Variation of poly(vinylidene fluoride) morphology due to radial cold flow in a flexible pipe.
The oil industry is one of the sectors with the highest number of production systems employing high technology. Inside the production chain, a great part of the oil and gas produced in the Exploration and Production sector is conveyed from subsea deposits through flexible risers, which connect the production wells to processing platforms [1-3]. When it comes to the exploitation of deposits in deep and ultra-deep waters, the tailoring of lightweight flexible pipes is of paramount importance. In this field, significant design innovations appear to be necessary. Moreover, it must be understood what structural changes the components of such a tube are subjected to during service and in case of damage. Unbonded flexible pipes for subsea applications are composite structures. They consist of highly engineered concentric layers of metallic wires, tapes, and extruded polymers tailored to the specific environmental requirements and characteristics of the transported fluids (Fig. 1).
The pipe is flexible, because small relative movements between its unbonded layers are possible. A common type of pipe is assembled on top of a tubular metallic layer made from an interlocked metallic spiral ("Carcass" in Fig. 1). An overlying polymeric wear liner ("Flexwear") is in direct contact with the fluid. It is followed by a second polymer layer ("Barrier"). Outside of the barrier layer is an interlocked metal coil, again ("Flexlok[R]"). Its purpose is stabilization of the polymer layers against the inner pressure of the fluid.
For conveying hot liquids, the polymer layers are often made from poly(vinylidene fluoride) (PVDF). Here the temperature fluctuations in operation can lead to significant axial stresses [4-7] in the PVDF layers of the pipe. However, the polymer layers deform in radial direction as well, and there are recent studies that deal with such "creep" of the material due to the bore pressure [8, 9]. In fact, the polymer flows into gaps between adjacent turns of the metallic coil. As we have observed, there the polymer becomes white. Thus, we aim to study how this radial cold flow is coupled to changes of the polymer nanostructure. It has been reported  that whitening is frequently observed during cold-drawing with PVDF that before has been solidified at low cooling rates. Whitening of polymers is frequently associated with the formation of voids that are big enough to scatter the visible light. Moreover, changes of the semicrystalline morphology of the PVDF may have occurred, and even a gradual variation of the morphology across the layer may develop during service. To our knowledge, there is no earlier study that documents such structure gradients in flexible pipes.
A deformation of material at temperatures below the melting point is generally referred to as cold forming. After cold forming of PVDF at temperatures between 60[degrees]C up to 160[degrees]C, improvements in mechanical properties have been found [11, 12], In addition, both a more or less pronounced change in crystal modification has been reported, and that the isotropic small-angle scattering pattern changes into a layer line pattern  even if the crystal modification persists.
Therefore, it appears interesting to study the structure gradient in the proximity of the white embossments of the layers. For this purpose, thin cuts of the polymer are scanned by an X-ray microbeam and the two-dimensional (2D) small-angle X-ray scattering (SAXS) is recorded. The studied material originates from a long-term rapid decompression test. Such tests are necessary, because rapid pressure drops occur during operation. Decompression may be intentional, e.g., before an inspection or during the operation of a safety relief valve. It may as well be accidental as a consequence of failure. After a series of decompression cycles, the polymeric liners should remain intact in order to protect the metallic Flexlok[R] layer from corrosion and to act as a barrier.
The polymer samples originate from dissections of two flexible pipes (diameter: 4 inch). The polymer liners are made from commercial poly(vinylidene fluoride) (PVDF). One of the pipes has been virgin, the other has been subjected to a rapid decompression test using a supercritical fluid (C[O.sub.2]/methane 75 vol%/ 25 vol%) which mimics severe service conditions. The test has been performed at a pressure of 414 bar C[O.sub.2] and at a temperature of 90[degrees]C. The pipe has been kept under these conditions for 1 month, just above the computed saturation period for all the PVDF liners. After 1 month, the sample has been depressurized at a rate of -70 bar/min.
From the dissections, platelets of 1 mm thickness have been cut using a Buehler Isomet 4000 low-speed saw. Figure 2 presents the samples and their origin. Figure 2a shows a sample as cut from the virgin reference pipe. Figure 2b presents the retrieved wear layer and Fig. 2c presents the barrier layer of the tested pipe. Figure 2d displays a thin slice of material cut from the tested pipeline. It shows whitened embossments due to the cold flow of the PVDF. Arrows indicate the paths of the X-ray microbeam across the sample. The step size in horizontal scans has been 100 pm. Vertical scans have been performed with astep size of 30 pm.
In the dissectioning of the tested pipe, a severe local damage of the metallic Flexlok[R] layer has been found similar to those described in the literature  (Fig. 3).
For this reason, two sets of PVDF samples have been prepared from the tested pipe. The first set is from a region far from the damage, the second from right under the damage, respectively. Table 1 presents the correlation between sample designation and the position in the flexible pipe from which it has been collected.
Small-angle X-ray scattering (SAXS) is carried out in the synchrotron beam-line P03 at HASYLAB, Hamburg, Germany with a microfocus beam of size 38 pm X 19 pm. The wavelength of radiation is [lambda] = 0.109 nm and the sample-detector distance is 2640 mm. Scattering patterns are collected by a two-dimensional PILATUS 1M detector (DECTRIS, Baden, Switzerland) with 981 x 1043 pixels (pixel size: 172 pm x 172 [micro]m). The samples are translated through the microbeam stepwise and SAXS patterns are recorded at each step. The exposure time is 10 s. The intensity of the beam before and after the sample is monitored. The machine background is recorded before each sample scan (for determination of the absorption factor and machine background subtraction). The patterns I(s) = I([s.sub.12], [s.sub.3]) cover the region 0.00618 [nm.sup.-1] [less than or equal to] [absolute value of [s.sub.12, [s.sub.13]] [less than or equal to] 0.42 [nm.sup.-1]. s = ([s.sub.12], [S.sub.3]) is the scattering vector with its modulus defined by [absolute value of s] = s = (2/[lambda]) sin 0. 20 is the scattering angle. In real space, the monitored area corresponds to 160 nm [greater than or equal to] [absolute value of [r.sub.12], [r.sub.3]] [greater than or equal to] 2.4 nm. The scattering patterns are normalized and background corrected . This means intensity normalization for constant primary beam flux, zero absorption, and constant irradiated volume [V.sub.0]. The PILATUS detector is composed of sensitive tiles separated by blind gaps. These blind areas have partly been filled exploiting the four-quadrant symmetry of SAXS patterns with fiber symmetry. Data for the remaining "cheese holes" have been extrapolated assuming that SAXS patterns do not show sharp reflections which might hide in such a hole .
SAXS Data Evaluation
The patterns look either isotropic or exhibit two-point patterns. Therefore, we assume uniaxial symmetry with its axis [s.sub.3] (meridian) running through the centers of the two SAXS peak maxima. The recorded scattering patterns I(s) = I([s.sub.12], [s.sub.3]) are transformed into a representation of the nanostructure in real space. The only assumption is presence of a multiphase topology. The result is a multidimensional chord distribution function (CDF), z(r) . The method has been demonstrated elsewhere [17, 18]. Here, we only summarize the steps and introduce important quantities. The CDF with fiber symmetry in real space, I([r.sub.12], [r.sub.3]), is computed from the fiber-symmetrical SAXS pattern, I([s.sub.12], [s.sub.3]), of a multi-phase material. In order to compute z([r.sub.12], [r.sub.3]). I([s.sub.12], [s.sub.3]) is projected on the representative fiber plane. Multiplication by [s.sub.2] applies the real-space Laplacian. The density fluctuation background is determined by low-pass filtering. It is eliminated by subtraction. The resulting interference function, (G([s.sub.12], [s.sub.3]), describes the ideal multiphase system. Its 2D Fourier transform is the sought CDF. In the historical context, the CDF is an extension of Ruland's interface distribution function (IDF)  to the multidimensional case or, in a different view, the Laplacian of Vonk's multidimensional correlation function . The CDF is an "edge-enhanced autocorrelation function" [21-24]--the autocorrelation of the gradient field, [nabla][rho](r). [rho](r) is the electron density inside the sample that is constant within a domain (crystalline, amorphous, and void). Thus as a function of ghost displacement r, the multidimensional CDF z(r) shows peaks wherever there are domain surface contacts between domains in p(r') and in its displaced ghost [rho](r' - r). Such peaks [h.sub.i]([r.sub.12], [r.sub.3] are called distance distributions . The distance r = ([r.sub.12], [r.sub.3]) is the ghost displacement. One of the analysis methods is tracking of such distance distributions. We compute their position and their widths both in the direction of the principal orientation (meridional) and in the direction transverse to the principal orientation axis (equatorial) by fitting a bivariate polynomial to the cap of the peak. The method has been described earlier .
SAXS Evaluation of Isotropic Reference Patterns
In each material, regions with isotropic SAXS have been identified and analyzed to describe the morphology and its changes far away from the cold-flow zones. The respective scattering curves are analyzed by, first, transforming the curves into IDFs  and, second, fitting the IDFs by a one-dimensional stacking model [15, 27]. The model assumes that the layer thickness distributions are Gaussians that may be skewed , The parameters of the model are a weight w, the average thickness of the amorphous and the crystalline layers ([d.sub.a] and [d.sub.c], respectively), and three relative variances ([[sigma].sub.a]/[d.sub.a], [[sigma].sub.c]/[d.sub.c], and [[sigma].sub.H]). [[sigma].sub.H] is supplied in order to allow the effective layer thickness distributions to become skewed (by Mellin convolution of two Gaussians) , Effective relative variances [[sigma].sub.e, a]/[d.sub.a] and [[sigma].sub.e, e]/[d.sub.c] computed thereof describe the observable widths of the layer thickness distributions. Of practical interest is the long period [L.sub.IDF] = [d.sub.a] + [d.sub.c] and the volume crystallinity [v.sub.c] = [d.sub.c]/[L.sub.IDF]. The relative variation of the long periods, oJLiDF, is computed using the stacking-model relation [[sigma].sup.2.sub.L] = [[sigma].sup.2.sub.a,e] + [[sigma].sup.2.sub.a,c].
RESULTS AND DISCUSSION
Visual Inspection of the SAXS Data
SAXS of PVDF From the Virgin Pipe. The polymer layers of the virgin pipe show the same isotropic SAXS everywhere with a long period of about 9 nm.
SAXS of PVDF From the Tested Pipe. Vertical Scans. After the decompression test, the PVDF layers appear significantly changed (Fig. 2d). Material has flowed into the gaps of the metallic Carcass and Flexlok[R] layers, where it has formed white "noses". SAXS patterns of microbeam scans through the noses show the change of the nanostructure in the PVDF. Figure 4 presents selected patterns from vertical microbeam scans through the center of the noses. The CDFs are used for automated tracking of the long-period peak along the scans (cf. Fig. 5 and related text). Only in the CDF, the long-period peak appears qualified for such a simple analysis, because it has a clear maximum and is relatively narrow. In similar manner, the automated void-shape analysis (cf. Fig. 6) is based on the respective feature in the CDF.
The patterns shown in the top row of Fig. 4 have been taken close to the tip of the nose. The patterns in the bottom row are from the opposite edge of the scanned layer. The numerical labels indicate the distance from the nose-tip in units of micrometers. All the patterns are normalized to identical flux and identical irradiated volume. They are on the same logarithmic intensity scale.
The lower images of the WD (wear layer, damaged zone) and BD (barrier, damaged zone) layers are very similar as is expected, since these surfaces are in close contact with each other. The same applies to the bottom patterns of the W and B layers. Let us first discuss the scans of samples W and B (from the undamaged region). Moving upward from the edge of the layers towards the nose, the pattern changes fundamentally as the whitened region is entered. In its center the intensity increases taking the shape of a rather diffuse equatorial streak. It is commonly identified as void scattering [30-33]. Further more, the ring-shaped long-period peak of the lamellar two-phase system deforms. It gradually turns into two distinct reflections. Finally, in the top patterns, the lateral extension of the reflections (horizontal in Fig. 4) may be taken as an indication that the crystalline domains are no extended lamellae, and the strain-induced conversion into microfibrils [34-37] has already set in. The principal axis of the SAXS pattern indicates the direction in which the polymer has been strained from the cold flow. It is perpendicular to the scanning direction (cf. Fig. 2d). Such a rearrangement with orientation is frequently observed when thermoplastic polymers are cold-drawn , The difference compared to the samples taken from the damage zone (BD and WD) is, that there also the bottom patterns exhibit some orientation. Thus, in the damage zone the cold flow has permeated the entire polymer layer and created orientation.
It is remarkable that the material becomes so strongly oriented by the radial cold flow. A reason may be that the polymer layer is also exposed to tensile stresses in the axial direction due to temperature changes, and radial flow and axial stress interfere constructively. From the finding of strong polymer orientation, the question raises, whether even the mechanical properties of the polymer layers are changed by the cold flow. However, the mechanical properties of a composite flexible pipe are mainly determined by the reinforcing metal coils but not by the barrier polymer.
Variations of both intensity and orientation are observed along the scan paths. Where the orientation is low, we observe low intensity simply because it is more evenly distributed over the solid angle. The principal axis of the orientation is constant in the vertical scans because of the chosen path (along the central axis through the embossment).
Horizontal SAXS Scans. In the horizontal scans, the principal axis of orientation changes continuously and follows contours that connect locations with an identical degree of whitening. In Fig. 7, the variation of the orientation axis is indicated. As outlined in Fig. 2d, the horizontal scans have been carried out as close as possible to the outer surface of the layer. Start point and end point of the whitened zone are readily determined from the onset of a variation of the orientation direction as a function of the microbeam position. Because the widths of the whitened regions are different in each nose that has been scanned, the presentation in Fig. 8 has been adapted row-by-row to display this interval in which orientation-axis rotation is observed. Simultaneously this interval covers the whitened zone. Nevertheless, the formation of anisotropy starts already outside the whitened zones. In this way, the data from the horizontal scans indicate that successive mechanisms of the flow are mapped into space. First axial strain causes breaking and uniaxial orientation of the crystallites (turning lamellae stacks into microfibrils). This mechanism reaches out beyond the whitened nose regions. Second come both whitening (void formation) and tilting of the orientation axis by the radial flow into the gap.
Comparison of the four scans shows that the barrier (B) develops a higher degree of orientation than the wear layer (W). The milder cycling conditions in the barrier (away from the fluid) appear to cause higher perfection of orientation. The orientation appears highest in the damage region (BD, WD). In both samples from the wear layer (W, WD) an intensity gradient is observed: The SAXS intensity "on the left side" is lower than that "on the right side" of the scanned interval. This unexplained effect may be related to geometry, e.g. a tilt of the scan path with respect to the optimum scan direction along the pipe.
The SAXS patterns in Fig. 8 show two dominant features: There is a long-period peak with varying orientation distribution and a central equatorial streak of varying extension. Thus compared to the unaffected part of the PVDF layer, the white zone is characterized by both an orientation of the crystalline domains and the presence of an equatorial streak. We identify this streak by a very small fraction of needle-shaped voids . Because the void fraction is so small, the separation of void scattering and semicrystalline scattering is simple [38, 39], In the SAXS pattern, a narrow equatorial band is dominated by the void scattering, outside the band, the scattering of the semicrystalline morphology is observed and the void scattering is negligible.
The long axis of the observed voids is parallel to the direction of orientation, i.e. parallel to the double-arrows in Fig. 7. Therefore, most of these voids should hardly increase the permeability of the PVDF barrier. An exception is voids that form in the vicinity of sharp edges of the metal coils, where they extend almost perpendicular to the polymer layer.
In Fig. 8, the top scan (sample B) shows almost perfect symmetry about the center of the white embossment. At the edges of the white zone (outer patterns), the central scattering is weak. Towards the center, it develops into a clear equatorial streak, indicating an increasing void fraction. The orientation of the semicrystalline stacks appears highest at some offset from the nose center. There also the peak intensity appears higher. This higher intensity is explained by the higher concentration of intensity in narrower peaks.
For the BD-material, the scan reveals one important difference: Here the orientation of the semicrystalline stacks is highest in the center of the white zone. This finding may be related to deformation of the layer, because the failure of the Flexlok[R] has caused an outward bending of the complete barrier and the "straight" scan is, in fact, following a curved path with respect to an undamaged layer.
Let us discuss the two bottom scans in Fig. 8. In the W-material (undamaged zone), the orientation of the semicrystalline stacks is only moderate. It is much higher in the WD-material from the damaged zone (bottom scan). As with the B-material, the W-material exhibits an increased amount of voids slightly offset from the center of the white embossment. In the WD-material, the center of the white embossment shows a relatively low amount of voids and a low orientation, whereas the material from the outer part of the whitened embossment exhibits both voids and highly oriented semicrystalline stacks. An explanation has already been given at the end of the previous paragraph: the scan has been performed straight through the damage-induced bulge of the wear layer.
Morphology Away From the Cold-Flow Zones. Even in the samples from the tested pipe, there are regions in which the SAXS shows no voids and is isotropic. This is the case for the W- and B-samples along a vertical line in the middle between the embossments. Here the lamellar semicrystalline structure of PVDF has not been transformed fundamentally. Patterns from opposite sides of the double PVDF layer are analyzed. For this purpose, isotropic scattering curves are extracted. It is assumed that a lamellar two-phase system is present. Ruland's IDF  is computed and fitted with a stacking model. Table 2 presents descriptive morphological parameters, which result from fits to the IDF. The estimated intervals of confidence for the parameter values are smaller than the last given digit. The virgin material and the tested material from the wear layer show a volume crystallinity [v.sub.c] = 0.5. This is common with PVDF. In the wear layer, the average long period has increased and the distribution of long periods has narrowed. Both changes are typical annealing effects.
In the barrier layer, the thickness [d.sub.c] of the crystalline layer is highest. In major part, it has grown at the expense of the amorphous layers, i.e. the crystallinity in the layer stacks has increased. Crystallinity increase is typical for the annealing of semicrystalline polymers under mild conditions, and during the test, the conditions at the surface of the barrier layer (away from the fluid) are presumably milder than those at the surface of the wear layer. The transfer of the IDF evaluation method to the whole series is impossible, because anisotropy and void content vary continuously.
Degree of Orientation in Vertical Scans as a Function of Depth.
It has not been possible to quantify the degree of orientation in vertical scans. The interference of the semi-crystalline stack orientation with the variation of void scattering is too strong.
Long Periods. Only by an automated method, the many scattering data can be analyzed in reasonable time. A suitable method is the tracking of peak positions and peak shapes. The broad peak in the SAXS does not show a clear maximum for complete series and most peaks of the CDF are rather unclear, because the arrangement of the crystalline domains is poor. Only the long-period peak of the CDF is clearly separated in all data sets. Thus, it is selected for analysis. The location of the peak maximum on the meridian is a measure of the most frequent distance [bar.L] between adjacent crystalline domains. From the peak shape in meridional direction ([s.sub.3]), we calculate the relative variation interval [[sigma].sub.L]/[bar.L] of the long periods ,
Figure 5 presents the variations of the most probable long period [bar.L](y) as a function of the depth y below the respective nose tip. In order to assess the significance of the presented curves, we have also directly tracked the broad long-period peak in l(s) where it has been clear enough. We find coincidence for y > 2 mm.
There are similarities for higher y in the curves of material from damaged and undamaged regions. For example, the top two curves are from the barrier. The B-sample shows a constant long period of 13.5 nm down to y [approximately equal to] 1.5 mm. For lower depth, the long period decreases smoothly to 12 nm. The BD-sample from the damage zone behaves similar to sample B. In BD, the long-period decrease is observed for y < 2.5 mm. The fact that it reaches further down than with B is probably due to the increased cold flow of the PVDF under the fracture zone. The samples from the wear layer (W and WD) do not show the plateau of the B and BD for large values of y. A wavy course of [bar.L](y) appears to be typical for both samples. Again, the material from the damaged zone exhibits lower long periods, in general.
The curves of the horizontal scans are not shown. For all materials they only demonstrate, that inside the whitened zones [bar.L] decreases slightly from 13 nm to 12 nm, while [[sigma].sub.L]/[bar.L] increases from 0.15 to 0.25. Thus close to the filled gap the main effect of the cold flow is a broadening of the long period distribution.
Voids. SAXS can detect voids only up to a certain limit. The size depends on the optical adjustment of the instrument. It is 160 nm for the experiments presented here (cf. Experimental Section). We assume that there are also longer voids because the embossment zones appear white. The relatively diffuse equatorial streak in the scattering pattern can hardly be analyzed automatically. Therefore, we examine the corresponding feature in the CDF. It is represented by two weak long peaks running parallel to the meridian (in the vertical direction). Its extension in the meridional direction is a measure of the straight height [[bar.h].sub.v] of the voids that are detected by the setup, its distance from the meridian characterizes their average diameter [[bar.d].sub.v].
For the vertical scans, Fig. 6 shows the variation of the void dimensions. The curves end at different depths y. Below this level, no more voids can be analyzed quantitatively. In WD, voids range farthest down into the layer. This is explained by the harsher test conditions in the wear layer as compared to the barrier. In sample B, voids can only be detected up to 1 mm below the embossment tip. In sample W, the equatorial streak is rather noisy. This fact decreases the accuracy by which the void height can be determined. Nevertheless, in the areas where we trust the values, the heights (see Fig. 6a) for sample W and WD match. The void heights are longest 2 mm below the embossment tip. The heights of detectable voids in the barrier are lower than those found in the wear layer (explanation: harsher test conditions). In summary, the barrier is less penetrated by voids as the wear layer. Moreover, the needle-shaped voids detected in the barrier are shorter. Thus, the wear layer performs its task: it protects the barrier layer. Figure 6b shows the average void diameter [[bar.d].sub.v](y) in the vertical scans. Again, the data of the wear layer appear to be less influenced by the proximity to the damage area--probably because the voids are already fully developed in W because of the harsh cycling conditions. All the determined diameters [[bar.d].sub.v] are much lower than the resolution limit of our setup (160 nm). This means that we can only expect voids with very large diameter, if the void diameter distribution is not unimodal.
Horizontal scans give an impression of the lateral extension of the void-rich embossment zones. Visual inspection of the samples themselves (Fig. 2d) shows that the lateral widths of the whitened zones vary considerably from nose to nose. So, it makes no sense to draw detailed conclusions from the shapes of the corresponding curves.
In contrast to axial loads of the polymer layers in flexible risers, respective radial loads have hardly been investigated . In the present study, we have shown that the color change of the cold-flowed PVDF material is actually linked to the formation of voids. The white color indicates that probably even longer voids than the detected ones exist. Fortunately, the needle-shaped voids are oriented almost in axial direction. So, they do not form suitably directed channels for the passage of gases and liquids through the barrier layer. However, according to our results, sharp edges lead to tilting of marginal voids into the radial direction, which might decrease the barrier effect. Nevertheless, the orientation of marginal voids can be controlled by the geometrical shape of the Carcass and Flexlok[R] segments, some of which have failed in the test. Remarkably appear the morphological differences between the two polymer layers. Further investigations could help to understand them from a fundamental point of view. Concerning future research, it might be interesting to study if the cold flow in the PVDF is accompanied by a change of the crystal modification.
[1.] Y. Bai and Q. Bai, Subsea Pipelines and Risers, Elsevier, Oxford (2005).
[2.] B. Guo, S. Song, J. Chacko, and A. Ghalambor, Offshore Pipelines, Gulf Professional Publishing, Oxford (2005).
[3.] F.G. Aquino, Estudo do envelhecimento de poliuretanos aplicados na industria de Petroleo, Ph.D. thesis, Universidade do Estado do Rio de Janeiro (2009), Master thesis, 102 p.
[4.] C.S. J.L. Gacougnolle and P. Dang, J. Mater. Sei., 34, 5133 (1999).
[5.] S. Castagnet, S. Girault, J.L. Gacougnolle, and P. Dang, Polymer, 41, 7523 (2000).
[6.] B. Mel ve, in 20th International Conference on Offshore Mechanics and Arctic Engineering, Vol. 3, 383 (2001).
[7.] F. Demanze, in 22nd International Conference on Offshore Mechanics and Arctic Engineering, 141 (2003).
[8.] Y. Shen, J. Zhao, Z. Tan, and T. Sheldrake, in 30th International Conference on Ocean, Offshore and Arctic Engineering, Vol. 4, 353 (2011).
[9.] T. Sheldrake, Y. Shen, J. Zhao, and Z. Tan, in 31st International Conference on Ocean, Offshore and Arctic Engineering, Vol. 3, 153 (2012).
[10.] N. Osaka, K. Yanagi, and H. Saito, Polynt. J., 45, 1033 (2013).
[11.] H. Sobhani, M. Razavi-Nouri, and A.A. Yousefi, J. Appl. Polym. Sci., 104, 89 (2007).
[12.] K. Nakamura, M. Nagai, T. Kanamoto, Y. Takahashi, and T. Furukawa, J. Polym. Sci. Part B: Polym. Pliys.,39, 1371 (2001).
[13.] T.C. Hsu and P.H. Geil, J. Mater. Sci., 24, 1219 (1989).
[14.] K.-A. Fames, C. Kristensen, S. Kristoffersen, J. Muren, and N. Spdahl, in 32nd International Conference on Ocean, Offshore and Arctic Engineering, Vol. 4A, OMAE2013-10210 (2013).
[15.] N. Stribeck, X-ray Scattering of Soft Matter, Springer, Heidelberg, New York (2007).
[16.] N. Stribeck, K. Schneider, A. Zeinolebadi, X. Li, C.G. Sanporean, Z. Vuluga, S. Iancu, M. Duldner, G. Santoro, and S.V. Roth, Sci. Tech. Adv. Mater., 15, 015004 (2014).
[17.] N. Stribeck, J. Appl. Ciyst., 34, 496 (2001).
[18.] N. Stribeck, X-ray Scattering of Soft Matter, Springer, Heidelberg, New York (2007), sect. 8.5.5.
[19.] W. Ruland, Colloid Polym. Sci., 255, 417 (1977).
[20.] C.G. Vonk, Colloid Polym. Sci., 257, 1021 (1979).
[21.] P. Debye and A.M. Bueche, J. Appl. Pliys., 20, 518 (1949).
[22.] G. Porod, Colloid Polym. Sci., 124, 83 (1951).
[23.] C.G. Vonk, J. Appl. Ciyst., 6, 81 (1973).
[24.] F.J. Balta Calleja and C.G. Vonk, X-ray Scattering of Synthetic Polymers, Elsevier, Amsterdam (1989).
[25.] Z. Denchev, N. Dencheva, S.S. Funari, M. Motovilin, T. Schubert, and N. Stribeck, J. Polym. Sci. Part B: Polym. Phys., 48, 237 (2010).
[26.] W. Ruland, Colloid Polym. Sci., 256, 932 (1978).
[27.] J.J. Hermans, Rec. Trav. Chim. Pays-Bas, 63, 211 (1944).
[28.] N. Stribeck, Colloid Polym. Sci., 271, 1007 (1993).
[29.] N. Stribeck, J. Phys. IV, 3, 507 (1993).
[30.] G. Porod, Makromol. Chem., 35, 1 (1960).
[31.] W.O. Station, J. Polym. Sci., 58, 205 (1962).
[32.] R. Bonart, Kolloid Z. U. Z. Polymere, 211, 14 (1966).
[33.] R. Perret and W. Ruland, J. Appl. Cryst., 3, 525 (1970).
[34.] A. Peterlin, J. Mater. Sci., 6, 490 (1971).
[35.] A. Peterlin, Text. Res. J., 42, 20 (1972).
[36.] G. Porod, Fortschr. Hochpolym.-Forsch., 2, 363 (1961).
[37.] Y. Tang, Z. Jiang, Y. Men, L. An, H.F. Endere, D. Lilge, S.V. Roth, R. Gehrke, and J. Rieger, Polymer, 48, 5125 (2007).
[38.] N. Stribeck, J. Polym. Sci., Part B: Polym. Phys., 37, 975 (1999).
[39.] N. Stribeck, ACS Symp. Ser., 739, 41 (2000).
[40.] N. Stribeck, A. Zeinolebadi, M. Ganjaee Sari, S. Botta, K. Jankova, S. Hvilsted, A. Droz-dov, R. Klitkou, C.G. Potamiche, J. Christiansen, and V. Ermini, Macromolecules, 45, 962 (2012).
Fabio Aquino, (1) Almut Stribeck, (1) Xuke Li, (1) Ahmad Zeinolebadi, (2) Stefan Buchner, (2) Gonzalo Santoro (3)
(1) Institute TMC, Department of Chemistry, University of Hamburg, Bundesstr. 45, Hamburg, D-20146, Germany
(2) Polymer Consult GmbH, Schwarzer Weg 34, Hamburg 22309, Germany
(3) HASYLAB At DESY, Notkestr. 85, Hamburg D-22607, Germany
Correspondence to: A. Stribeck; e-mail: email@example.com
Contract grant sponsor: Hamburg Synchrotron Radiation Laboratory (HASYLAB); contract grant number: 1-2011-0087.
TABLE 1. Sample designation (first column) and their origin in the unbonded flexible pipe (for second column cf. Fig. 3, for third and fourth column cf. Fig. 2). Sample Damage Wear Barrier label zone layer layer Virgin x x W x WD x x B x BD x x TABLE 2. Pure semicrystalline isotropic morphology far from cold-flow zones as determined by IDF analysis. [d.sub.c] is the number-average thickness of the crystalline layer and [v.sub.c] is the volume crystallinity in the lamellae stacks. Additionally, the numerical-average long period [L.sub.IDF] , and the relative variance [[sigma].sub.L]/[L.sub.IDF] of the distribution are shown. [d.sub.c] [L.sub.IDF] [[sigma].sub.L]/ Sample (nm) [v.sub.c] (nm) [L.sub.IDF] Virgin 4.5 0.50 8.9 0.38 Wear 5.0 0.50 9.9 0.31 Barrier 5.4 0.58 9.2 0.33
|Printer friendly Cite/link Email Feedback|
|Author:||Aquino, Fabio; Stribeck, Almut; Li, Xuke; Zeinolebadi, Ahmad; Buchner, Stefan; Santoro, Gonzalo|
|Publication:||Polymer Engineering and Science|
|Date:||Dec 1, 2015|
|Previous Article:||Phase structure and mechanical properties of PP/EPR/CaC[O.sub.3] nanocomposites: effect of particle's size and treatment.|
|Next Article:||Thin polymeric film microstructure manipulation for diffused reflectance applications.|