The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene
The influence of damaging of the ultra-high-molecular polyethylene (PE-UHMW) Chirulen ®1120, which is applied, among others, to produce hip endoprostheses, on spectra of positrons lifetime in this material was investigated. Polyethylene samples were damaged by: impact, rolling friction and collis...
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Фізико-механічний інститут ім. Г.В. Карпенка НАН України
2012
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| Цитувати: | The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene / R. Pietrzak, R. Szatanik, R. Olchawa, K. Książek // Фізико-хімічна механіка матеріалів. — 2012. — Т. 48, № 6. — С. 36-44. — Бібліогр.: 29 назв. — англ. |
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irk-123456789-1358242018-06-16T03:06:24Z The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene Pietrzak, R. Szatanik, R. Olchawa, R. Książek, K. The influence of damaging of the ultra-high-molecular polyethylene (PE-UHMW) Chirulen ®1120, which is applied, among others, to produce hip endoprostheses, on spectra of positrons lifetime in this material was investigated. Polyethylene samples were damaged by: impact, rolling friction and collisions with metal balls in a planetary mill. Changes in the parameters of positrons lifetime spectra related to annihilation of ortho-positronium (o-Ps) were analyzed in dependence on the mechanical energy passed to the sample. On the basis of the Eldrup–Tao model, changes in the radii of voids in which a positronium is formed and annihilated, as well as changes in the degree of filling up the space atoms in the examined polymer were determined. Досліджували вплив пошкоджень ультрависокомолекулярного поліетилену марки Chirulen®1120, який застосовують для виготовлення тазостегнових ендопротезів, на час існування позитронів в цьому матеріалі після опромінення. Зразки поліетилену пошкоджували в лабораторних умовах методами удару, вальцювання та тертя, а також шляхом зіткнення з металевими кульками у планетарному млині. Зміни часу існування орто-позитронів аналізували залежно від механічної енергії, отриманої зразком, а зміни радіусів порожнин, в яких утворюються та анігілюються позитрони, визначали, застосовуючи модель Елдрупа–Тао. Исследовали влияние повреждений ультравысокомолекулярного полиэтилена марки Chirulen®1120, который применяют для изготовления тазобедренных эндопротезов, на время существования позитронов в этом материале после облучения. Образцы полиэтилена были повреждены в лабораторных условиях методами удара, прокатывания и трения, а также путем столкновения с металлическими шариками в планетарной мельнице. Изменения времени существования орто-позитронов анализировали в зависимости от механической энергии, полученной образцом, а изменения радиусов полостей, в которых образуются и аннигилируются позитроны, определяли с применением модели Елдрупа–Тао. 2012 Article The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene / R. Pietrzak, R. Szatanik, R. Olchawa, K. Książek // Фізико-хімічна механіка матеріалів. — 2012. — Т. 48, № 6. — С. 36-44. — Бібліогр.: 29 назв. — англ. 0430-6252 http://dspace.nbuv.gov.ua/handle/123456789/135824 en Фізико-хімічна механіка матеріалів Фізико-механічний інститут ім. Г.В. Карпенка НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The influence of damaging of the ultra-high-molecular polyethylene (PE-UHMW) Chirulen
®1120, which is applied, among others, to produce hip endoprostheses, on spectra of
positrons lifetime in this material was investigated. Polyethylene samples were damaged
by: impact, rolling friction and collisions with metal balls in a planetary mill. Changes in
the parameters of positrons lifetime spectra related to annihilation of ortho-positronium
(o-Ps) were analyzed in dependence on the mechanical energy passed to the sample. On
the basis of the Eldrup–Tao model, changes in the radii of voids in which a positronium is
formed and annihilated, as well as changes in the degree of filling up the space atoms in
the examined polymer were determined. |
| format |
Article |
| author |
Pietrzak, R. Szatanik, R. Olchawa, R. Książek, K. |
| spellingShingle |
Pietrzak, R. Szatanik, R. Olchawa, R. Książek, K. The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene Фізико-хімічна механіка матеріалів |
| author_facet |
Pietrzak, R. Szatanik, R. Olchawa, R. Książek, K. |
| author_sort |
Pietrzak, R. |
| title |
The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene |
| title_short |
The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene |
| title_full |
The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene |
| title_fullStr |
The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene |
| title_full_unstemmed |
The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene |
| title_sort |
influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene |
| publisher |
Фізико-механічний інститут ім. Г.В. Карпенка НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/135824 |
| citation_txt |
The influence of mechanical damaging on positrons lifetime in ultra-high-molecular polyethylene / R. Pietrzak, R. Szatanik, R. Olchawa, K. Książek // Фізико-хімічна механіка матеріалів. — 2012. — Т. 48, № 6. — С. 36-44. — Бібліогр.: 29 назв. — англ. |
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Фізико-хімічна механіка матеріалів |
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36
Ô³çèêî-õ³ì³÷íà ìåõàí³êà ìàòåð³àë³â. – 2012. – ¹ 6. – Physicochemical Mechanics of Materials
THE INFLUENCE OF MECHANICAL DAMAGING ON POSITRONS
LIFETIME IN ULTRA-HIGH-MOLECULAR POLYETHYLENE
R. PIETRZAK, R. SZATANIK, R. OLCHAWA, K. KSIĄŻEK
Institute of Physics, Opole University, Poland
The influence of damaging of the ultra-high-molecular polyethylene (PE-UHMW) Chi-
rulen®1120, which is applied, among others, to produce hip endoprostheses, on spectra of
positrons lifetime in this material was investigated. Polyethylene samples were damaged
by: impact, rolling friction and collisions with metal balls in a planetary mill. Changes in
the parameters of positrons lifetime spectra related to annihilation of ortho-positronium
(o-Ps) were analyzed in dependence on the mechanical energy passed to the sample. On
the basis of the Eldrup–Tao model, changes in the radii of voids in which a positronium is
formed and annihilated, as well as changes in the degree of filling up the space atoms in
the examined polymer were determined.
Keywords: polyethylene, positronium, damaging, positrons lifetime.
For many years new Polyethylene (PE) has been one of the polymers that is the
most frequently used in practice. Its physical properties, and especially the mechanical
and thermal ones, depend, among others, on the manner of its production and, there-
fore, it is an object of continuous researches concerning its morphology, structure and
relaxation behavior [1–5].
PE is obtained in a high-pressure process, in the presence of initiators of radical
polymerization or in a low-pressure process in which metal-organic catalysts of coordi-
nating polymerization take part. Macro-molecules of PE which is formed in the high-
pressure process, due to the considerable participation in them of the long branching
side chains, which makes the dense packing difficult, are characterized by a low den-
sity (the so-called LDPE). On the other hand, the PE obtained in the low-pressure syn-
thesis contains few short branchings, being a polymer of nearly linear structure thanks
to which it possesses a higher density. It is labeled HDPE (High Density PE).
In the recent decade, PE of a very big mol mass, one exceeding 1000 kg/mol, and
of the linear structure of its macro-molecules has been produced. It is labeled as PE-
UHMW (Ultra High Molecular Weight Polyethylene). It is characterized by a good
chemical and mechanical resistance, physiological indifference, good biological tole-
rance and by a relatively low production cost. For these reasons it is used in medicine
on a broad scale to make surgical endoprostheses [5]. During the insertion in the pa-
tient and also while being exploited, the endoprosthesis is exposed to strong and cycli-
cal mechanical stresses which can affect the duration and comfort of its usage. So far,
in order to investigate destructions of PE-UHWM caused by mechanical factors macro-
scopic methods have been used mainly for researches. They consist in determining
changes in, for instance, elasticity, hardness, friction coefficient, without penetrating in
the microscopic changes occurring in the material.
Since 1996 [6] research in the mechanisms of formation and kinetics of defects in
polymers has made use of the phenomenon of positrons annihilation, in particular the
technique of measurement of positrons lifetime. The condition which allows applying
Corresponding author: R. SZATANIK, e-mail: szata@uni.opole.pl
37
this technique is the fact that part of the positrons which penetrate into the polymer
sample can form positronium in it and the latter can come in two forms: ortho (o-Ps)
and para (p-Ps). The positronium annihilating from the o-Ps state is characterized by
the lifetime of 1–2 ns in the pick-off process. The time depends on, among others, the
size and shape of free atoms of the polymer space.
Annihilation of positrons in PE has been investigated by many authors [7–18]. In
the first works, the experimentally obtained spectra of positrons lifetime were distribu-
ted into two components, still the interpretation of the results turned out to be easier
using de-convolution of spectra into three components, of which one was characterized
by a long lifetime of the nanoseconds order. Some researchers [8, 10, 13] noticed the
occurrence of one more long-lived component of the spectrum, also connected with the
formation of o-Ps. An interpretation of the obtained values of positrons lifetime is diffi-
cult, for the reason that, generally speaking, the examined polymers had partially amor-
phous and crystalline structures. The crystalline phase of PE contains different forms of
the polymer macro-chains ordering from lamellar and non-lamellar macro-crystals, in
which the whole macro-particles are built in the crystalline structure through different
forms of crystallites, where only fragments of macro-chains compose an ordered form.
As Dlubek [10] and Dębowska [11] proved, the value of the long-lived component of
the positrons lifetime spectrum in the crystalline state is lower than in the amorphous
phase. For HDPE polymers, the long-lived component takes, generally, a lower value
than that for LDPE polymers. Furthermore, the value of the long-lived component of
this spectrum depends on a great number of physical factors such as temperature, time
of initial annealing, pressure, illumination of samples with visible light while taking
measurements, as well as cyclically changing strains.
At first the annihilation techniques were applied to investigations of equilibrium
defects, and then of non-equilibrium ones in solids, assuming that the defects are distri-
buted evenly over the whole volume of the material. Making use of the sources emit-
ting mono-energetic positrons of regulated energy allowed examining the defect states
in the top layer of solids. This in the most interesting question because the top layer can
have completely different physical properties than the layers of material, which are
deep inside the samples. The top layer of solids is often plastically deformed. The
thickness of this layer depends, among others, on the way of mechanical interacting
with the external layers.
The results of research by Dryzek, Pietrzak et al. [19–22] indicate, however, that
application of the positron sources of a continuous energetistic spectrum of positrons
can be used to investigate properties of the top layers of solids.
The primary mechanical and physiochemical properties of polyethylene of which
an endoprosthesis is built can undergo considerable destructive changes both in the
process of its installation and as a result of mechanical strains that change cyclically
over a long period during movements. Therefore, it is indispensable to determine the
changes occurring in the material of polyethylene under the influence of various factors
leading to such a destruction.
We presented the results of research of positrons annihilation in PE-UHMW
Chirulen®1120 polyethylene [23]. We proved there that after damaging caused by an
impact, the parameters of o-Ps component of the positrons lifetime spectrum undergo
changes. We also found that when the deformation caused by an impact is of the plastic
character, the lifetime of the positronium and the intensity of the component correspon-
ding to this channel of annihilation are subject to far clearer changes than after an elas-
tic deformation. The value of the changes depends on the density of surface energy
passed to the sample over a time unit. We come to deal with an impact-related action
on PE-UHMW applied in an endoprosthesis mainly during its installation in the
38
patient’s body, whereas, while it is in use, we often deal with damaging the polyethylene
material through rolling friction, as well as the joint stroke action and rolling friction.
This work presents the results of research on changes in positrons lifetime in the
top layer of PE-UHMW Chirulen®1120 induced by defects formed in this layer by
repetitive bombarding of the samples with metal balls in a planetary mill and by rolling
friction.
Despite the fact that the results of the investigation of the influence of the stroke-
based damaging were partially presented in [23], in this paper we are going to make
references to them since it is only jointly that they can yield a certain picture of PE-
UHMW Chirulen®1120 degradation in an endoprosthesis during its installation and
usage. The stroke-based action described in [23] is connected with transferring mecha-
nical energy in the direction perpendicular to the surface, while damaging which
follows during rolling friction consists in passing energy in the direction parallel to the
surface (Fig. 1). In turn, damaging in a planetary mill is connected with both a stroke
and friction (Fig. 2). As it follows from a good amount of researches, the parameters of
o-Ps component of positrons lifetime spectrum can be connected with the sizes of natu-
ral volumes that are free from atoms and with the degree of filling-up the space in the
material with atoms [24–27].
Fig. 1. Fig. 2.
Fig. 1. Scheme of mechanical action on polyethylene during damaging: a – by an impact;
b – by rolling friction (A – polyethylene sample; B – steel element acting on the sample;
C – steel cylinder).
Fig. 2. Scheme of mechanical action on polyethylene during damaging in a planetary mill:
A – steel balls; B – polyethylene sample; C – container.
One of the goals of the present work was also to determine to what degree the
radii of voids in which positronium annihilates depend on the manner of passing
energy to the sample and its value. We hope that the obtained information can prove to
be useful in the technology of new types of this polymer to equip it with even better
physiochemical properties.
Experimental part. The samples used in the research were 3 mm thick discs,
with the diameters of 10 mm (for impact-and slide-based investigations in the mill) and
21 mm (for the tribological investigations), respectively. The samples were cut out of
large blocks of material at temperatures not exceeding 100°C. On having been cut out,
they were being annealed for 5 h at 60°C, under lowered pressure, and slowly cooled
down to room temperature. Then, the surfaces of the samples were cleaned for a few
hours in an ultrasonic cleaner, also at 60°C. For the thus prepared samples, before da-
maging them, positrons lifetime were measured. The source of 22 Na positrons was
placed between two identical samples. Thanks to that, positrons penetrated into the area
of the surface layer and the majority of them annihilated there. The samples were da-
maged after the measurement and their positrons lifetime spectra were measured again.
39
The stroke-slide damaging of the samples took place in Pulversisete 7 planetary
mill manufactured by Fritsch. On the bearing plate of the mill there was a container in
which there were placed two samples and 8 steel balls with the masses of 8 g or 16 g,
respectively, and the diameters of 6.3 mm and 7.9 mm, respectively. The bearing plate
of the mill and the container were rotating in the opposite directions. While the plate
and the container were rotating, the balls in it crashed against and then rolled over the
sample, altering partially its surface structure. The time of damaging always amounted
to 10 min. The used frequencies ω of the mill rotating were 400 and 1066.5 min–1.
The tribological damaging of the
samples (through rolling friction) took
place at a specially constructed device
(Fig. 3). A steel cylinder rolled 10 times
over the samples placed in special reces-
sions, at the speed of 1.1 and 1.31 cm/s,
respectively. The applied parameters of
stress N on the sample were 22.1 and
46.2 MPa, which corresponded to a rela-
tive decrease in the thickness by 3.33 and
6.66%.
The description of damaging of the
samples by a stroke and the manner of de-
termining the duration of a collision are
included in [23].
The lifetime spectra were measured
by means of a fast-fast spectroscope with the resolution of 220 ps. The source of posi-
trons was placed between two samples of the same degree of damaging. The experi-
mentally measured spectra of positrons lifetime always exceeded 106 impulses. The
de-convolution of the spectra into discreet components was made with the use of Life-
time 9 program [28]. The spectra were analyzed by accepting that they were composed
of: one component, two free components, three free components, four components, of
which one had an assumed value of 125 ps.
In order to interpret the results, distributions were chosen for which the index of
experimental data adjustment to a selected annihilation model (χ2) was the closest to
one and the scatter of points on the so-called error strip did not display systematic
changes. The obtained results indicate that the best adjustment is always obtained with
the distribution of spectra into two free components, still the component of a greater
value of positrons lifetime took on values exceeding 2.1 ns. That testified to the forma-
tion of o-Ps in the investigated samples.
Results of the measurements and their interpretation. The majority of resear-
chers investigating positrons annihilation in polyethylene have managed to resolve the
experimentally obtained spectra of positrons lifetime into three and even four compo-
nents, of which, at least, one component has the lifetime of the nanoseconds order.
Perhaps the reason why it has not been possible to distinguish, in the spectrum, two
components of the picoseconds order was the insufficient temporal dissolution ability
of the spectrometer used, and the determined short-lived component of the spectrum is
a composition of two components of the similar lifetime values. The physical interpre-
tation of the changes in this component is difficult and not unambiguous. Therefore,
further in the work, we will discuss the changes in the clearly distinguished long-lived
component of the spectrum, interpreted as a result of the creation and annihilation of
o-Ps in the pick-off process.
It seemed natural to us to accept the assumption that the annihilation parameters
of this long-lived component of the spectrum (positrons lifetime τ2 and intensity of the
Fig. 3. Scheme for damaging samples during
rolling friction: A – steel cylinder;
B – polyethylene samples;
C – steel plate with recesses for samples.
40
component I2) depend on energy (falling to a unit of deactivated surface) passed to the
sample over a unit of time. That is why we will discuss the changes in the values of
lifetime τ2 of positrons which annihilate in the pick-off process induced by different
factors: rolling friction, damaging in a planetary mill and a stroke in dependence on the
energy passed.
For samples damaged by a stroke in the direction perpendicular to the surface.
The energy passed to the sample was calculated as the difference in the potential ener-
gies of the Charper hammer before and after a stroke. A half of the measured time of
the stroke was accepted to be the time of compression action during the stroke.
For samples damaged by friction. Work done during the rolling friction of the
metal cylinder against the sample was accepted to be the energy passed to the sample.
Work W done against the forces of friction T during rolling along path d equals:
W T d= ⋅ , (1)
Whereas, the force of friction is equal:
T N= µ ⋅ , (2)
where µ is rolling friction coefficient; N is force of pressure exerted by the cylinder on
the sample during rolling.
The initial calculations pointed to the fact that the stresses applied in the experi-
ment resulted in elastic deformations in the sample. Thus:
lN S E
l
∆
= ⋅ ⋅ , (3)
where S is area of cross-section of the sample; ∆l/l is relative decrease in the thickness
of the sample; E is Young’s modulus. Since the cylinder was rolling along path d with
constant velocity υ , hence /t d= υ . Substituting dependences (2) and (3) in Eq. (1),
we will finally notice that during one rolling of the cylinder over the sample the follo-
wing energy will be passed to the sample within a time unit:
W lE
S t l
∆
ε = = µ ⋅ ⋅ υ ⋅
⋅
, (4)
On the other hand, after the n-th (n = 10) rolling, the sample will receive the
energy:
ln E
l
∆
ε = ⋅µ ⋅ ⋅ υ ⋅ , (5)
For further calculations we accept that µ = 0.007, E = 750 MPa. The values υ and
∆l are included in Section 2.
For samples damaged in a planetary mill. It was proved [29] that in the process
of interaction between the balls and the sample there is the passed energy W which
equals as follows:
W = A⋅m⋅ω2⋅r3, (6)
where m is mass of the balls; ω is frequency of rotating of the mill wheel; r is diameter
of the balls; A is constant, dependent on the type of material, number of balls and num-
ber of strokes of the balls against the sample.
For further calculations we accept that the mean time of interaction between the
balls and the sample equals the mean time of interacting during a stroke, which
amounts to 1.02⋅10–3 s. Knowing the sizes and masses of the balls, it is possible to de-
termine the value W
S t
ε =
⋅
.
41
Fig. 4 shows the dependence of lifetime τ2 on the energy passed to a unit surface
over a unit of time. It can be seen that for all the ways of damaging time τ2 rises appro-
ximately in a logarithmic manner along with a rise in the energy passed to the sample
during damaging.
Fig. 4. Fig. 5.
Fig. 4. Dependence of the o-Ps component of lifetime, τ2, of the spectrum of positrons lifetime
in PE Chirulen®1120 on the energy passed to the sample during damaging:
by rolling friction ( ); in a planetary mill ( ); by an impact ( ).
Fig. 5. Dependence of the value of the radii of spherical voids in which positronium forms
on the energy passed to the sample during damaging: by rolling friction ( );
in a planetary mill ( ); by an impact ( ).
In compliance with Eldrup’s [24] and Tao’s [25] models, o-Ps component of the
spectrum of positrons lifetime in polymers, liquids and porous materials is connected
with the mean radius of free volume, in which positronium is formed. For the voids of
spherical symmetry and radius R, the relation takes on the form:
1
1
2 0
21 (2 ) sinR R
R R R R
−
−⎡ ⎤π
τ = λ − + π⎢ ⎥+∆ +∆⎣ ⎦
, (7)
where ∆R is a constant parameter determined experimentally. In this work, we accepted
that ∆R = 0.1656. The dependence of the values of radii R, calculated with the use of
(7) on the energy passed to the sample, is presented in Fig. 5. As it is visible, the values
of the radii of empty space, in which o-Ps annihilates, increase very clearly together
with the amount of the energy passed, and their values change from 44% to 14% in
relation to the voids in non-defected PE Chirulen®1120, in dependence on the manner
of damaging.
The energy absorbed by the polymer initiates cracking of the bonds of both C–H
and C–C. As a result the hydrogenous radicals, as well as alkyl radicals of the first and
the second order are formed. They are characterized by (especially the hydrogenous
radicals) a high motility. Their transfer within the matrix causes the occurrence of
voids of spherical symmetry in which positronium is formed. As it can be seen, the
radii of these voids depend on the size of the energy passed to the sample, still their
concentration, determined by intensity I2 of the long-lived component of the spectrum
of positrons lifetime depends also on the way of passing energy to the sample.
Fig. 6 presents the dependence of I2 on the energy passed to the sample in a unit
of time. For the manners of damaging described in this paper the intensity I2 decreases
along with the amount of the transferred energy; however, the drop in the intensity is
the fastest for damaging of samples during rolling friction and the slowest – during
damaging in a planetary mill. The character of the dependences of the radii of the voids
in which positronium is formed and the concentration of these voids on energy sug-
42
gests that looser spaces in the PE Chirulen®1120 sample are formed probably as a
result of associations existing still before damaging of voids of a smaller radii. It can
also be thought that the passing energy in the direction parallel to the surface of the
sample favours loosening of close-to-surface layers of defected samples.
Measurements of the spectra of positrons lifetime in systems in which positro-
nium is formed allow determining the parameter called a relative free volume, which is
significant from the point of view of medical applications of the examined polymer.
The parameter is defined in the following way:
0
0
( )tV V
F
V
−
= , (8)
where Vt is the total macroscopic volume of the examined sample; V0 is a sum of the
volumes occupied by all the atoms of the sample.
Wang [26] and also Kobayashi [27] proposed a half-empirical dependence to de-
termine the value of this parameter on the basis of parameters of the positrons lifetime
spectra:
3
2
4
3
F A R I= ⋅ π ⋅ , (9)
where A is a normalizing constant, equaling, approximately, unity (at room tempera-
ture); R is the radius of a spherical void calculated from the Eldrup–Tao formula.
Fig. 7 presents the dependence of the relative free volume calculated from Eq. (9)
on the surface density of mechanical energy passed to the investigated samples over a
unit of time. As it can be seen, for damaging during rolling friction and a stroke the
relative free volume in the close-to-surface layers of this polymer decreases along with
the rise in the energy passed, whereas it increases during damaging in a planetary mill.
The mechanism of these changes is not yet fully understood and will make a
subject of further research.
Fig. 6. Fig. 7.
Fig. 6. Dependence of intensity, I2, of the o-Ps component of the spectrum of positrons lifetime
in PE Chirulen®1120 on the energy passed to the sample during damaging:
by rolling friction ( ); in a planetary mill ( ); by an impact ( ).
Fig. 7. Dependence of relative free volume, F, in PE Chirulen®1120 on the energy passed
to the sample during damaging: by rolling friction ( ); in a planetary mill ( );
by an impact ( ).
CONCLUSIONS
The conducted research shows that regarding PE Chirulen®1120 there occur con-
ditions for positronium to form; during mechanical damaging, the radii of voids of
spherical symmetry increase along with a rise in energy passed to the sample, indepen-
dent of the manner of damaging; concentration of voids decreases along with a rise in
43
energy passed to the sample, still the rate of the changes in the concentration depends
on the manner of damaging; damaging of PE Chirulen®1120 samples in a planetary
mill causes expansion of relative free volumes, while damaging by friction and impact
decreases this parameter together with the amount of mechanical energy passed during
the damaging.
РЕЗЮМЕ. Досліджували вплив пошкоджень ультрависокомолекулярного поліетиле-
ну марки Chirulen®1120, який застосовують для виготовлення тазостегнових ендопроте-
зів, на час існування позитронів в цьому матеріалі після опромінення. Зразки поліетилену
пошкоджували в лабораторних умовах методами удару, вальцювання та тертя, а також
шляхом зіткнення з металевими кульками у планетарному млині. Зміни часу існування
орто-позитронів аналізували залежно від механічної енергії, отриманої зразком, а зміни
радіусів порожнин, в яких утворюються та анігілюються позитрони, визначали, застосо-
вуючи модель Елдрупа–Тао.
РЕЗЮМЕ. Исследовали влияние повреждений ультравысокомолекулярного поли-
этилена марки Chirulen®1120, который применяют для изготовления тазобедренных эн-
допротезов, на время существования позитронов в этом материале после облучения.
Образцы полиэтилена были повреждены в лабораторных условиях методами удара, про-
катывания и трения, а также путем столкновения с металлическими шариками в планетар-
ной мельнице. Изменения времени существования орто-позитронов анализировали в зави-
симости от механической энергии, полученной образцом, а изменения радиусов полостей,
в которых образуются и аннигилируются позитроны, определяли с применением модели
Елдрупа–Тао.
1. McCrum N. G., Read B. E., and Williams G. Anelastic and dielectric effects in polymeric
solids. – London: Wiley J. & Sons, 1967. – P. 102–121.
2. Ward I. M. Mechanical properties of solid polymers. – London: Wiley J. & Sons, 1971.
– Chapter 4.
3. Kobayashi K. and Nagasawa T. Mechanical properties of polyethylene crystals. II. Deforma-
tion process of spherulite // J. Polym. Sci. Part C. – 1966. – 15. – P. 163–183.
4. Sizes and interfacial free energies of crystallites formed from fractionated linear polyethy-
lene / L. Mandelkern, J. M. Price, M. Gopalan, and J. G. Fatou // J. Polym. Sci. Part A-2.
– 1966. – 4. – P. 385–400.
5. Sudoł M. Studies on electron-beam irradiation and plastic deformation of medical-grade
ultra-high molecular weight polyethylene (UHMWPE). – Opole: Opole University, 2006.
– P. 12–53.
6. Study of relaxation process in polyethylene and polystyrene by positron annihilation / A. Uedo-
no, T. Kawano, S. Tanigawa et al. // J. Polym. Sci. B. – 1996. – 34. – P. 2145.
7. Mallon E. and Schreder D. M. Principles and application of positron and positronium che-
mistry. – Singapore: Jean Y. C. World Scientific, 2003. – P. 253–280.
8. Chlorined poyethylene studiem by positron annihilation / M. Dębowska, A. Baranowski,
K. Jerie et al. // Reactive & Functional Polymers. – 1997. – 33. – P. 337–341.
9. The effect of visible light irradiation on positronium formation in polyethylene AT low
temperature / Y. Ito, T. Hirade, E. Hamada et al. // Acta Phys. Pol. A. – 1999. – 95, № 4.
– P. 533–537.
10. Relations between hole volume and macroscopic volume in various polymers / G. Dlubek,
M. A. Alam, K. Saarinen et al. // Ibid. – 1999. – 95, № 4. – P. 521–526.
11. Carbon Black-polyethylene composites studied by positron annihilation / M. Dębowska,
J. Rudzińska-Girulska, A. Pasternak, and R. Poźniak // Ibid. – 1999. – 95, № 4. – P. 509–514.
12. Osoba W. Investigation of the free-volume changes in thermally treated polyethylene by po-
sitron annihilation // Ibid. – 1999. – 95, № 4. – P. 632–636.
13. Badia A. and Duplatre G. Electron beam and gamma irradiation effect on high density poly-
ethylene studied via positron annihilation lifetime spectroscopy // Radiation Phys. and
Chem. – 1999. – 54. – P. 151–158.
14. Schmidt M. and Maurer F. H. J. Relaxation between free-volume quantities from PVT-EOS
analysis and PALS // Polymer. – 2000. – 41. – P. 8419.
44
15. Osoba W. Influence of the isothermal annealing on the free-volume changes in thermo-
shrunken polyethylene by positron annihilation // Acta Phys. Pol. A. – 2001. – 99, № 3/4.
– P. 447–454.
16. Relaxation behavior of polymers probed by positron annihilation lifetime spectroscopy
/ T. Suzuki, Ch. He, V. Shantarowich et al. // Mat Res. Innovat. – 2003. – 7. – P. 31–36.
17. Correlation between free-volume parameters and physical properties of poyethylene-nitride
rubber blend / E. Gomoa, N. Mostafa, M. Mohsen, and M. Mohammed // J. of Mater. Engng
and Performance. – 2004. – 13. – P. 538–587.
18. Danch A., Osoba W., and Wawryszczuk J. Influence of temperature and pressure on the free-
volume in thermo-shrunken polyethylene by positron annihilation // Acta Phys. Pol. A.
– 2008. – 113, № 5. – P. 1307–1313.
19. Dryzek J., Dryzek E., and Cleff B. Defect Profile Induced by Friction and Wear Processes
Detected by Positron Annihilation Method // Ibid. – 1995. – 88, № 1. – P. 129–133.
20. Dryzek E. and Dryzek J. Positron Annihilation Studies of the Subsurface Zone in Aluminium
Alloys // Ibid. – 2006. – 110, № 95. – P. 569–575.
21. Pietrzak R., Szatanik R., and Szuszkiewicz M. Measurements of positrons lifetimes in cor-
roded nickel // Ibid. – 1999. – 95, № 4. – P. 647–651.
22. Pietrzak R., Smiatek W., and Szatanik R. Positron Annihilation in Corroded Steels St20 and
St3S // Ibid. – 2006. – 110, № 5. – P. 667–676.
23. Pietrzak R. and Szatanik R. The effect of impact pressure on positron lifetime in ultra high
molecular weight polyethylene (PE-UHMW) Chirulen®1120 // Material Science Forum.
– 2010. – 666. – P. 85–88.
24. Eldrup M., Lightbody D., and Sherwood J. N. The temperature dependence of positron life-
times in solid pivalic acid // Chem Phys. – 1981. – 63. – P. 51–58.
25. Tao S. J. Positronium Annihilation in Molecular Substances // J. Chem. Phys. – 1972. – 56.
– P. 5499–5510.
26. Pressure dependence of positron annihilation in epoxy polymers / Y. Y. Wang, H. Naka-
nishi, Y. C. Jean, and T. C. Sandreczki // J. Polym. Sci. B, Polym. Phys. – 1990. – 28.
– P. 1431–1441.
27. Free volume and physical aging of poly(vinyl-acetate) studied by positron annihilation / Y. Ko-
bayashi, W. Zheng, E. F. Meyer et al. // Macromolecules. – 1989. – 22. – P. 2302–2306.
28. Kansy J. Microcomputer program for analysis of positron annihilation lifetime spectra
// Nucl. Instrum. Methods, A. – 1996. – 374. – P. 235–244.
29. Abdellaoui M. and Gaffet E. Mechanical alloying in a planetary ball mill-kinematic descrip-
tion // J. de Physique IV. – 1994. – 4. – P. 291–296.
Received 01.02.2012
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