Cavitation during tensile deformation of isothermally crystallized polypropylene and high-density polyethylene
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The cavitation phenomenon was studied in isothermally and non-isothermally crystallized polypropylene and high-density polyethylene. It was found that nano-voids were not present in the crystallized samples, but were formed during their tensile deformation. The process of cavitation was initiated before reaching the yield point. The ellipsoidal voids were initially elongated perpendicularly to the deformation direction, but if the polymer (i.e., high-density polyethylene) was able to deform beyond the yield, then the reorientation of voids into the deformation direction was observed at local strains of 100–200 %. This behavior was similar to that observed previously in the samples crystallized without an exact control of solidification conditions. The calculations of Guinier’s radius showed that voids in deformed polypropylene samples were characterized by the gyration radii of 28–50 nm. Smaller voids were observed in polyethylene. The scale of cavitation during deformation, studied on the example of polyethylene, depended on the preceding crystallization process and was most intensive for the specimens crystallized at the highest temperature of 125 °C.
KeywordsPolypropylene Polyethylene Cavitation Tensile properties Plastic deformation Isothermal crystallization
The cavitation phenomenon was discovered in many semicrystalline polymers. The generation of voids (cavities) is usually observed in two different circumstances: during isothermal crystallization [1, 2, 3, 4, 5, 6, 7, 8, 9] and during tensile deformation [10, 11, 12, 13, 14]. To my knowledge, so far, both cases have been analyzed and described separately. The reason of cavitation during isothermal crystallization is the existence of pockets of melt surrounded by growing spherulites. The volume of molten material in these pockets (called weak spots) is not sufficient for complete crystallization because the density of the crystalline phase is higher than the density of the molten polymer . The negative (i.e., 3D tensile) pressure arises inside the weak spot with time, and as a result, the growth of neighbor spherulites becomes slower and the polymer melt is stretched. Estimations show that the negative pressure in polypropylene (PP) weak spots may be high, even 19–40 MPa [1, 3].
When the negative pressure reaches the level of cohesive strength of melt, then a rapid break of melt occurs and 1-μm or more micrometer voids are formed. The presence of a cavitation nucleus (e.g., impurities) supports the initiation of the process at lower pressure. Often, the fracture of melt is observed at the same time in adjacent weak spots, which suggests that the propagation of an acoustic wave emitted in the cavitation act, resulting from a sudden pressure change, induces the cavitation in other weak spots. The acoustic emission from the crystallizing polymer was recorded by Galeski et al. . Cavitation relaxes stresses inside the weak spot and the growth rate of spherulite increases to the initial level .
If the pocket of melt occluded by spherulites is small, the negative pressure may be insufficient for the rupture of the structure and the material solidifies without a break, but with frozen internal stresses. Nowacki et al.  reported that the large weak spots tended to cavitate at lower negative pressure than smaller ones, which resulted from an increased probability of the presence of a cavitation nucleus inside the confined melt. It was also found that the shape of the cavities in polypropylene depended on the temperature of crystallization—at low temperatures, the voids were spherical; at high temperatures (i.e., >135 °C), the voids were elongated (similar to cracks), formed along interspherulitic boundaries [5, 6]. Voiding in weak spots was not observed in thin films of polymers crystallized with a free surface because the deficiency of the crystallizing material was compensated here by the thinning of the film. The cavitation during crystallization usually did not occur when the process was non-isothermal because the spherulites were small, a typical size of weak spots was also small, the time of crystallization was short, and the value of negative pressure was below the limit of melt strength.
The above discussed experiments were focused on the studies of cavitation in thin films of crystallizing polymers [5, 6, 7, 8, 9]. Galeski and Piorkowska  examined volume samples of polypropylene which were crystallized isothermally at 125 °C. They confirmed the existence of weak spots by means of infrared microscopy and the relaxation of stresses after cavitation using Raman spectroscopy. In the second experiment, with the same polymer crystallized in non-isothermal conditions, the authors observed the formation of large, 1- to 2-mm, cavities when the temperature inside the thick specimen decreased much slower than the temperature of the skin layer. Similar conditions often exist in the central parts of the injected PP shapes, where—if the time of solidification is long enough—large cavities visible even by the naked eye are formed. The pressure inside these cavities, detected by a glow discharge from residual gases under high-frequency electromagnetic field, was <0.1 kPa (i.e., <0.1 % of atmospheric pressure) .
It is known that non-isothermally crystallized semicrystalline polymers can cavitate during deformation [10, 11]. This happens only in tensile mode, never during compression. Usually, prime voids are generated around the yield point [12, 13]. We showed that there is a competition between two processes possible at yield in the semicrystalline polymer: plastic deformation of crystals by a chain-slip mechanism and the breaking of the amorphous phase (cavitation) . If the polymer crystals are defected, including many dislocations, then with an increase of force, the initiation of plastic deformation of the lamellae is more probable than the break of the amorphous phase. The phenomenon of cavitation in such a polymer is not observed. If lamellae in the polymer are thick, with a reduced number of defects, then the strength of the amorphous phase is lower than the stress of initiation plastic deformation of crystals and cavitation occurs. It was shown that the same kind of polymer, depending on the crystallization and testing conditions (i.e., strain rate, temperature), might cavitate or not [13, 14].
The voids, if present, play an important role during the plastic deformation of semicrystalline polymers. The rapid change of local stress due to void formation stimulates the deformation processes in surroundings crystals, making the deformation of crystals easier. It is visible as a decrease of yield stress, more intensive fragmentation of the lamellae, and an increase of heat generated in the cavitating polymer, when compared with the same kind of material which does not cavitate [10, 15].
Usually, the studies of isothermal crystallization are performed on small pieces of thin polymeric films, and this is a reason why information about the mechanical properties of polymers crystallized in this way is limited. The ductile–brittle transition of isotactic polypropylene and its blend with poly(ethylene-co-octene), controlled by isothermal crystallization, was studied by Pang et al. . The mechanical properties of the samples, crystallized at 130 °C, were poor, with breaking at strain of 9 %, immediately after the yield. Cavities were not visible in non-deformed samples.
Some studies of the mechanical properties of isothermally crystallized linear polyethylene were performed by Kennedy et al.  who analyzed the influence of molecular weight on tensile properties and brittle–ductile transition. The narrow fractions of polyethylenes with molecular mass below 105 g/mol were brittle when crystallized at 125–130 °C, but showed transitional properties when their molecular mass was larger. Crystallinity was usually high, e.g., 91 % for polyethylene with Mw = 1.39 × 105 g/mol, crystallized at 125 or 130 °C.
To my knowledge, there was no report on studies on cavitation during the tensile deformation of polymers crystallized isothermally, containing some micrometer-sized cavities due to the crystallization process. It is not even known whether nano-voids accompany micro-voids in an isothermally crystallized polymer. The main subject of this work was to observe nano-cavitation during deformation in isothermally and non-isothermally crystallized polyolefins: high-density polyethylene and polypropylene.
Materials and methods
The polypropylene used in these studies was Malen P, F401 (Mw = 297,200 g/mol, Mn = 56,400 g/mol, MFR = 3 g/10 min (at 190 °C, 2.16 kg)), produced by Basell Orlen Polyolefins. The second polymer, high-density polyethylene (HDPE) Lupolen 6021D (Mw = 1.8 × 105 g/mol, Mw/Mn = 7.2), was produced by BASF. The isothermal crystallization process and the crystallinity of the materials were studied using differential scanning calorimetry (DSC). Thermal Analysis TA 2000 apparatus was used to determine the total time of crystallization. Polymers for DSC studies were formed into 0.5-mm-thick films using a hot laboratory press. Pieces weighing 8–9 mg were cut from these films, encapsulated, and crystallized isothermally in the DSC apparatus after melting.
Times of crystallization determined from DSC studies as appropriate for the crystallization of samples designed for mechanical studies
Crystallization temperature (°C)
Time of crystallization (min)
Crystallization temperature (°C)
Time of crystallization (min)
The DSC apparatus was also used to determine the crystallization times for high-density polyethylene. The studies were done at crystallization temperatures of 122, 125, and 129 °C. The crystallization times selected for the preparation of HDPE samples designed for mechanical tests are shown in Table 1. The crystallization process was very slow for a sample remaining at 129 °C, so I concluded that this temperature was too high for sample preparation because there was a risk of thermal degradation.
Samples for a mechanical test were prepared using a hot stage constructed in my laboratory. The main elements of the hot stage were two copper blocks containing heaters. The heaters and thermometers (resistors) were placed inside the blocks whose temperature was controlled by two programmable 535 Process Controllers (Omega, USA). A thin (0.5 mm) film of polymer was placed between two microscopic glasses; such a sandwich was positioned between the heating blocks. The hot stage with the sample was fixed in a polarizing microscope, replacing an original microscopic stage. Two small holes drilled inside the blocks gave a possibility to observe the growth of the crystalline structures inside the examined film. The polypropylene film was heated at the rate of 10 °C/min to the temperature of 220 °C, kept 3 min at that temperature, and cooled down to the final crystallization temperature, again at the rate of 10 °C/min. The crystallization temperature for polypropylene was 125, 129, 133, or 137 °C. The growth of spherulites was observed during solidification, and it was concluded that the images were invariable after times of 20, 30, 60, and 100 min; therefore, after these times, the samples were cooled to room temperature. The aforementioned times of crystallization were the same as determined by DSC (Fig. 1).
List of samples studied in mechanical and SAXS tests
Non-isothermal, melting at 220 °C, 3 min, and cooling 5 °C/min
Isothermal, 125 °C, 20 min
Isothermal, 129 °C, 30 min
Isothermal, 133 °C, 60 min
Isothermal, 137 °C, 100 min
Non-isothermal, melting at 190 °C, 2 min, and cooling 4 °C/min
Isothermal, 122 °C, 25 min
Isothermal, 125 °C, 40 min
High-density polyethylene films were prepared similarly to PP films. The 0.5-mm-thick foils, formed by the hot press, were melted inside the heating stage, conditioned for 2 min at T = 190 °C, and cooled down at the rate of 10 °C/min to one of two crystallization temperatures: 122 or 125 °C. At these temperatures, the film was kept for 25 or 40 min, respectively. The structures growing in polyethylene were small, the evolution of morphology poorly visible with the microscope, and the end of crystallization difficult to determine. This was the reason why the crystallization times were a bit longer than recommended by the DSC observations (see Table 1), remembering that the DSC measurements were done in similar, but not exactly the same, conditions. Moreover, the longer time should result in the thickening of crystals, which would increase the possibility of a cavitation.
Part of the polyethylene samples was also crystallized in non-isothermal conditions. In this case, the polymer film was melted inside the crystallizing device at 190 °C; after 2 min of conditioning at this temperature, the samples were cooled down at the rate of 4 °C/min to the final temperature of 100 °C. Microscopic observations confirmed that the crystallization was finished before reaching the final temperature, so the film was next cooled down to room temperature and removed from the apparatus.
It is known that the process of isothermal crystallization examined in the microscale depends on temperature. For PP and HDPE, three crystallization regimes are distinguished, and the architecture of the solidified polymers depends on these regimes [7, 20, 21]. All the polypropylene samples studied here were crystallized in regime III and the HDPE samples crystallized in regime II.
Samples for the tensile test were cut from the aforementioned films. They had a dog bone shape with an initial gauge zone length of 12.5 mm, width of 4.1 mm, and thickness of 0.3–0.5 mm (PP) or 0.5–0.6 mm (HDPE). Table 2 describes the symbols used in the text and the crystallization procedures for polymer samples examined by the tensile test and by X-ray scattering measurements.
The mechanical properties of polymers were studied at room temperature using an Instron 5582 tensile machine. Five samples of each kind were tested in uniaxial drawing. The rate of deformation was 5 %/min (i.e., 8.3 × 10−4 s−1) for HDPE and 2 %/min (i.e., 3.3 × 10−4 s−1) for PP. Black marks were drawn on the surface of each specimen. Changes of the initial 1-mm distances between the marks were recorded using a Canon D50 digital photo camera. At the same time, the actual sample width was recorded. My samples were too thin for accurate measurements of thickness by the photo method, so it was assumed that the thickness changed proportionally to the changes of width.
Some mechanical experiments were performed using a laboratory tensile machine, constructed in the Hasylab Laboratory in Hamburg. The technical characteristic of this device was similar to Instron, but with the applied force limited to 100 N. This machine was movable, so it was possible to place the stretched sample on the way of the X-ray beam from the DORIS III synchrotron source (A2 beamline) and conduct X-ray scattering measurements in situ during deformation. Radiation, with a wavelength of 0.15 nm, scattered under small angles (SAXS) was detected by a MarCCD 2D detector. SAXS patterns were later used to detect cavities and to determine crystalline structure parameters. It was possible to detect nano-cavities with dimensions below 80 nm. The times of a single pattern registration were 24 s for PP and 6 s for HDPE. The CCTV camera connected to a monitor and computer helped in the observation and recording of distances between the marks on the specimen surface and in the observation of the X-ray beam position on this surface. Before deformation, the beam was positioned in place where the beginning of plastic deformation could be expected. If the neck was formed in the expected illuminated area, then the results of the test were analyzed. The examined PP samples were deformed to break, which happened quickly after the yield point. Mechanical tests of HDPE specimens were stopped at the engineering strains of 90–110 % because in this polymer the most interesting phenomena occur earlier, around the yield point.
The wide-angle X-ray scattering (WAXS) camera was used for observations of possible crystallographic transformations. A source of CuKα radiation, operating at 30 kV and 50 mA, was used. Two-dimensional scattering images were recorded by a camera equipped with a Kodak imaging plate. The distance between a sample and a recording plate was 5 cm. Exposed imaging plates were analyzed with a PhosphorImager SI system (Molecular Dynamics). The stretching of the samples was interrupted at a selected strain and the sample fixed in a special frame, which preserved the state of the strain. The frame with the sample was then placed in a holder of WAXS apparatus. Typical time of acquisition was 7 min. For some samples, the WAXS patterns were recorded after releasing the mechanical stress with the aim of detecting eventual changes of diffraction patterns.
The spherulitic morphology of polypropylene was studied using the polarized light microscope. Thin (20 μm) slices were cut from polymer films with a microtome equipped with a glass knife. This procedure was not applied for polyethylene because the expected size of spherulites (based on crystallization observation) was too small for exact microscopy observations.
Results and discussion
Results of SAXS and DSC experiments for non-deformed PP samples
Temperature of crystallization (°C)
Long period from intensity curve (nm)
Long period determined from the correlation function (nm)
Lamellae thickness determined from the correlation function (nm)
Temperature of melting, max (°C)
Lamellae thickness (nm)
Heat of melting (J/g)
Table 3 shows that the long period of polypropylene structure depends on the crystallization temperature. It was the smallest (15.6 nm) for non-isothermally crystallized PP and increased with isothermal crystallization temperature to 20.7 nm at T = 137 °C. A similar tendency was observed when the long period was calculated from the correlation function. In all the examined materials, the crystalline layers were thicker than the amorphous ones and lamellae thickness increased with the crystallization temperature.
The second source of information on the crystalline structure of polypropylene was the DSC technique. The results of these studies are also presented in Table 3, where the following parameters are shown: temperature of melting (maximum of peak), lamellae thickness, heat of melting, and crystallinity.
The DSC thermogram of the non-isothermally crystallized PP sample shows that the melting peak was wide, with a maximum at 165.3 °C. Melting peaks in the isothermally crystallized specimens were narrower. The shift of position of the maximum in the direction of the higher temperature was observed with the increase of crystallization temperature. Calculations of the lamellae thickness (Eq. 1) showed its increase with the crystallization temperature. It follows from Table 3 that the heat of melting is higher at higher temperatures, which means an increase of crystallinity from 69 to 73 %, when the temperature of isothermal crystallization changes from 125 to 137 °C. Non-isothermally crystallized PP samples had a lower crystallinity of 65 %.
The main conclusion from the data in Table 3 is that crystals are thicker and crystallinity is higher when the temperature of crystallization increases. The observed differences in lamellar thickness are the result of the specifics of the applied DSC and SAXS methods. The different methods applied for thickness measurements were compared some years ago by Zhou and Wilkes . Previously, I studied the properties of the same polymer, but prepared with a different cooling procedure during crystallization . The comparison of the results showed that if the PP film was slowly cooled from melt, then its melting temperature was 163.1 °C and the heat of melting is 90.9 J/g. If the same material was quickly cooled in water, the melting temperature decreased to 162.2 °C and the heat of melting was only 82.0 J/g. In both cases, the process of solidification was faster than for the samples discussed in this manuscript.
Mechanical properties of PP samples deformed in tension at the rate of 2 %/min
Crystallization conditions (°C)
Elastic modulus (GPa)
Yield stress (MPa)
Yield strain (%)
Stress at break (MPa)
Strain at break (%)
Simultaneously with the results of the mechanical test, the small-angle X-ray scattering patterns were recorded. The goal of these observations was to detect cavities. Figure 3 shows the stress–strain curves measured for individual samples and the accompanying X-ray patterns recorded in situ during tensile drawing. The samples with maximum available strains were examined here with the aim of getting maximum information on scattering and cavitation, so the strains to break on curves in Fig. 3 differ from the average values given in Table 4.
In the patterns representing the non-deformed polypropylene, only the scattering from periodic crystalline structure is visible. It is the evidence of an important fact that nano-voids are not formed in PP during isothermal crystallization. The very small black dots visible near the beam stop are traces of the non-completely covered initial beam. In some images representing the deformed samples, dark spots representing the scattering on cavities are visible. The first voids arise when the deformation is close to the yield. It happens for the samples crystallized non-isothermally and for the samples crystallized isothermally at 125 and 129 °C. Polypropylenes which were crystallized at higher temperatures cavitated earlier, before the yield point (see Fig. 3d, e). It follows from Fig. 3e that first voids in the PP 137 specimen were formed at a strain of 1.3 % only. The vertical orientation of the dark spots in scattering images is the evidence that the nano-sized voids were elongated horizontally, i.e., perpendicularly to the deformation direction which was vertical.
The increase of volume before the yield is usually attributed to elastic deformation. In many cases, this increase is small and the accurate measurements of volume are difficult. A much larger increase of volume is often observed during the plastic deformation phase. Cavities formed inside the amorphous phase are responsible for it. Fortunately, for the PP129 sample, it was possible to measure correctly its dimensions up to the moment of break at 17 % of strain. I found that the 2D (i.e., defined as length × width2) volume strain at this deformation was equal to 0.16.
It was more than the value of 0.1 determined previously for specimens of the same material, which were formed from the air-cooled melt . The other PP specimens, crystallized in different conditions, broke around the yield, and the experimental error of measurements was too large to determine the volume correctly.
Properties of non-deformed HDPE samples determined by the SAXS and DSC methods
Temperature of crystallization (°C)
Long period (Is2 vs. s) (nm)
Long period from the correlation function (nm)
Lamellae thickness from the correlation function (nm)
Temperature of maximum of melting peak (°C)
Lamellae thickness from Eq. 1 (nm)
Heat of melting (J/g)
The crystalline properties of HDPE have also been studied using the DSC technique; the results of the measurements are shown in Table 5. This table shows a small increase of the melting temperature, heat of melting, and crystallinity when comparing PE-N with PE122 and PE125. Bassett showed that polyethylene lamellae are planar when the crystallization temperature is higher than 127 °C . A lower crystallization temperature produces spherulites whose lamellae have C- or S-shaped profiles, in which the angle between the lamellar normal and c-axis changes continuously, but with a maximum at ~35° [27, 28]. The values of lamellae thickness measured by SAXS were slightly different from those calculated from the DSC data, which resulted from the specifics of both methods; however, the general tendency—increase of thickness with the temperature of crystallization—was preserved.
From the data in Table 5 and from previous observations [29, 30], I expected that cavitation would appear in the samples crystallized isothermally and probably in the non-isothermal ones too. When the same polyethylene was solidified in air, it had 21.1-nm-thick lamellae and cavitated during stretching. However, if the molten HDPE samples were cooled in cold water, then thinner lamellae grew (13.9 nm) and the polymer did not cavitate .
Similarly to polypropylene, the evolution of morphology during crystallization was observed in polyethylene by a polarized light microscope. The spherulitic structures were formed in all HDPE samples crystallized from melt. Spherulites were fine, with diameters of a few micrometers only, so details of the structure were difficult to observe. The cavitation during crystallization was not visible.
Mechanical properties of polyethylenes
Crystallization conditions (°C)
Elastic modulus (GPa)
Yield stress (MPa)
Yield strain (%)
Parts of the HDPE specimens were tensile tested with a simultaneous registration of scattered X-ray radiation. Examples of the stress–strain curves and related scattering patterns are shown in Fig. 7. The deformation of HDPE was non-uniform and the neck was formed in all samples. Local strains in the neck were larger than macroscopic engineering strains. This is illustrated in Fig. 7, where the numbers near the curves show the values of local strain. Like polypropylene, the SAXS patterns for the non-deformed samples contain only the contribution from scattering on the crystalline periodic structure. It means that cavities with sizes of 2–80 nm were absent in the isothermally crystallized HDPE specimens before deformation. The intensive scattering on cavities is clearly visible in the deformed samples. It is first observed shortly before the yield, at strains of 11–12 %.
The patterns recorded beyond the yield are oriented in the deformation direction (i.e., vertically in Fig. 7), which means that the cavities were elongated perpendicularly to the deformation direction. At some local strain (in the range of 100–200 %), the shape of the pattern changes. This is interpreted as a reorientation of voids into the deformation direction. From the evolution of the patterns, it may be deduced that voids were more elongated at higher strains. The changes of void shapes were similar to those observed previously for HDPE [29, 30], when the samples were slowly solidified in air or were annealed.
In addition to the profiles in Fig. 8, total scatterings from the samples, registered by a Mar CCD detector, were determined. Darkening of the scattering pattern was analyzed using the ImageJ 1.41 software (public domain, W. Rasband, National Institute of Mental Health, USA). It was done for specimens deformed to engineering strains of 25 %, i.e., when the cavitation was relatively intensive, but the local strains in the samples were comparable. The performed analysis showed that if scattering from the non-isothermally crystallized sample was normalized to 1.0, then it was 1.18 for PE122 and 1.42 for PE125. These results confirm that at the beginning of plastic deformation, the scale of cavitation strongly depends on the previous crystallization process.
An important aspect of the cavitation process is the size of cavities because, together with the number of voids, it affects the behavior and properties of the material. It is known that the intensity of scattering is proportional to the square of the total volume of scattering objects. Guinier’s approach (Eq. 4) may be used to calculate the size if the voids are dispersed in the polymer , which happens at the beginning of cavitation. Computations of the radius of gyration were carried out for samples deformed to 20 % of the engineering strain. Here, the vertical profiles of intensities were analyzed, taken from the scattering patterns in Fig. 7. Because the scattering from voids dominated, it was assumed that the background and scattering from the crystalline structures were on the same level as the scattering from the non-deformed polymer and both components were subtracted from the total scattering. The calculations showed that only one population of nano-voids existed in the HDPE samples. The radius of gyration was equal to 14.8 nm for the non-isothermally crystallized HDPE, 16.7 nm for the same polymer crystallized at 122 °C, and 16.5 nm for the HDPE sample crystallized at 125 °C.
A significant increase of volume was observed in all samples, beginning from the yield point. The volume strain was similar for the PE-N and PE122 specimens, but a much stronger increase was observed for PE125, where the volume of the analyzed element was even twice as big as the original one.
The experiments performed with two polymers—polypropylene and high-density polyethylene—showed that plastic deformation of these materials occurs with cavitation. Their mechanical properties and the process of cavitation depend on the conditions at which the polymer was crystallized.
Although both polymers were crystallized isothermally, their morphologies were different. In polyethylene, small (a few micrometers in diameter) spherulites grew, so also small weak spots were formed between them and micrometer-sized cavities were not formed during crystallization . The SAXS studies showed that nano-voids were not present in the non-deformed HDPE. The cavitation happened when the external force was applied to the HDPE specimen. Voids were observed for the first time before the yield point, at strains of 1–2 % below the yield strain.
The DSC and SAXS measurements confirmed that crystallinity and the crystal thickness of polyethylene increased with the temperature and time available for crystallization. It is known that higher crystallinity and thicker, less defected crystals favor the cavitation during deformation . These resulted in the most intensive cavitation (both nano- and micrometer-sized) observed in polyethylene samples crystallized at the highest temperature. The nano-voids were at yields elongated perpendicularly to the deformation direction, which indicates that they were formed between the lamellae inside spherulites, not on the spherulitic borders or not inside the weak spots. Inside the spots and on the borders, more random orientation and less elongated voids are expected. Moreover, some observations of the isothermally crystallized samples showed that melting inside weak spots occurred at lower temperatures than melting of surrounding spherulites, which means that the matter inside these spots is less organized, with more defected crystals. The conditions for cavitation inside weak spots are worse than those existing inside the spherulites.
The elongated shapes of the SAXS patterns mean that the radius of gyration, R, is not directly related to the real dimension of voids and depends on the measurement direction. In current studies, the radius of gyration in the vertical direction was 15–17 nm.
Evolution of the shape of nano-cavities with elongation was similar in all samples and resembled those studied previously . The voids were initially elongated perpendicularly to the deformation direction, but this orientation changed for large strains, where cavities were elongated in the deformation direction. The change was forced by the reorganization of the surrounding lamellae, just as it was described in previous papers [13, 14, 29, 30]. The small voids were accompanied by larger, micrometer-sized voids. Their presence was confirmed by the whitening of material which occurred after yield.
The internal structure of the second examined polymer, polypropylene, was different because larger spherulites were grown during crystallization. Morphological observations showed that large weak spots, with diameters of 10–100 μm, were formed between spherulites in the isothermally crystallized films. In some of them, the polymer cavitated near the end of crystallization, forming micrometer-sized voids. The SEM photographs showed that weak spots were not very frequent. Nowacki et al.  observed that the negative pressure buildup was slower in large weak spots formed in polypropylene specimens crystallized at the highest temperatures. The reason was some relaxation of stretched molecules possible during long crystallization and the reduced viscosity of melt. This resulted in less frequent micro-cavitation observed during crystallization in the highest temperatures, although the weak spots were larger. The SAXS studies showed that the large voids in PP were not accompanied by smaller, nanometer-sized voids.
The crystals in PP samples were thick, so it was supposed that tensile deformation would occur with cavitation, which was confirmed experimentally for all the examined samples. When the polymer was deformed, voids were observed for the first time before the yield point. In polypropylene, the cavitation began earlier (i.e., at smaller strains) for these samples which were crystallized at higher temperatures. The DSC and SAXS measurements confirmed that the crystallinity and crystal thickness of polypropylene increased with the temperature and time available for crystallization. It is known that more regular chain folding in higher crystallization temperatures results in a decrease in the number of tie molecules . These molecules connecting adjacent crystallites play an important role in the mechanical performance of polymers [32, 33]. A limited number of the molecules bridging lamellae cannot preserve the continuity of the amorphous phase when the polymer is stretched. This is a possible reason of the early cavitation observed in these polypropylene specimens which were formed at the highest temperatures.
The SAXS patterns confirmed that nano-cavities in PP were elongated perpendicularly to the drawing direction. The intensities of scattering at yield, depending on the scale of cavitation, were larger for the specimens crystallized at higher temperatures. The volume strain for the PP129 sample was larger than those reported previously for the same polymer crystallized when cooling was in air [12, 13, 14].
Polypropylene spherulites usually are built from the lamellae of α-crystallographic form, creating a so-called cross-hatching structure. Previous studies of the cavitation in α- and β-allotropic modifications of PP showed that the scale of voiding was larger in the β-form, where this structure is not present, but only the radial lamellae growth . Norton and Keller  and Janimak et al.  found that the cross-hatching density in the isothermally crystallized PP is reduced with temperature and that radial lamellae dominate at higher crystallization temperatures. Therefore, the arrangement of lamellae crystallized at a higher temperature resembles that characteristic for β-form specimens, and it should result in more intensive cavitation during deformation. This is a reason, aside from the decreasing number of tie molecules, why the amorphous phase is weaker and a more intensive cavitation is observed in the samples crystallized at higher temperatures.
The size of the cavities was estimated from the radius of gyration. The samples which were crystallized in controlled isothermal conditions had values of R (i.e., 28–50 nm) larger than those found previously for PP crystallized by another cooling procedure (13–18 nm). The larger values of R were not associated with the increase of the amorphous layer thickness.
The above observations led to the conclusion that cavitation is more intensive when the crystallinity is higher and crystals are thicker, which happens during isothermal crystallization at high temperatures. Comparison of the cavitation during deformation in polypropylene containing some micro-voids resulting from crystallization and in polyethylene without such voids shows that the nano-voiding process occurs similarly, i.e., without visible influence of preexisting micro-voids. Those micro-voids are present in the interspherulitic areas, separated from the interlamellar amorphous layers inside spherulites, where the new nano-voids are generated during deformation. The large weak spots and big voids disturbing the internal distribution of stresses are probably responsible for the poor tensile properties and the early break of PP samples.
I wish to express thanks to the Hamburg Synchrotron Radiation Laboratory for the beam time granted within the projects I 20100253 EC and I 20110505 EC. Also, the statutory fund of the Centre of Molecular and Macromolecular Studies, Polish Academy of Sciences is acknowledged.
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