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Long Periods in Drawn Polyethylene.

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Table 5. Fiber properties of poly(4,4-dimethylazetidinone)
in comparison with Nylon-6 and silk
Physical and mechanical
M. p. of crystallite [ “C]
Specific gravity
Tensile strength, dry [glden]
Elongation to break, dry [
Relative tensile strength,wet[ %
Tenacity (knot), [%I
Moisture uptake (65 % rel.
humidity, 20 “C)[
Nylon 6
(normal) Silk
4.1 -5,8
ca. 80
remarkable stability to oxidative attack, which prevents
yellowing of the fiber on heating. This stability is
apparently due to the two methyl groups in the nionomer unit (XXVI) which shield the neighboring atoms
from attack by oxidizing agents. The poly-P-lactam
with the isomeric monomer tinit (XXVII) discolors on
heating just like normal polyamides.
[*I Fasertafel des Deutschen Forschungsinstilutsfur Textilindustrie
(Fiber Table of the German Textile Research Institute), Reutlingen
(Values from Sept. 1960).
In comparison to other polyamides, fibers made from
poly(4,4-dimethylazetidinone) are characterized by their
Fibers made from poly(4,4-dimethylazetidinone)can be
dyed like those from poly-ecaprolactam, but they have
a poorer affinity for most of the dyestuffs tested so far.
The best results were obtained with dispersion dyestuffs.
Received, March 27th, 1962 [A 205/40 IEI
Long Periods in Drawn Polyethylene [*]
Meridional reflections appearing in small-angle X-ray diflraction diagrams of drawn
polyethylene are caused by a nearly periodic arrangement of crystalline and disordered
regions. The long period, which is determined by the average distance between two consecutive crystallites, depend on the method ofpreparing the sample. The time and temperature
dependences of the positions of the small-angle reflections have been investigated. The
growth of the long period of unoriented bulk polyethylene and polyethylene single crystals
follows the same time dependence as that of stretchedfilms. However, characteristic diflerences were observed in the relationship between density and long period; they are attributed
to the fact that in single crystals and in material crystallized from the melt, the chains are
folded at the boundaries of the crystallites, whereas this is not the case in stretched polyethylene.
I. Introduction
The properties of high polymeric solids depend not
only on the chemical structure of the macromolecules
but also on the thermal and mechanical treatment of the
samples. This is especially true for crystallizable high
polymers, where the pretreatment affects the relative
arrangement of the chains; for example, one may
obtain samples with different lattice modifications or
different degrees of crystallinity. These effects can be
measured by wideangle scattering of X-rays and other
methods. In addition, pretreatment also has an effect
on the size of the crystallites, on their relative arrangement, and on their structural relationship to disordered
[*] From a lecture delivered on Apr. 11th 1962 at the meeting of
the GDCh-Fachgruppe “Kunststoffe und Kautschuk’ (Plastics
and Rubber Division of the German Chemical Society) in Bad
regions. These three structural characteristics are
grouped together under the term “microstructure”.
Their characteristiclinear dimensions are in the order of
magnitude of 100 to 1OOO A; suitable methods of
investigating them are, therefore, measurements of the
small-angle diffraction of X-rays and electron microsCOPY.
Hess and Kiessig [I] were the first to recognize the importance
of small-angle diffraction of X-rays for determinating the
relative arrangement of the crystallites. They found long
periods of the order of magnitude of 100 A for stretched polyamides and polyesters; these could not be associated with the
structure of the molecular chains, so they, therefore, considered the positions of these small-angle reflections on the
meridian as a measure of the relative distance between the
centers of gravity of two consecutive crystallites lying along
the fiber’s axis. This interpretation is still accepted today,
although certain aspects of the original model appear to be
questionable in the light of more recent investigations.
[I] K . Hess and H. Kiessig, Z. physik. Chem. (A) 193, 196 (1944);
Kolloid-Z. 130, 10 (1953).
Angew. Chem. internat. Edit. I Vol. I (1962) 1 No. 9
Since the discovery of these long periods in polyamides,
similar effects have been observed in many other
synthetic high polymers. It can therefore be assumed
that the nearly periodic arrangement of approximately
equally large crystallites in the chain direction indicated
by the small-angle period is a general and typical
structural characteristic of crystalline polymers. The
as yet unexplained process leading to this structure
is designated as “periodic crystallization” [2].
In order to interpret the small-angle effect, two points
must be clarified: the structure, responsible for the
observed diffraction phenomena has to be determined;
and the cause of the formation of these structures must
be sought.
To clarify to the first issue, a number of structural models
have been proposed. These will be discussed below and
compared with electron microscopic observations.
The second point is more difficult to clarify, because
until now only few systematic investigations of the
dependence of microstructure on the conditions of
formation are available. Therefore, it is desirable to
have measurements of the dependence of the long
period on the crystallization or annealing temperature,
the annealing time, the chemical nature of the polymer,
and other parameters.
We limited our initial measurements to annealing experiments on polyethylene. This substance was chosen
because of its relative stability toward degradation and
chemical changes during long annealing times and
because it can easily be prepared in the form of single
crystals. Their structure is well known, thus simplifying
interpretation of the changes that take place during
annealing. Other high polymers appear to behave in
much the same manner as polyethylene, with regard to
the effects measured by us.
The dependence of the long period on the annealing
time and temperature, as well as the density, birefringence, and wideangle X-ray diffraction were measured
€or the annealed samples. We attached special significance to a comparison of observations on drawn
material with observations on polyethylene single
crystals end on isotropic filmscrystallized from the melt.
With a structure according to Fig. 1 or Fig. 2a, in addition
to the meridionalreflectionscaused by the disordered regions,
an intense equatorial scattering should be expected as a
result of the extended voids between the fibrils. Such small-
Fig. 1. String model of a drawn fiber.The elementary fibrils are composed
of crystalline and disordered regions in a uracticallv ueriodical arrangement (after [31)
Fig. 2a. Electron microscopic photograph by transmitted radiation of
the stretched zone of a thin film of polyethylene, which was composed
of spherulites before drawing
II. Microstructure of Drawn Fibers and Films
The structural model of Hess and Kiessig [l] assumes
that the drawn polymer is composed of thin elementary fibrils, in which amorphous and crystalline regions
alternate more or less regularly along the length of the
fiber (Fig. 1). In electron microscopic investigations,
structures similar to the fibrillar structure of the model
are frequently found. Fig. 2a shows the stretched zone
of a thin polyethylene film. In the fibrils appearing
there, the chain molecules are predominantly oriented
parallel to the fiber axis, as can be seen from the position
of the (002) reflection of the corresponding electron
diffraction pattern (Fig. 2b).
angle patterns have actually been observed (Fig. 3a). This
however, is not normally the case but usually only occurs
with “overstretched” films. The opaque, milky appearance
of these samples and their anomalously low densities indicate
that voids of considerable size can occur. By pressing the
[2]E. W. Fischer, Ann. N.Y. Acad. Sci. 89,620 (1961).
[3] W. 0.Statfon, J. Polymer Sci. 41, 143 (1959).
Angew. Chem. internat. Edit.
Vol. I (1962) 1 No. 9
Fig. 2b. Electron diffractionphotographof the same region as in Fig. 2a.
Tbe position of the (002) reflection shows that the chains are oriented
parallel to the direction of the fibrils
voids can be made to disappear partially and the equatorial
scattering decreases 141, as can be understood from Fig. 2a.
Fig. 3. Small-angle reflections of drawn polyethylene:
a) With intense equatorial scattering; drawn at room temperature;
b) Drawn at 70 "C
If the stretching is done under normal conditions, i. e.,
at elevated temperature and with moderate elongation,
then small-angle patterns are obtained such as are
shown in Fig. 3 b. Here, only the meridional reflections
caused by the long periods along the length of the fiber
appear. In this case, interpretation of the diagram in
terms of the model shown in Fig. 1 can present
difficulties [5]. This is partly due to the fact that the
dilatation chains in the amorphous regions of Fig. 1
would prevent close packing of the fibrils and would
therefore tend to prevent the disappearance of the
equatorial scattering. Bonart and Hosemann [ 5 ] therefore proposed a structural model in which the difference
in electron density between the disordered and crystalline regions that is necessary to produce the observed
diffraction effect is obtained by folding some of the
chains at the boundary of the crystalline regions (Fig.4).
that the voids caused by these regions cannot be
correlated with the equatorial diffractions such as
shown for example in Fig. 3b. Furthermore, other
characteristics of the small-angle patterns can be
explained using either model, According to the model
of Fig. 1, any broadening of the meridional reflections
in the direction of the layer lines would depend on the
cross-sectional dimensions of the fibrils and on the
relative longitudinal displacement of the crystalline
regions. Bonart and Hosemann conceive the cause of
the broadening to be the bending of the crystalline
regions indicated in Fig. 4.
To solve this problem, other methods of investigation
must be brought into play. For example, certain conclusions can be drawn by observing the behavior of
drawn materials during annealing (see below). Electron microscopic investigations can also be used to
obtain further information. Thus, the periods of cellulose, poly(viny1 alcohol), and Perlon determined by
X-ray techniques can also be verified by electron microscopy by embedding substances of sufficiently high
electron contrast in the amorphous regions [7,8]. Fig. 5
shows an example of a hydrocellulose fibril with a
clearly discernible periodic structure [ S ] . Naturally,
embedding (in this case, of iodine) is possible with
Fig. 4. Model proposed for the transition region between the crystalline
and amorphous regions in drawn fibers. Some chains are folded at the
crystallite boundary (after [41)
Keller [6] also expressed the idea that just as in single
crystals, a large part of the chains in the drawn material
does not connect consecutive crystallites but is folded
at the boundary surfaces.
A decision in favor of one or the other of the two
models, i.e. whether the chains are folded or not, does
not appear to us to be possible on the basis of X-ray
measurements alone. In particular, the space requirement of the amorphous regions in the model of Hess
and Kiessig can easily be estimated, but then it is found
[4] R. Bonart and R . Hosemann, personal communication.
151 R. Bonart and R. Hosemann; Makromolekulare Chem. 39,
105 (1960).
[6] A . Keller, Kolloid-Z. 165, 34 (1959).
Fib. 5. Electron microscopic photograph of a hydrocellulose fibril with
embedded iodine [81.
( b)
Fig. 6. Shadowed replica of drawn low-pressure polyethylene.
Obliquely shadowed with Au/Pd at an angle of 25 O , reinforced by carbon
I71 K. Hem and H. Mahl, Naturwissenschaften 41, 86 (1954).
[U] K. Hess, H. Mahl, and E, Gutter, Kolloid-Z. 155, 1 (1957);
168, 37 (1960).
Angew. Chem. internat. Edit. 1 Vol. I (1962) I No. 9
both of the models mentioned above. On the other hand,
oblique shadowing of stretched samples should only
expose the dilated regions. By using this method, we
have in fact found periodicities with the electron
microscope, these being of the order of magnitude of
150 to 400 A. This is shown in the replicas of lowpressure polyethylene (Figs. 6a and 6b), which was
stretched at a temperature of about 50 "C.The periodicity along the length of the fibrils is clearly recognizable.
Systematic investigations of appropriate shadowing
materials and methods of pretreating the samples are
currently in progress. In Figs. 7a and 7b, individual
Fig. 7. Polyethylene fibrils obtained by drawing of single crystals.
Obliquely shadowed with Au/Pd at an angle of 25 '
polyethylene fibrils, which were obtained by stretching
polyethylene single c ysta,ls are reproduced. Periodicities
of the expected order of magnitude are also encountered
here. In addition, in these experiments, another long
period of ca. 600 8, was also found [9].
The results of electron microscopic investigations
obtained so far do not allow an unequivocal answer to
the question whether the chains are folded or laterally
dilated. Nevertheless, these experiments, particularly
those of Hess, Mahl and Guetter, offer strong support
to the assumption that the long-period diffractions are
caused by alternation of crystalline and amorphous
regions. Without going further into the divergent
assumptions concerning the structure of the amorphous
regions, we will base the following considerations and
evaluations of measurements on this common feature
of the two models. Other possibilities, such as the
existence of helical structural elements, whose pitch
is supposed to determine the position of the small-angle
reflections, will be excluded [lo, 111.
Our assumption is also supported by other investigations.
If one integrates the total region of small-angle diffraction,
then one obtains the "diffraction power" [i2] of the samples,
which is dependent only on the composition of the diffracting system and not on its geometric structure. By comparing
the diffractionpowerwith the density of thesamples,it could be
shown that in polyethylene the small-angle diffraction is caused only by the"crysta1line" and"amorphous" phases [I 3,141.
[9] H. A . Stuart, Ann. N . Y . Acad. Sci. 83, 3 (1959).
[lo] L. B. Morgan, A . KeZZer et at., Philos. Trans. Roy. SOC.London, Ser. A 247, 1 (1954).
[ l l ] W . Cochran, F. A. C. Crick,and V . Vand, Acta crystallog.
5, 581 (1952).
[12] G. Porod, Fortschr. Hochpolym. Forsch. 2, 363 (1961).
[I31Herrmann and Weidinger,MakromolekulareChem.39,67(1960).
[I41 B. BelbPoch and A. Guinier, Makromolekulare Chem. 31, 1
Angew. Chern. ijiternat. Edit. / Vol. I (I9621 / N o . 9
It should also be mentioned that, in consideration of this
result, still another structural model is possible, viz. the
small-angle diffraction can be considered as pure particle
diffraction [14]. The maxima would then no longer be
measures of the distances between the crystallites, but would
provide information about their size and shape. However,
we do not consider this concept - at least for polyethyleneto be sufficiently well established as yet.
III. Periods of the Small-angle Diffraction of
Drawn Polyethylene as a Function of
Thermal Treatment
The positions of the reflections of small-angle diffraction
of polyamides and polyesters change on annealing [l].
This is also true for polyurethane [15], poly(ethy1ene
glycol terephthdate) [16], and polyethylene. For exRmple, during thermal shrinking of fibers of lowpressure polyethylene, the long period initially increases
with increasing contrzction rate, and then decreases
[17]. Belbeoch and Guinier [14] described the effect of
annealing on four-point patterns obtained by them
with branched polyethylene. In both cases the annealing
effects overlap with relaxation phenomena, so that it
becomes very difficult to interpret the changes in the
period of the small-angle diffraction. For our measurements on highly oriented low-pressure polyethylene,
we selected a temperature range in which no relaxation
can be noticed. Up to temperatures of 133 "C,even at
annealing times of 24 hours, the length of the stretched
samples remained constant, and no desonentation
could be observed in wide-angle X-ray patterns. The
samples could theref ore be annealed without holding
them under tension; measurements on samples annealed
Fig. 8. Temperature dependence of the long period of drawn
polyethylene. The initial samples were stretched approximately 16-fold
at 70 O C
Annealing time: 24 hrs.
Ordinate: Length of the long period [A1
Abscissa: Temperature [ "Cl
[15] H. Zahn and U. Winter, Kolloid-2. 128, 142 (1952).
[la] W.0.Statton, J. Polymer Sci. 41, 143 (1959).
[17] A. S. Posner, L. MandeUcern, C. R . Worthington, and A . F.
Diorio, J. appl. Phys. 31, 536 (1960).
49 1
at constant length gave no differencein the long periods
within the temperature range selected by us.
Fig. 8 shows the temperature dependence of the lwng
period at constant annealing time. As with other
polymers, the long period increases with increase in
temperature. It doubles after annealing for 24 hours at
133°C. Obviously, such a chmge in size cannot be
explained by growth of crystallites at the expense of the
interstitial amorphous regions. The expansion of the
long period associated with this would be fzr too small.
On the contrary, it must be assumed that the microstructure breaks down completely, with concomitant
new crystallization.
According to Eq. 1, the long period should change only
very little after long annealing times. Apparently, this
has often led t o the view that the value of the long
period is dependent only on the temperature. Therefore
annealing times are frequently not given in the literature.
Furthermore, measurements on the time dependence of
other polymers are unavailable. According to our
investigations, the loiig period still increases even after
very long periods of time. Only after 500 hrs., does the
long period become constant at elevated temperatures
(130 and 132 "0;however, under these conditions,
chemical changes in the samples may come into play.
Investigations of this matter are in progress.
Fig. 9. Dependence of the long period of drawn polyethylene on the
annealing time.
Ordinate: Length of the long period [A]
Abscissa: Time [tuin]
As our measurements of the time dependence show, this
process goes on continuously. In Fig. 9, the dependence of
the long period on the annealing time at three different
temperatures is plotted. At first, the long period increases very
rapidly, but thereafter changes very little. Figure 10 shows
Fig. 10. Dependence of the long period on the logarithm of the annealing
Ordinate: Length of the long period [A]
Abscissa: Time [min.]
that the long period is linearly dependent on the logarithm
of the annealing time, i.e., the variation can be descrited by
the relationship
P = K log t + p
Fig. 1 1 . Temperature dependence of the gradients K of the logarithmic
curves from Eq. 1 for drawn low-pressure polyethylene
(-o-o-) drawn approximately 10-fold
(-O-o-) drawn approximately 16-fold
Ordmate: K values from Eq. 1 [A]
Abscissa: Temperature [ "Cl
The gradient K of the logarithmic straight line depends
on the temperatures as is shown in Fig. 11 for two
series of experiments. From this it can be seen that the
rate of growth of the long period depends on the temperature and pretreatment of the sample. Moreover, it
appears that the predominant effect depends on the
degree of drawing; the smaller the elongation, the
more rapidly K increases with temperature. In agreement
with this, undrawn polyethylene and polyethylene
single crystals show a much sharper increase of the
gradient constant K with temperature (cf. Fig. 18).
The dependence of the growth of the period on the
extent of drawing is also shown in Fig. 12. The change
of the long period after annealing for 24 hours at 125 "C
where K is the gradient of the straight line and p is its intercept on the ordinate. Eq. 1 can also be written in the form
P = K log t/to
+ Po
K log (t/to
+ 1) + Po
where PO is the long period of the unannealed sample and
to is the time obtained by extrapolating to the starting period
PO.This is of the order of magnitude of 10-2 to 10-6 minutes,
so that at the times measured by us, log t / b may be approximated by using log (t/to + 1). This takcs the fact into account
that at time t = 0, the long period is P = PO.
Fig. 12. Dependence of the increase of the long period on the drawing
ratio after annealing for 24 hours at 125 "C.
Ordinate: Length of the long period [A]
Abscissa: Drawing ratio
is plotted here for samples of different degrees of
drawing. Surprisingly, the value measured for the
unstretched sample fits well into the curve.
Angew. Cliem. internat. Edit.
Vol. I (1962) / No.9
However, the long period increases not only with the
temperature during annealing but, in much the same
sense, it also depends on the temperature during
stretching [14]. This dependence is shown in Fig. 13. It
is appment that the curves for branched and unbranched polyethylene exhibit much the same behavior and are
merely shifted about 55 A relative to one another along
the ordinate. This appears to us to furnish evidence thzt
the frequently expressed viewpoint that the long period
is in branched polyethylene determined by the average
length between neighboring branch points is incorrect.
Fig. 13. Dependence of the long period on the drawing temperature for
and left ordinate)[l4] and unbranched (-0-0and
branched (-0-0right ordinate) polyethylene.
After these effects were noted by Keller and OConnor [23],
the temperature dependence of small-angle diffraction patterns of polyethylene single crystals were thoroughly investigated by Statton and Geil [22]. Hirai et al. [24] have
drawn attention to the time dependence of this process.
Sfatton [25] observed that the growth of the long period
proceeds much faster in liquids than in air.
We have measured the time and temperature dependence
of the growth of the long period during annealing of
unoriented polyethylene and polyethylene single crystals.
Low-pressure polyethylene was melted and then quenched in
ice water. The samples were annealed a t different temperatures and subsequently again quenched in ice water. For
measuring the period of the small-angle scattering, a camera
according to Kratky was used [*I. Polyethylene single crystals were prepared from dilute solution at various temperatures. The aggregates of superimposed crystal lamellae obtained by slow sedimentation were dried carefully in a vacuum
and then annealed and investigated in the manner described
The dependence of the long periods of these samples on
the annealing temperature at constant annealing time
(24 hours) is shown in Figs. 14 and 15. Curves similar
to those with drawn polyethylene are obtained (cf.
Fig. 8). One striking difference occurs. With stretched
material, the long period increases continuously with
temperature, whereas in the case of single crystals there
is a sharp inflection at 1O5-llO0C. Below this temperature, the long period increases only slightly. Statton
and Geil[22] also found changes in the loag period only
at temperatures above 110 "C [**I.
Ordinate: Length of the long period [A]
Abscissa: Temperature [ "C1
Summarizing, it can be said that: 1. in stretched polyethylene, the long period increases as the stretching
temperature increases; 2. during annealing, the long
period increases with the logarithm of time, and it
increases mole rapidly, the higher the annealing temperature; and 3. the greater the degree of drawing, the
smaller the gradient of the logarithmic time curve.
IV. Changes in the Long Period of Unoriented
Polyethylene and Polyethylene Single Crystals
during Annealing
Up to the present, very little data have been presented
concerning the variation of the long period during
annealing of unoriented bulk polyethylene. They show
that, here, as with the drawn material, the long period
increases with increasing temperature [14,18,19] and
that the annealing time is also important [20]. In
addition, the degree of branching has some effect on
the increase of the period during annealing [21].
Fig. 14. Temperature dependence of the long period of unstretched
polyethylene. The starting samples were quenched at 0 "Cfrom the melt.
Annealing time: 24 hrs.
Ordinate: Length of the long period [.&I
Abscissa: Temperature [ "Cl
[23] A . KeIler and A . O'Connor, Discuss. Faraday SOC.25, 114
[I81 H . Hendus, Ergebn. exakt. Naturwiss. 31, 331 (1959).
[I91 D . H. Geil, personal communication.
[20] L. Mandelkern, A . S. Posner, A . F. Diorio, and D. E. Roberts,
J. appl. Physics 32, 1509 (1961).
[21] C. Sella, Lecture, IUPAC-Symposium on Macromolecules
Wiesbaden (Germany) 1959.
[22] W. 0. Statton and P. H . Ceil, J. appl. Polymer Sci. 3, 357
Angew. Chem. internat. Edit. 1 Vol. I (1962) i No. 9
[24] N.Hirai, Y. Yamashita, T. Mifsuhata, and Y. Tamura, Rep.
Res. Lab. Surface Sci. Okayama University 2, 1 (1961).
[25] W. 0. Statton, J. appl. Physics 32, 2332 (1961).
[*I Details of the experimental technique and evaluation of the
data will be reported elsewhere.
[**I With crystals with a smaller folding period, a stronger increase in the period also occurs below this inflection (cf. 1261).
[26] E. W. Fischer and G. F. Schmidt, unpublished.
There may be a connectioa with the results of nuclear
magnetic resonance measurements [27], according to
which the mobility of the segments starts within this
temperature range. It should be mentioned that, in
order to exclude any possible effect of the cooling
The time dependence of the long period at different
annealing temperatures is shown in Figs. 16 and 17. In
both quenched bulk polyethylene and single crystals,
the long period again increases linearly with the logarithm of the time. Large deviations only with the
Fig. 17. Dependence of the long period on the annealing time for
polyethylene single crystals precipitated a t 80°C from a solution in
Ordinate: Length of the long period
Abscissa: Time [min]
Fig. 15. Temperature dependence of the long period of polyethylene
single crystals crystallized at 70 "Cfrom a dilute solution in
tetrachloroethylene. Annealing time: 24 brs.
Ordinate: Length of the long period
Abscissa: Temperature [ "Cl
process on the long period, we recorded the small-angle
diffraction at the annealing temperature with a camera
according to Kiessig. The values obtained from these
experiments are in good agreement with the values
obtained with samples at room temperature, especially
with regard to the time dependence of the long period.
Still, these values were all a few Bngstroms higher
(about 10%). At present we are unable to offer an
unambiguous explanation for this.
quenched polyethylene at 132 "C. At the present time
we are unable to offer an explanation for this. According
to Hirai [24], the long periods of polyethylene single
crystals increase stepwise. We have so far been unable
to observe this effect and assume that it was produced
by the latter's measurement method (the same sample
was repeatedly cooled and reheated for photographing
the diffraction pattern).
120 -
100 80 -
Fig. 18. Temperature dependence of the gradients K of the
logarithmic curves from Eq. 1 for unstretched, annealed polyethylene
and for polyethylene single crystals
Ordinate: K values from Eq. 1 [A]
Abscissa: Temperature [ "C]
Fig. 16. Dependence of the long period of the quenched and
subsequently annealed polyethylene on the annealing time.
Ordinate: Length of the long period [A]
Abscissa: Time [min].
[27] W. P. Slichter, J. appl. Physics 32, 2339 (1961).
In both unorientated bulk material and single crystals,
the long period increases at a much greater rate than in
stretched polyethylene. The temperature dependence of
the constant K from Eqs. 1 and 2 is shown in Fig. 18.
To a good approximation, the same value is found for
quetxhed material and single crystals. This again is
Angew. Chem. internat. Edit. 1 VoI. 1 (1962) /
evidence that both preparations behave very similarly
during annealing and are quite different from stretched
V. Changes in Crystallinity during Annealing
The growth of the long periods described in the preceding sections occurs within a temperature range which
approximately corresponds to the so-called "melting
range" of polyethylene. In this range, one observes a
decrease in the degree of crystallinity, which is dependent
on the temperature and any thermal pretreatment of the
sample; this phenomenon is called "partial melting".
Since one must assume that the growth of the long
period necessitates a complete transformation of the
microstructure, the question arises whether some sort of
relationship exists between this recrystallization and the
partial melting. It is in fact to be expected that two
processes are necessary for the growth of the long period:
at least partial melting of the original structure, and
recrystallization, which leads to new crystallite dimensions and therefore to a new long period. The superposition of the two processes should be observable from
the manner in which the crystallinity changes with time.
As will be shown, this is so with single crystals and with
t =6h
I bJ
unstretched polyethylene. Because of the overlapping of
the two processes, at a certain time, the crystallinity is
at a minimum. With orientated polyethylene, such an
effect does not occur or only occurs to a very small
The melting of polyethylene single crystals during
annealing can be demonstrated by means of wideangle X-ray diffraction [2]. In Figs. 19a-c, the change
with time of the X-ray patterns of three samples is
shown. With single crystals and samples quenched from
the melt, the first two crystalline reflections (110) and
(220) nearly disappearand are replaced by an amorphous
halo.On further annealing,their intensity increases again.
In stretched polyethylene the intensity decreases somewhat because of the raise in temperature, but it remains
constant with time. Only after cooling to room temperature does the higher crystallinity (relative to the
starting sample) resulting from the annealing process
become detectable.
In these experiments, it was not possible to bring the samples
instantaneously up to the annealing temperature. Since the
samples are already changing during the heating up, no
quantitative comparisons with density measurements can be
For density measurements, the annealed samples were
quenched in ice water. The density was measured at
30°C in a gradient tube [*I. The dependence of the
density on the annealing time at various temperatures
is shown in Figs. 20a-c. For the single crystals, the
density first decreases rapidly and then slowly increases
again. The higher the annealing temperature, the lower
the minimum. Annealing for longer times leads to a
further increase in density, which soon exceeds the value
for the unannealed sample [28].
A density minimum also occurs at higher temperatures
with quenched polyethylene albeit somewhat later
(Fig. 20b). These results are in agreement with observations of Kovacs and Gubler [29] and of Rabesiaka and
Kovacs [30]. The latter authors measured the effect of
annealing on the specific volume of the quenched
samples dilatometrically at the annealing temperature.
The density minima occur at the same times but are
much more pronounced, since during the quenching
the partially molten state can only be partially frozen.
This could also be the reason why we did not observe
minima at lower temperatures.
Stretched pclyethylene behaves differently. The density
increases continuously with the annealing time, without
passing through a minimum (Fig. 20c).
This different behavior was also observed during
measurements of optical birefringence, for which the
Fig. 19. Time dependence of the X-ray diffraction pattern of several
polyethylene preparations during annealing. The first diagram of each
series was obtained at room temperature.
a) polyethylene single crystals crystallized at 80 "C from a solution in
xylene, annealed at 130 "C
b) polyethylene quenched from the melt, annealed at 130 "C
c) drawn polyethylene, annealed at 132 "C
Ordinate: Intensity of the X-ray reflections
Abscissa: Scattering angle
Angew. Chem. internat. Edit. / Vol. I (1962)/ No. 9
[*I We have not yet undertaken dilatometric experiments because only a very small amount of material is obtained during
the preparation of the single crystals from very dilute solution,
and besides, the effects of interest to us occur within relatively
short time periods. The construction of a dilatometer for these
investigations is planned.
1281 The density of the unannealed single crystals depends
on the temperature of crystallization [26].
[29] A. J. Kovacs and M . G. Gubler, Lecture, IUPAC-Symposium
on Macromolecules, Wiesbaden (Germany) 1959.
[30] J. Rubisiaka and A . J. Kovacs, personal communication by
A . J. Kovacs.
samples wete not quenched after annealing, but were
measured at the annealing temperature. In contrast to
the X-ray measurements, because of the small volumes
of the samples investigated, here it was possible to use a
relatively high rate of heating; the samples could be
0.9 6 0
isotropic polyethylene quenched from the melt passes
through a minimum relative to the time, whereas in
drawn samples it increases, albeit more slowly.
1 - (
0.965p * < o
Fig. 21. Dependence of the percent change in birefringence on the
annealing time, measured at tbe annealing temperature. (-o-o-)
single crystals, (-A- A-) drawn polyethylene.
Ordinate: Percentage
Abscissa: Time [min]
VI. Relationship between Density and the Long
Period of Annealed Polyethylene
0.9650 ~~~v'v-v-v-v-~-v--v0.9600
0.9650 -@.o-~o0-0-o-o0.9600
As previously mentioned, the minimum in the density
can be thought of as arising from superposition of
partial melting and recryatallization. If comparisons are
made between the densities of the samples and their
long periods, an interesting relationship is observed.
First, let us consider only samples whose annealing
times are greater than the times which correspond to the
minima in Figs. 20a and 20b.
\\ \
Fig. 20. Dependence of density on the annealing time. After annealing
the samples were quenched in ice water and the density was measured
at 30°C.
a) polyethylene single crystals crystallized at 80 "C from a solution in
b) polyethylene quenched out of the melt (values in bold-faced type
after [201)
c) polyethylene drawn at 70 "C.
Ordinate: Density [glcc]
Abscissa: Time [ n h ]
brought up to the annealing temperature in 10 to 15 sec.
For these experiments, cross sections perpendicular to
the planes of the crystal lamellae were prepared with a
microtome from the single crystal aggregates, so that the
birefringence could be measured in the direction of and
transverse to the direction of the chains. The dependence
of the percent change of birefringence with time is
plotted in Fig. 21 for single crystals and for stretched
polyethylene. Again, one observes in the first case a
well-defined minimum which is progressively lower at
higher temperatures.
Summarizing, it may be stated that, during annealing
the crystallinity of the single crystals as well as of the
0.9 9 0
0.9 70
0.001 0.002 0.003 0.004 0.005
1000 500 1350 I 250
LOO 300
Fig. 22. Relationship between density and lonb period for polyethylene
single crystals annealed at constant temperatures for various lengths of
time. (The black square represents the unannealed sample).
Ordinate: Density [g/ccl
Abscissa: Top: reciprocal length of the long period [.&-I];
Bottom: length of the long period [A]
In Fig. 22, densities vs the reciprocal values of the long
period are plotted for several single-crystal aggregates
annealed for various lengths of time. For each annealing
temperature, to a good approximation, a straight line
is obtained, so that the relationship between the density
p and the long period P may be represented by the
p = pk--
Angew. Chem. internat. Edit. i Vol. I (1962) 1 No. 9
wheie A is a constant dependent upon temperature,
defined as the gradient of the straight lines in the p vs 1/P
diagram. Pk is the density that a single crystal of infinitely
long period would possess. This figure shows that Pk is
independent of the temperature and has a value of
With drawn samples (Fig. a),
despite deviations in the
points measured, two fundamental differences, from the
other two preparations are found: first, the measured
points do not lie on a straight line that gives an intercept on the ordinate p equal to the ideal density as
determined by the X-ray method, and, second, the
position of the measured points on the stretched-sample
curve do not permit identification of the corresponding
annealing temperatures.
0970 -
0965 '0
A value for & of 1.0033 f 0.0010 g/cc was obtained, in
excellent agreement with the value found for single
crystals. Thus it was confirmed experimentally that
there is a simple reciproc~lrelationship between density
and long period. Extrapolation to infinitely large crystals
gives the density of the polyethylene crystals.
L ~ O
W.Discussion of the Results
Fig. 23. Relationship between density and long period of annealed
undrawn polyethylene.
Ordinate: Density [g/ccl
Abscissa: Top: reciprocal length of the long period rA-11
Bottom: length of the long period [A1
1.002 g/ml. Interestingly, this density of an infinitely
large crystal is in good agreement with the density
calculated from X-ray data for an ideal crystal. The
literature values (after conversion to 30 "C) lie between
1.OOO and 1.008 g/ml. The discrepancies probably result
from differences in the types of polyethylene, and are
of no further concern [*I.
The relationship between density and long period in
bulk polyethylene is also given by Eq. 3. The values ?re
shown in Fig. 23. At 100 "C, the changes of p and P are
extremely small for the annealing times used so far.
Therefore, we have not made further use of the points at
that temperature. At the other temperatures,the gradient
and the intercept on the ordinate of the straight lines
were calculated according to the method of least squares.
The relationship between density and long period of the
annealed samples is considered first, utilizing the simple
and obvious model of Fig. 25. Laterally extended
crystallites of density & with a distance P between their
centers of gravity are separated by an amorphous
boundary layer of thickness d and density pa. One
obtains for the average density p of this arrangement
0.9 7 5
Although our measuxements and the theoretical interpretation of our results have not yet been completed,
we would like to point out some consequences which
may be of significance for understanding the thermal
behavior of crystalline high polymers.
0.965 I
I '
Fig. 24. Relationship between density and long period of drawn
0 at 70°C. drawn ca. 16-fold. uuannealed
0 at 70 "C,drawn ca. 16-fold, annealed at 120 ' C
,A at 70 "C, drawn ca. 16-fold, annealed at 125 "C
at 50 "C,drawn ca. 10-fold, annealed at 100 "C
v at 50°C, drawn ca. 10-fold, annealed at 125 "C
at 50 O C , drawn ca. 10-fold, annealed at 130 "C
m at 50 "C, drawn ca. 10-fold. annealed at 132 'C
Ordinate: Density [glccl
Abscissa: Reciprocal length of the long period [A-ll
Fig. 25. Schematic representation of the structure of crystalline high
polymers with interval P between the crystallites and thickness d of the
amorphous boundary layer.
This relationship is identical with Eq. 3, which was
determined experimentally, if we set
A = d(pk - pa)
[*] These deviations correspond to variations of only about
f 0.02
A in the lattice constants.
Angew. Chem. internat. Edit. I Vol. I (19621 I No. 9
Thus, our findings may be interpreted easily using a
crystalline/amorphous two-phase model with the
following properties : 1. the so-called "amorphous"
region is identical with the boundary layer between two
crystalline lamellae, and 2) the product of the thickness
d of the boundary layer times the difference in density
between it and the crystalline phase is constant
for a given temperature. In other words, this means
that the entire difference between the density of the
annealed samples and the X-ray density is caused by
the lower density of the crystal boundary layers, the
thickness of these grain boundaries between the consecutively stacked crystals being dependant on the temperature.
This temperature dependence suggests that there may
be some relationship between the group of straight
lines plotted in Figs. 22 and 23 and the partial melting
effect generally observed in high polymers. In this
connection, attention is called to the value obtained for
unnanealed single crystals in Fig. 22. If the temperature
of the single-crqstal aggregate is raised, at first the
density defect caused by the boundary layer increases,
until it attains a value appropriate for the particular
annealing temperature. As a result, the density decreases. Simultaneously, the long period begins to
increase, the measured point moves along the line
belonging to the corresponding temperature, and the
density again slowly increases.
The same considerations apply to bulk polyethylene
(Fig. 23). If we also plot in Fig. 23 the values of samples
with annealing times before the density minimum, then
these points lie on a curve joining the point for the
unannealed sample to the straight line corresponding
to the annealing temperature. The higher the annealing
temperature, the lower the density of the sample
Stretched polyethylene behaves completely differently.
In this case, straight lines corresponding to some
specific temperature are not obtained on plotting p vs
(1/P) (Fig. 24). Not only does the long period increase
during annealing, but there is also a corresponding
continuous increase in the density (cf. Fig. 20c). No
partial melting occurs.
Although our measurements urgently require supplementation by dilatometric experiments in order to
exclude density changes during the quenching, we may
present the following tentative interpretation of our
results. It can be show that at constant long period P,
the number of chain members per loop of a folded chain
depends on the temperature [31]. This number increases
with increasing temperature so that crystallite melts
upon heating, starting from the surface areas containing
the loops, and the thickness, d of the boundary layer
increases. This is not the case with continuous chains
such as are shown in Fig. 1, as calculations show [*I.
Hence, the differences exhibited in Figs. 22-24 between
the single crystals and quenched polyethylene on the
one hand, and the stretched material on the other, can
be interpreted in the following manner: in the first two
materials, the chains are folded at the boundary areas of
the crystallites, whereas, in the stretched material, the
crystallites are interconnected by chains which pass
[31] E. W. Fischer, unpublished.
[*I Here it is assumed that the ratio of the length of
the chain
segments in the amorphous region to the distance between the
crystalliteboundary layers does not exceed a certain value which
can be dealt with in calculations, i.e., the chain may not form
loops of unlimited size.
through the amorphous region. Furthermore, the uniform value obtained for the constant K (Fig. 18), which
governs the rate of growth of the periods, permits the
conjecture that the single crystals and polyethylene
crystallized from melt have basically the same structure.
The increase of the long period in unstretched polyethylene up to values of 650 or lo00 A [20] does not
exclude the possibility of chain folding, which might
otherwise be assumed not to exist, since the folding
period in this case approaches the same order of magnitude as the chain length. The experiments of Hess and
Kiessig [32] on mixtures of soaps of different chain
length, and especially the work of Zahn et al. [33] and
of Kern et al. [34] on the long periods of oligomers,
clearly demonstrate that chain folding is also possibile
when the chain length is only slightly larger than the
folding period. Attention was already called above to
relevance of this fact to the theory of chain folding [2].
Now we turn our attention to the growth of the long
period. With all of the three materials investigated by
us, the long period increased continuously with the
logarithm of the time (cf. Figs. 10, 16, and 17). By
differentiation of Eq. 2, it is easily found that the rate
(6P& of the growth of the period is given by the
The rate therefore decreases exponentially with increasing long period. The constants C and B are dependent on
temperature and may be calculated from the quantities
to, K, and POin Eq. 2.
We have not yet found a satisfactory explanation for the
relationship formulated in Eq. 4; however, we do believe
that we can eliminate a few possible explanations for the
growth of the long periods. For example, it is often assumed
that the long period grows during annealing in the melt
owing to melting of the smaller crystallites whereby, the
average size of the crystallite increases. With single crystals,
this is certainly not the case, since Hosemann et at. [35] found
by analysis of the breadths of the small-angle X-ray diffractions, that the average relative variation in thickness of the
crystal lamellae was no greater than 4 %. However, we consider this explanation to be improbable for polyethylene
crystallized from the melt, too.
Hirai et al. [24] suggested another interpretation for single
crystals. They assumed that the increase of the long period
proceeds by a repeated secondary nucleation, the nucleation
energy being dependent on the long period P. The constant
B in Eq. 6 would then vary only slightly with temperature.
According to the results of Hirai et at., this is actually the
case, whereas our measurements gave a strong temperature
dependence (cf. Figs. 1 1 and 18). Again, we believe that this
discrepancy results from the fact that Hirai et al. cooled the
samples between the two annealing times used for the measurement of the long period.
The dependence of the long period on time according
to Eq. 2 also precludes the assumption that the long
period is related to the size of the critical nucleus, as was
postulated by Mandelkern et al. [20] for primary iso[32] K. Hess and H. Kiessig, Chem. Ber. 81, 327 (1928).
[33] H. Zahn and W. Pieper, Kolloid-Z. 180,97 (1962).
1341 W. Kern, I. Davidovifs, K . J. Rauterkus, and G. F. Schmidt,
Makromolekulare Chem. 53, 106 (1961).
[35] R. Hosemann, R. Bonart, and M. Klein, Physik. Verh. 11,
162 (1960).
Angew. Chem. internat. Edit. I Vol. I (1962)I No. 9
thermal crystallization of polyethylene. Furthermore,
the dependence of the long period on the stretching
temperature cannot be explained by this assumption
because the temperature dependence shown in Fig. 13
does not agree with it. This will be discussed in detail
elsewhere. It should be mentioned here, however, that
the long periods obtained at different stretching temperatures only differ by an added constant from those
obtained at the same temperature for single crystals
obtained from dilute solution. Therefore, the temperature dependence can be explained in terms of the theory
of thermodynamic stability of macromolecular crystals
developed by us [36]. From this theory, it follows that,
above a certain temperature which according to Reinhold [36] lies between 100 and 120°C, the size of the
crystallite in the chain direction is no longer determined
by a minimum in the density of free energy. Above this
temperature, only infinitely large crystals (in the direc-
tion of the chain) are thermodynamically stable. During
annealing, the system tends towards this state.
In conclusion, attention is called to a possible relationship
of the growth of the periods to the phenomenon of “secondary crystallization”. This term designates the process during
the isothermal crystallizationof high polymers, which follows
the main crystallization associated with the growth of morphological entities (spherulites). Secondary crystallization is
observed as an increase in density of long duration. If the time
dependence of the long period according to Eq. 2 is shbstituted in Eq. 3, then c w e s are obtained for the dependence
of the density on time which qualitatively agree with the
measured curves [37]. It can therefore be assumed that the
increase in density observed during secondary crystallization is caused by the growth of the long period.
Thanks are due to Prof. Dr. H. A . Stuart for his many
valuable suggestions and advice, to our co-workers for
their aid in the experiments, and to the Deutsche Forschungsgemeinschaftfor providing equipment.
Received, April 10th. 1962
[A 202/42 IE]
[36] A. Peterlin, E. W. Fischer, and R. Reinhold, J. Polymer Sci.,
in press.
[37] S. Buckser and L. H. Tung 3,. physic. Chem. 63, 763 (1959).
The Patenting of Chemical Inventions in the Federal Republic of Germany
Under German Patent Law, the patenting of chemical inventions is subject to special rules
which need not be observed with inventions in the mechanical field. These rules will be
discussed in detail.
I. Exceptional Provisions of Section 1, Q 2
of the Patent Act
provisions, the consequences resulting from this regulation of the patent protection of chemical inventions
in the Federal Republic of Germany will now be
Under German Patent Law, the following inventions
are excepted from patent protection:
According to Sec. 1 , s 2,No. 1 of the Patent Act of 1953,
inventions, the exploitation of which would be contrary
to law or public policy, were excepted from patent
protection. In accordance with the new Patent Act
effective as of July 1st, 1961,patents are also granted for
new inventions concerning materials, the sale of which
is restricted by German law (e.g. Act for Amending
and Supplementing the Foodstuff Act, of December
21 st, 1958; the decree on tobacco and tobacco products
of December 19th, 1959). Such inventions are, for
example, processes for the preservation of foodstuffs
with specific preserving agents, processes for treating
foodstuffs with high-energy radiation, treatments for
increasing the yield in meat of useful animals by means
of e.g. anabolic steroids, and other inventions relating
to the production and treatment of foodstuffs; these
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The products obtained from these processes cannot,
however, be offered for sale or sold in Germany, since
or if they do not correspond to the legal provisions on
foodstuffs. However, no objections are made on the
German side against exporting these products.
1. Inventions, the exploitation of which would be
contrary to law or public policy, unless the provisions
of law only restrict the offering for sale or trading of the
subject matter of the invention or, if the subject matter
of the invention is a process, of the product directly
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2. Inventions of foodstuffs, luxury foods, medicaments,
and materials produced by chemical means, unless the
inventions concern only a specific process for producing
the products.
Owing to this provision, the claim under public law of
an inventor or applicant to the granting of a patent for
his invention is considerably restricted. In all other
fields, the new products themselves may be patented,
whereas in the case of foodstuffs, luxury foods, medicaments, and materials produced by chemical means,
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Angew. Chem. internat. Edit. 1 Vol. I (1962) I No. 9
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