hardness

were attributed to packing in the matrix due to synergistic

effects of radiation and high temperature. The authors postu-

late that small amounts of chain scission occurred at molecu-

lar entanglements inducing higher packing. At lower

temperatures, the rearrangement is difficult and dramatic

increases in hardness are not noted. They monitored density

changes and found that PC samples irradiated at high tem-

peratures increased in density. The highest hardness occurred

at a 1% density increase. Samples irradiated at room temper-

ature exhibited a slight decrease in density.

The results reported herein evidence enhanced hardness

that increases with annealing time, temperature, and dose.

Control samples exhibit physical aging behavior and the

hardness increases as annealing time and temperature

increases. This is likely to be a result of tighter molecular

packing when samples are annealed at elevated temperatures.

TABLE III. The enthalpy change DE (kJ/mol) accompanying structural rear-

rangements that affect the hardness in PMMA and HEMA irradiated with

different doses.

Polymer U (kGy) 400 600 800 1000

PMMA �2.05 �1.84 �1.76 �1.75

HEMA �7.24 �8.52 �9.53 �11.01

FIG. 7. The plot of hardness of PC vs. gamma ray dose with different

annealing temperatures at annealing time 1.5 h.

113509-5 Yeh et al. J. Appl. Phys. 112, 113509 (2012)

Both irradiated and control samples exhibit the expected

rapid initial rise in temperature versus aging time.23 The

increase in hardness with dose is related to an increased

number of radiation events that go on to generate defects

that tighten the matrix. This accompanies the densification

that normally occurs in the aging of non-irradiated matrices.

The radiolysis products may be trapped gas molecules that

escape and tighten the matrix, or entanglements that have

undergone scission as suggested above.25 Free radicals and

other unstable radiation products may react to yield a variety

of more stable molecules in the matrix. All of this requires

mobility in the matrix, and this mobility is enhanced as the

annealing temperature increases. During the annealing pro-

cess, a denser matrix is generated due to structural defects

that evolve and change the original PC matrix. As these new,

“stable” structural elements are generated from nonequili-

brium structures. While Seguchi et al.3 irradiated at elevated

temperatures, we note that the unstable radiolysis products

are formed and remain in the matrix for extended periods at

low temperatures. By annealing the pre-irradiated samples,

different and more rapid reactions occur than those noted at

room temperatures and the irradiated matrices approach dif-

ferent equilibrium conformations than those of nonirradiated

matrices. Seguchi et al.3 suggest that it radiation induces

chain scission at entanglement and molecular rearrange-

ments that follow lead to tighter packing that that observed

in annealed control samples. This will lead to hardness

increases that are noted in irradiated samples.

IV. CONCLUSIONS

This study investigated generation of radiation induced

structures that affect the hardness in PC. The hardness of

irradiated PC increases with increasing gamma ray dose,

annealing time, and annealing temperature. The generation

of defects controlling the hardness is shown to follow a mix-

ture of zeroith order and first order kinetic processes.

The experimental data are in good agreement with the

theoretical predictions. This model is also valid for the evo-

lution of hardness in irradiated PMMA and HEMA copoly-

mer. The activation energy for evolution of defects that

influence the hardness in PC and PMMA decreases with

increasing dose, but it is independent in HEMA copolymer.

The kinetics for hardness evolution in PC is an endothermic

process, and the corresponding enthalpy change increases

with increasing dose. However, the kinetics observed in

PMMA and HEMA copolymer are exothermic. The model

proposed herein sheds light on the fact that with radiation

processing it is possible to generate new structural elements

that enhance mechanical properties.

ACKNOWLEDGMENTS

This work was financially supported by the National

Science Council, Taiwan.

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