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:
[email protected]. 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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