On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K
The stereoregular radical polymerization in photo- or g-irradiated crystals of p-diethynylbenzene (DEB) has been found to proceed in the temperature range of 4.2–300 K [J. Low Temp. Phys. 139, 675 (2005)]. We have studied the kinetics of this process. The polymerization of acetylene monomers due to...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1171072017-05-20T03:03:39Z On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K Gordon, D.A. Mikhaylov, A.I. 7th International Conference on Cryocrystals and Quantum Crystals The stereoregular radical polymerization in photo- or g-irradiated crystals of p-diethynylbenzene (DEB) has been found to proceed in the temperature range of 4.2–300 K [J. Low Temp. Phys. 139, 675 (2005)]. We have studied the kinetics of this process. The polymerization of acetylene monomers due to the system of conjugated bonds formation results in the shift of a crystal absorption band from UV to visible. Being compared with gravimetrical data on the polymer yield, it allowed the direct detection of polymerization process in a crystal. The monomer radicals, initiating the polymerization process, as well as propagating macroradicals were detected by ESR method. The rates of both radical formation and chemical reaction of polymerization retard, as it inherent to solid phase processes, already at small yields. Thus we applied a mechanism pertaining to the first stages of the processes only. It has been proved that both photo- and g-induced polymerization have chain character in the temperature range 77–300 K but it is most probably not chained at 4.2 K and, for photo-polymerization, every act of monomer addition to the polymer needs an extra quantum of light. The kinetic chain length (the number of added monomer molecules per radical) turned out to be around of 200 at 300 K and of 20 at 77 K. It was interesting to note that polymer just formed was able to be modified — the radicals then created in polymer chain were able to add monomer molecules forming, in such a way, a branched polymer. This process, of course, is not chained too. 2009 Article On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K / D.A. Gordon, A.I. Mikhaylov // Физика низких температур. — 2009. — Т. 35, № 4. — С. 355-361. — Бібліогр.: 5 назв. — англ. 0132-6414 PACS: 66.70.Hk, 61.82.Pv http://dspace.nbuv.gov.ua/handle/123456789/117107 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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7th International Conference on Cryocrystals and Quantum Crystals 7th International Conference on Cryocrystals and Quantum Crystals |
| spellingShingle |
7th International Conference on Cryocrystals and Quantum Crystals 7th International Conference on Cryocrystals and Quantum Crystals Gordon, D.A. Mikhaylov, A.I. On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K Физика низких температур |
| description |
The stereoregular radical polymerization in photo- or g-irradiated crystals of p-diethynylbenzene (DEB) has been found to proceed in the temperature range of 4.2–300 K [J. Low Temp. Phys. 139, 675 (2005)]. We have studied the kinetics of this process. The polymerization of acetylene monomers due to the system of conjugated bonds formation results in the shift of a crystal absorption band from UV to visible. Being compared with gravimetrical data on the polymer yield, it allowed the direct detection of polymerization process in a crystal. The monomer radicals, initiating the polymerization process, as well as propagating macroradicals were detected by ESR method. The rates of both radical formation and chemical reaction of polymerization retard, as it inherent to solid phase processes, already at small yields. Thus we applied a mechanism pertaining to the first stages of the processes only. It has been proved that both photo- and g-induced polymerization have chain character in the temperature range 77–300 K but it is most probably not chained at 4.2 K and, for photo-polymerization, every act of monomer addition to the polymer needs an extra quantum of light. The kinetic chain length (the number of added monomer molecules per radical) turned out to be around of 200 at 300 K and of 20 at 77 K. It was interesting to note that polymer just formed was able to be modified — the radicals then created in polymer chain were able to add monomer molecules forming, in such a way, a branched polymer. This process, of course, is not chained too. |
| format |
Article |
| author |
Gordon, D.A. Mikhaylov, A.I. |
| author_facet |
Gordon, D.A. Mikhaylov, A.I. |
| author_sort |
Gordon, D.A. |
| title |
On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K |
| title_short |
On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K |
| title_full |
On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K |
| title_fullStr |
On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K |
| title_full_unstemmed |
On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K |
| title_sort |
on kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 k |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2009 |
| topic_facet |
7th International Conference on Cryocrystals and Quantum Crystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117107 |
| citation_txt |
On kinetic features of photo- or g-induced polymerization in p-diethynylbenzene crystals in the temperature range of 4.2-300 K / D.A. Gordon, A.I. Mikhaylov // Физика низких температур. — 2009. — Т. 35, № 4. — С. 355-361. — Бібліогр.: 5 назв. — англ. |
| series |
Физика низких температур |
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2025-07-08T11:39:40Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4, p. 355–361
On kinetic features of photo- or �-induced polymerization
in p-diethynylbenzene crystals in the temperature range
of 4.2–300 K
D.A. Gordon and A.I. Mikhaylov
Institute of Problems of Chemical Physics of RAS, 1 Semenov Ave., Chernogolovka 142432, Russia
E-mail: diliarag@gmail.com
Received January 26, 2009
The stereoregular radical polymerization in photo- or �-irradiated crystals of p-diethynylbenzene (DEB)
has been found to proceed in the temperature range of 4.2–300 K [J. Low Temp. Phys. 139, 675 (2005)]. We
have studied the kinetics of this process. The polymerization of acetylene monomers due to the system of
conjugated bonds formation results in the shift of a crystal absorption band from UV to visible. Being com-
pared with gravimetrical data on the polymer yield, it allowed the direct detection of polymerization process
in a crystal. The monomer radicals, initiating the polymerization process, as well as propagating macro-
radicals were detected by ESR method. The rates of both radical formation and chemical reaction of poly-
merization retard, as it inherent to solid phase processes, already at small yields. Thus we applied a mecha-
nism pertaining to the first stages of the processes only. It has been proved that both photo- and �-induced
polymerization have chain character in the temperature range 77–300 K but it is most probably not chained
at 4.2 K and, for photo-polymerization, every act of monomer addition to the polymer needs an extra quan-
tum of light. The kinetic chain length (the number of added monomer molecules per radical) turned out to be
around of 200 at 300 K and of 20 at 77 K. It was interesting to note that polymer just formed was able to be
modified — the radicals then created in polymer chain were able to add monomer molecules forming, in
such a way, a branched polymer. This process, of course, is not chained too.
PACS: 66.70.Hk Glasses and polymers;
61.82.Pv Polymers, organic compounds.
Keywords: polymerization, low temperature, conjugated bonds, free radicals, chain processes.
1. Introduction
The polymers with conjugated bonds are of great inter-
est because of their properties. The fact of stereoregular
polymer formation under photo- or �-irradiation of pa-
ra-diethynylbenzene (DEB) crystals may be thought of
as proved [1]. The present work is concerned with study
of polymerization mechanism and kinetics, in particular,
with elucidation of the problem whether the process has
chain character and with determination of polymerization
efficiency. During increase of the irradiated samples tem-
perature, to remove the nonreacted monomer, the contri-
bution of post-polymerization in the process is promi-
nent. Therefore the methods of optical and ESR
spectroscopy were used because they allow to investigate
the reaction and analyze products obtained directly in
solid phase without the sample structure distraction. The
�- or UV irradiation of samples leads to a significant red
shift of DEB absorption band: colorless crystals become
yellow. That the yellow color is due to polymerization
rather than to conversion of individual molecules was
proved by experiments where DEB molecules were di-
luted by xenon; in the latter case the samples did not dem-
onstrate red shift of the absorption band. The conjugated
bonds formed during polymerization surely shall contrib-
ute to this red shift.
2. Experimental
The crystals of DEB for optical investigations were
grown, from the melt, between two quartz plates in their
central calibrated part, where it was possible to grow spe-
cies of thickness L of 1–50 �m and area of 2–20 mm2. Ab-
sorption spectra were recorded on a Hitachi spectro-
© D.A. Gordon and A.I. Mikhaylov, 2009
photometer; ESR spectra were recorded on EPR-21
spectrometer (3 cm) at microwave power 10–4 W. The
polymerization was initiated by 60Co irradiation or by
light from DRSH-1000 or DRSH-500 mercury lamps.
Low-temperature irradiation and investigation were per-
formed using optical cryostats.
3. Results and discussions
As it is seen from Fig. 1, all kinds of radiation: �-radia-
tion, light with � = 253.7 nm or with 300 nm < � <
< 340 nm, cause the appearance of an absorption band
with the center near 400 nm; there is more red shift (up to
700 nm), contribution of which is different for different
kinds of irradiation (Fig. 1,a–d). However, in the region
320–470 nm, where basic absorption takes place, spectra
are absolutely identical. It means that their absorption
cross-sections in this region shall be close. To establish an
agreement between absorption density change and poly-
merization efficiency, the following approach has been
used. In the case of polymerization at 300 K nonreacted
monomer (or the monomer and solvent) was removed by
evacuation. The optical spectra were then recorded and,
after that, the polymer yields were determined gravimet-
rically.
Both the yield of polymerization determined in such
a way and the polymer absorption intensities decrease
with an increase of irradiation dose (Fig. 2). This is typi-
356 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
D.A. Gordon and A.I. Mikhaylov
��
�360
b
D
1.0
0.5
0
0.5
1.0
300 500 700
�, nm
300 500 700
�, nm
D
1.0
0.5
0
300 500 700
�, nm
a
0
D
1.0
0.5
0 0
400 500 600
253.7 nm
313 nm
60
Co
d
�, nm
c
0
105
72
35
25
15
10
60 3
138
105
0.65
1
3
2
6
25
10
45
60
Fig. 1. Absorption spectra of DEB crystals (L = 1 �m, 300 K) before (0) and after irradiation (time in min shown in figure) by:
a) �-radiation (500 kGy); b) light (300 nm < � < 340 nm, I0 = 2.4·10
17
quant/cm
2
·s); c) light (� = 253.7 nm, I0 =
= 1·10
16
quant/cm
2
·s); d) DEB crystals absorption spectra for different types of irradiation.
cal for radiation-chemical processes in solid phase, e.g.,
for the processes of radical accumulation, including radi-
cal formation in DEB [2], and for chemical reactions in
solid state [3], including polymerization reaction [4]. It is
commonly agreeable to call these effects kinetic stop ef-
fect («kinetic», because the changes of process conditions
may lead to its «reviving» [2,4,5]). Similarly as in these
cases, the effect observed in our work is not associated
with reagents expenditure because, during temperature
rise, the process rate sharply increases and significant
conversion yield can be reached. It is not connected with
a decay of radical centers. ESR investigations have
shown that process «reviving» is not due to formation of
new radicals but due to propagation of «stilled» macro-
molecules. Since this effect was observed for reactions of
radical recombination and for low-temperature oxidation
of macro-radicals, it is hard to assume that in polymeri-
zation reactions it has been caused by macromolecules
lengthening or by their interlock.
3.1. Connection between absorption spectra and poly-
merization characteristics
At very small irradiation doses, the polymerization
yield and optical absorption (in the polymer absorption
range) depend linearly on the absorbed dose, which al-
lows one to determine correctly the radiation and/or quan-
tum yields. In the case of gamma-irradiation, it is possible
because one can use sample as large as is wished, but in
the case of UV irradiation it is hard to accomplish. There-
fore, it was necessary to create models which could help
to describe correctly the linearity of polymerization yield
at small doses and reaching the limit of yield at large
doses, and help to make correct interpolation for the
range of middle doses.
The simplest interpolation is
dD
dt
D
t
�
�
0 43 0.
�
. (1)
Its solution
D D
t
� ��
�
�
0 43 10. ln
� (2)
gives the obvious asymptotes:
D
D
t� 0 43 0.
�
(short times) , (3)
D
D
t
0
� �log log � (long times) . (4)
The convenience of this equation lies in the possibility
of simple parametric description of kinetic curves ob-
tained experimentally, as well as in correct determination
of initial incline of kinetic curves, which enables to find
real values of polymerization quantum and/or radiation
yields. Actually, initial incline is equal, in our designa-
tions, to D0 /� and it is governed by the value of D0 — its
inclination in the coordinates (D, log t) and by the param-
eter � which can be found from the point of these lines in-
tersection with abscissa axis. As it seen from Fig. 2,d ki-
netic curve may have logarithmic character already at
very low conversions and, therefore, the observed initial
incline can differ from that found by interpolation for-
mula (2) by an order of magnitude. From the accepted
model, it follows that � is a time when (in the range of
more intensive polymerization, for strongly absorbing
monomer — in the front of sample) some critical concen-
tration of polymer molecules N p
c (T) can be reached, at
which point the polymer just formed retards further poly-
merization. One can show that
� � �� �N N Ip m( )0
1 , (5)
where � (�irrad ,T) is the quantum (radiation) yield, I0 is
intensity of incident light with �irrad (or dose intensity of
On kinetic features of photo- or �-induced polymerization
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 357
D
1.0
0.5
D
0.5
5 10
t, min t, min
20 100
a b
t, mint, h
D
20
10
1
2
10 20
c
t, min
D
D
1.4
1.0
0.6
0.2
0.2
0.1
25 50
d
0
0 0
0
0
1 3
Fig. 2. Dependence of polymer optical density D (at � =
= 400 nm) on time of DEB crystals irradiation (L = 1 �m, 300 K)
by light: a) � = 230–340 nm, I0 = 4.2·10
17
quant/cm
2
·s;
b) � = 253.7 nm, I0 = 1·10
16
quant/cm
2
·s; c) �-radiation (L =
= 1 �m (curve 1), L = 10 �m (curve 2), I = 22 kGy/h); d) light
(300 nm < � < 340 nm, I0 = 2.4·10
17
quant/cm
2
·s, L = 50 �m).
gamma-irradiation), Nm is monomer density, Np � N p
c ,
and � is polymer cross-section. It is important to point out
that the temperature dependence of the kinetic curves for
short and long times of irradiation has different nature. At
short times, it is determined by polymerization quantum
yield changes with temperature (that is, by microscopic
characteristics of the process); at long times it does not
depend on quantum yield but it is determined by macro-
scopic parameter — critical concentration of polymer
formed — N p
c .
Two important features of the kinetic curves, follow-
ing from the accepted model, are worth to be noted:
1. If the spectrum of polymer absorption does not de-
pend on dose, the curves of D dependence on time for dif-
ferent � in coordinates (D, log t) at long times present
bunch of lines rising from point (0, log t).
2. The kinetic curves inclinations for given � in loga-
rithmic range at photo-irradiation shall: a) not depend on
irradiation intensity; b) weakly depend on irradiation �;
c) not depend on thickness of samples. In case of
gamma-irradiation of thin samples, the inclinations shall
be 2 to 3 times greater than those at optical excitation.
We observed that polymerization takes place at irradi-
ation by light with � > 300 nm, which is longer than that
of monomer absorption red edge (300 nm). In this case,
very small part of incident light will be absorbed by the
monomer. Nevertheless, at comparable intensities of
short wave and long wave incident light, the rate of color
change (in the range of significant D) appeared to be com-
parable (Fig. 2,b and Fig. 3,a). This fact suggests that
polymer formed is able (by absorbing the light) to pro-
duce radicals which lead to further polymerization. The
autocatalytic character of D(t) dependence at irradiation
by light of 300 nm < � < 340 nm (Fig. 3,a) supports this
idea: polymer just formed stimulates further polymeriza-
tion. It is not clear, if polymerization first occurs due to
weak absorption of light with � = 313 nm (red wing of
monomer absorption line) or due to action of the traces of
light with more short waves on the sample (in the range of
monomer absorption). A comparison of initial portion of
kinetic curves of sample irradiated by light with 300 nm <
� � < 340 nm and curves of sample first irradiated by light
with � = 253.7 nm (Fig. 3,b) demonstrated disappearance
of autocatalytic character in the sample where polymer
was preliminarily obtained. Autocatalytic character re-
tains its nature until reaching significant optical density,
when practically all incident light is absorbed and poly-
mer volume begins linear growth with time.
3.2. Experimental determination of polymer cross-sec-
tion, quantum and/or radiation yields of polymerization,
and polymer critical concentration
The most simple case is gamma-irradiation one. Since
the absorption is uniform across the whole sample thick-
ness, it is possible to work with samples of such thickness
that significant absorption by the just formed polymer
would occur at low conversions. As a result, the
dependences of D on the dose show as lines (Fig. 2,c) and
their inclination give the polymerization radiation yield.
358 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
D.A. Gordon and A.I. Mikhaylov
a
b
1
2
3
D
1.5
1.0
0.5
30 90
t, min
3
t, min
10 30 50 70
1
2
D
0.5
0
0
Fig. 3. Dependence of polymer optical density D on time of
DEB crystals irradiation (L = 1 �m, 300 K) by light:
a) 300 nm < � < 340 nm, I0 = 2.4·10
17
quant/cm
2
·s; b) during
first 9 min (vertical line) sample was irradiated by light with
� = 253.7 nm, I0 = 1·10
16
quant/cm
2
·s, then it was irradiated
by light with 300 nm < � < 340 nm, I0 = 2.4·10
17
quant/cm
2
·s.
Dashed lines are the dependence of D on t during irradia-
tion of sample by light (300 nm < � < 340 nm, I0 =
= 2.4·10
17
quant/cm
2
·s) without preliminary irradiation (data
of Fig. 3,a). At � = 360 (curve 1), 400 (2), and 500 (3) nm.
A divergence from the linear law appeared only at large
doses (> 1000 kGy). At photo-irradiation, notable absorp-
tion by polymer molecules takes place when polymer lo-
cal concentration is significant and correct determination
of quantum yield can be done only taking in consideration
the «kinetic stop» effect. Our experiments have shown
that absorption spectra characteristics of irradiated DEB
crystals are well described by simple phenomenological
model given above. In fact, practically for all irradiation
times, the dependence of D on log t constitutes straight
lines for all used types of irradiation, intensities, and dif-
ferent sample thickness (Fig. 4). Moreover, for different
observation wavelengths, kinetic dependence in these co-
ordinates constitutes a bunch of lines rising from the same
point located on abscissa axis (Fig. 4,a,b). As mentioned
above, this is a proof that polymer absorption spectra
even at significant conversion rates are irrelevant. Ten
times light intensity enhancement (Fig. 4,c) as well as ten
times sample thickness increase does not lead to notable
change of lines incline in coordinates (D, log t). Interpo-
lation expression (2) gives good description of the de-
pendence (D, log t) for samples irradiated by light with
� = 253.7 nm in the range from shortest to longest time
(Fig. 5).
For open light of DRSH-1000 lamp, the picture of pro-
cess is more sophisticated, since in this case one has to
deal with the whole (230–340 nm) spectral range of UV
irradiation action on DEB. At that, the action of light in
the range of monomer own absorption (230–290 nm) is
superimposed on action of light with spectral range
(300–340 nm) which is weakly absorbed by monomer but
notably absorbed by polymer. Therefore, the curve in the
coordinate (D, log t) displays two parts with different in-
clination (Fig. 4,d). Polymer absorption efficiency was
found by the comparison of irradiated sample absorption
value and gravimetrically determined amount of polymer
in it. One should take into account that gravimetrical
method gives good results only in the case of low conver-
sions. It means that correct determination is possible for
gamma-irradiated samples where one can investigate
a sample of any thickness which allows of an amount of
polymer that can be suitable for correct results. The val-
ues of absorption cross-section and efficiency were found
as follows: �p (400 nm) � 3.0·10–17 cm2 and �p (400 nm) �
� 1.4·105 cm–1 (monomer density was Nm = 4.8·1021).
Since the absorption characteristics for polymers ob-
tained by different irradiation ways (Fig. 1,d) are close,
and there is independence of absorption spectrum on con-
version level, the values of polymer absorption cross-sec-
tion and efficiency obtained for gamma-irradiated sam-
ples can be used for photo-irradiated ones. Results
accounted on the base of the experimental data are sum-
marized in Table 1.
Making an interpretation for the samples irradiated by
light with � > 300 nm (beyond the monomer absorption
On kinetic features of photo- or �-induced polymerization
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 359
D
1.0
0.5
–1 1 12 2
D
0.5
log (t, min) log (t, min)
1
2
3
1
2
3
4
a b
–1 1 2
D
0.5
1
2
3
c D
1.0
0.5
–1 1 2
d
0
0
0
0
log (t, min)log (t, min)
Fig. 4. Dependence of polymer optical density D on logarithm
of DEB crystals irradiation time by light with: a) � = 253.7 nm
(irradiation conditions the same like in Fig. 2,b). At � = 360
(curve 1), 450 (2), 500 (3) nm; b) 300 nm < � < 340 nm (irra-
diation conditions like in Fig. 3,a). At � = 360 (curve 1),
400 (2), 450 (3), and 500 (4) nm; c) � = 253.7 nm. Sample
thickness: 50 �m (curve 1); 1 �m (2, 3). Intensities: I0 =
= 1·10
16
quant/cm
2
·s (1, 2); 10
15
quant/cm
2
·s (3). At � =
= 400 nm; d) � = 230–340 nm (irradiation conditions the same
like in Fig. 2,a). At � = 400 nm.
2.0
1.5
1.0
0.5
D
/D
0
0.5 1.00 1.5 2.0
log (1 + 1/ )�
Fig. 5. Checking of interpolation formula D D� �043 0.
� �ln ( / )1 t � for polymer optical density at DEB crystal (L =
= 1 �m, 300 K) irradiation by light with � = 253.7 nm. D0 =
= 0.23, � = 15 s.
range) is more difficult. In this case autocatalytic charac-
ter of kinetic data at low conversions (Fig. 3,a) points to
possibility that polymerization occurs due to light absorp-
tion by polymer molecules. The connection of kinetic
curves autocatalytic character with light absorption by
polymer formed during irradiation by this light is sup-
ported by experiments on irradiation of DEB crystals
which already contain polymer (Fig. 3,b). In turn, it
means that in this case, contrary to considered above
other cases, the amount of absorbed light and depth of its
penetration are changing during irradiation. However,
these results have basic importance to understanding po-
lymerization mechanism of acetylene monomers. There-
fore, we tried to gather even broad quantitative informa-
tion for this case too. Experiments with samples of large
thickness (L = 50 �m instead L = 1 �m) have shown that
the absorption of light with � > 300 nm in DEB molecules
is negligibly small, and that all indicated absorption is
connected with polymer thermally formed in the process
of monomer crystals growing (Table 1).
The comparison of polymerization quantum and/or ra-
diation yields of DEB crystals with those of radicals de-
termined by ESR method (which initiate polymerization)
has shown:
1. At low conversions polymerization kinetic length of
chain both for DEB crystals gamma-irradiation and/or
photo-irradiation (in monomer-own absorption range) is
rather large and equal to 2·102. It is worth to note that for
�-irradiation, when it was possible to define polymeri-
zation yield by gravimetrical method, the value of chain
kinetic length has appeared to be close to that value (see
Table 1), which confirmed corrections of optical investi-
gations interpretation.
2. Photo-irradiation of polymer molecules which were
obtained in one way or another leads to nonchain poly-
merization (chain kinetic length is equal to 2±1).
3. It is necessary to take in consideration that long ki-
netic chains appear only at low conversion. By all types of
irradiation, there is the polymer molecules critical con-
centration (about the same) starting with which the
polymerization kinetic lengths decrease. Such a «kinetic
stop» comes at conversions around of 7%. And at conver-
sions about of 30–40%, the rates of «monomer» (chain)
and «polymer» (nonchain) polymerizations are closely re-
lated.
Thus, DEB crystals polymerization at 300 K has
a chain character.
3.3. Low-temperature investigations
As it was mentioned above, the polymerization takes
place both at 77 and 4.2 K. Similarly as at 300 K, the irra-
diation by open light of DRSH-1000 lamp at 77 K leads to
red shift in absorption spectra (Fig. 6,a). The character of
spectra shows that there is a set of polymer molecules of
different length. If such molecule is a dimmer, its absorp-
tion spectrum would have a red shift but the edge of ab-
sorption band would be as sharp as monomers one. Pro-
cessed data showed that dependence (D versus log t) has
a logarithmic character at already very small conversions.
For correct definition of quantum and/or radiation yields
and critical concentration of polymer formed, an inter-
polation formula (2) was used as it was done at 300 K.
The determined quantum yield has appeared to be around
3·10–3. The kinetic length of chain is equal to 30±15
(Table 1). The same kinetic length of chain determined by
another way — as a ratio of gravimetrically found poly-
mer yield to concentration of radicals leading a chain —
appeared to be near and equal to 20 (this experiment was
carried out for gamma-irradiated sample). Post-polymer-
ization was observed during sample heating (Fig. 6,b). Its
amount depends on initial portion of polymer formed dur-
ing irradiation at 77 K: the more initial polymer fraction
the less post-polymerization fraction.
Thus, under photo- or gamma-irradiation of DEB crys-
tals at 77 K, the chain-type polymerization occurs with ki-
netic length around 20, which is an order of magnitude
360 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
D.A. Gordon and A.I. Mikhaylov
Table 1. Characteristics of DEB crystals polymerization
Initiation method
T,
K
Sample’s
thickness,
L, �m
Light beam
intensity,
I0, quant/cm
2
·s
D0
�,
s
�p ,
10
5
cm
–1
(� = 400 nm)
Polymerization
quantum and ra-
diation yield, ��
(� = 400 nm)
N p
c Nm/ ,
%
Quantum and
radiation yield
of radicals,
GR
Kinetic length
of chain,
v
� = 230–340 nm 300 1.0±0.2 (4.2±1.0)·1017 0.42 0.67 1.3±0.4 (2±4)·10–2 10 (1.1±0.2)·10–4 200
� = 253.7 nm 300 1.0±0.2 (1.0±0.3)·1016 0.23 15 1.3±0.4 5.68·10–2 7.0±2.0 (1.2±0.2)·10–4 (4.7±2.0)·102
�-irradiation 60Ñî 300 1.0±0.2 (12±1.2) kGy/h 1.3±0.4 8.1 10 (5.0±1.0)·10–2 (1.6±0.6)·102
� = 300–340 nm 300
1.0±0.2
(2.4±0.6)·10
17
1.4
1.3±0.4
3.0·10–4 37±10
(3.0±0.6)·10–4
1.0±0.5
1.25 2.1·102 0.88·10–3 32±8 3±2
� = 230–340 nm 77 2.0±0.4 (6.0±1.5)·1016 0.175 37.8 1.3±0.4 3.00·10–3 7.0±2.0 (1.1±0.2)·10–4 30±15
less than that for polymerization at 300 K. It is interesting
to note that the critical concentration has appeared to be
the same as for polymerization at 300 K. It means that
polymer chains interlock each other just geometrically
and the temperature governs kinetic length of chain, in
other words, the rate of critical concentration approach.
In case of polymerization at 4.2 K, all observations
were carried out only qualitatively. It has appeared that
with ratio like that at 77 K, photo- and gamma-irradiation
lead to red shift responsible for polymer formation. Poly-
mer formed thus shows a dichroism. Post-polymerization
process takes place during heating of the samples and
polymer obtained in such a way has the same absorption
spectra as polymer formed at higher temperatures.
To resolve if the chain process makes a contribution to
polymerization at 4.2 K, one should carry out further ex-
periments. Anyway the mechanism of monomer mole-
cules addition to polymer ones (even in succession) at
temperatures, at which the processes with activation en-
ergy of 0.1 kcal/mol cannot be performed, is of great
interest.
Conclusion
1. It was shown that the kinetics of polymer accumula-
tion is in a good agreement with the phenomenological
model
D D
t
� ��
�
�
0 43 10. ln
�
.
2. Polymer absorption efficiency, polymerization
quantum yield, and critical polymer concentration, begin-
ning with which the effect of «kinetic stop» has appeared,
have been determined.
3. The polymerization kinetic chain length (�) was de-
termined at low conversions by comparison of polymer-
ization quantum or radiation yields with yields of free
radicals initiating polymerization process. It is shown
that for �- or UV irradiation (in the range of monomer-
own absorption) the values of � are equal to 200 at 300 K
and 20 at 77 K.
4. Nonchain (� = 1) polymerization takes place in the
course of light absorption by polymer formed.
The most plausible hypothesis is that the polymeriza-
tion at 4.2 K (contrary to that at 300 or 77 K) is nonchain
(� = 1) and, for polymerization, every act of monomer ad-
dition to polymer needs extra quantum of light.
1. D.A. Gordon and A.I. Mikhaylov, J. Low Temp. Phys. 139,
675 (2005).
2. Delyara A. Gordon and Alfa I. Mikhailov, J. Polymer Sci.
B: Polymer Phys. 32, 2405 (1994).
3. A.I. Mikhaylov and S.I. Kuzina, Eur. Polymer J. 26, 105
(1990).
4. À.Ì. Kàplan, D.P. Kiryukhin, and V.I. Gol’danskii, DAN
SSSR 190, 1387 (1970).
5. A.I. Mikhaylov, À.I. Bol’shakov, Ya.S. Lebedev, and V.I.
Gol’danskii, Fiz. Tverd. Tela 14, 1172 (1972).
On kinetic features of photo- or �-induced polymerization
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 361
a
1
2 3
4 6
7
b
1
2
3
D
0.5
0.1
400 500 600
�, nm
400 500 600
�, nm
D·10
–2
4
2
5
Fig. 6. a — Absorption spectra of DEB crystal (L = 2 �m) ir-
radiated by light (� = 230–340 nm, I0 = 6·10
16
quant/cm
2
·s)
at 77 K. Time (min): 2 (1); 2.5 (2); 4 (3); 6 (4); 8 (5); 10 (6);
40 (7). b — Absorption spectra changes at heating of the irradi-
ated at 77 K DEB crystal: absorption spectrum of DEB crystal
irradiated at 77 K by light with � = 230–340 nm, I0 =
= 6·10
16
quant/cm
2
·s (curve 1); an increase of D after heating
(2.5 grad/min) of this sample up to 230 (2) and 300 (3) K.
Spectra were recorded at 77 K.
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