periodic patterns in solution grown polymer single crystals †

Institute of Physics, University of Freiburg, 7 reiter@physik.uni-freiburg.de Hermann Staudinger Graduate School, U Germany School of Materials Science & Engineering, Z People's Republic of China Chair of Chemical Materials Science, D Konstanz, 78464 Konstanz, Germany Institute of Macromolecular Chemistry, U Germany Freiburg Materials Research Centre, Univers † Electronic supplementary informa 10.1039/c4ra10563j Cite this: RSC Adv., 2015, 5, 12974


Introduction
Polymer crystals usually grow under conditions far away from thermodynamic equilibrium [1][2][3][4][5] , resulting in lamellar crystals 15 of highly folded chain-like molecules. 6, 7 These crystals may exhibit many different, often complex morphologies [8][9][10][11] . However, in particular in solutions, for many decades also polymer crystals with a simple faceted morphology have been frequently observed. [12][13][14][15] At the corresponding comparatively fast 20 growth rates [16][17][18] , polymers cannot equilibrate and meta-stable states of folded polymers are the rule. Consequently, although of simple shape, faceted polymer crystals should consist of polymers differing in degree of molecular order. [19][20][21] According to the Gibbs-Thomson relation, 22 the melting temperature depends 25 on the size of the crystal or the size of the domain of molecules of equal degree of order. Smaller or less ordered regions melt at lower temperatures than larger or better ordered ones. 23-27 Thus, when annealing faceted crystals at temperatures below the nominal melting temperature, 28,29 one may anticipate observing 30 morphological changes which may provide information on the spatial distribution of less ordered regions within faceted crystals and, possibly, on how the faceted crystals were grown.
Annealing-induced morphological changes in polymer single crystals at temperatures well below the nominal melting 35 [30][31][32][33] Local molecular reorganization processes were identified as the central mechanism 50 which allowed to partially remove chain folds with increasing annealing time or annealing temperature. 31, 34, 35 As a consequence, the mean lamellar thickness increased, leading to enhanced thermal stability. 36, 37 Pioneering microscopy works 38-42 on individual single crystals have demonstrated that, as a mere 55 consequence of mass conservation, such annealing induced local thickening 43 is accompanied by the formation of a "Swiss cheese" morphology or "saw-tooth' patterns. [44][45][46][47] Such spatially varying changes in morphology induced by annealing reflect heterogeneities, i.e., differences in molecular order within these 60 crystals. However, so far annealing did not reveal any evident spatial correlations of these heterogeneities. No relation to the initial growth conditions and to the conditions of annealing could be established.
One reason for not observing correlated patterns induced by 65 annealing may be attributed to the typically small differences in degree of order within a single crystal. Thus, to uncover heterogeneities, 48,49 differences in thermal stability have to be amplified first. Here, we have chosen a lengthy series of annealing steps which started at low temperatures and slowly 70 moved to higher temperatures. Annealing has to remove sequentially, and with high accuracy, crystalline parts which have an only slightly lower thermal stability than more perfect ones. Upon proper annealing, less stable regions will melt. Simultaneously, the remaining regions will become even more 75 stable, e.g., thicker. Consequently, the finally surviving regions reflect, to a large extent, the more stable crystalline parts formed already during crystal growth. By applying suitable annealing sequences, we attempted to unveil the less stable parts of a polymer crystal and aim to answer the following question: Are 80 heterogeneities within facetted lamellar single crystals distributed homogeneously or are they arranged according to some pattern?  10 polyethylene 50, 51 . The here reported phenomenon was first revealed and studied in detail for a partially deuterated sample of low polydispersity index (PDI). To demonstrate the generality of the phenomenon we verified that other PE-samples, including commercial products with high PDI, also exhibited analogous 15 morphological changes induced by appropriate annealing procedures. However, the changes were more accentuated and more uniform for polymers with a narrow molecular weight distribution.

Experimental
Here, we studied four high molecular weight polyethylene 20 samples, including two homopolymers of protonated polyethylene (PE), a deuterated PE (dPE) and a diblock copolymer of hydrogenated and deuterated polyethylene (hPE-b-dPE) of different molecular weights. 52 For all these polymers, single crystals were prepared by a self-seeding method, 53 from 25 dilute solutions at appropriate crystallization temperatures (Tc). The polymers were dissolved in p-xylene at rather low concentrations of 0.001 wt % or 0.0001 wt % by heating the solution (ca. 1 ml in a closed glass vial) first to 130 °C for 30 min, i.e., well above the nominal dissolution temperature of ca. 30 100 °C. This so homogenized polymer solution was then rapidly crystallized and aged for 2 hours at 70 °C in a thermostated bath filled with silicone oil. The solution was subsequently heated to the respective self-seeding temperature Ts, where it was kept for 10 minutes. For growing single crystals, the samples were 35 subsequently quickly transferred to another thermostated bath at a pre-set crystallization temperature Tc. Drops of such solutions containing suspended PE single crystals were then deposited onto a silicon wafer, an often used substrate. 47,[54][55][56][57] After deposition, the solvent was allowed to evaporate completely in vacuum at 25 40 °C for 12 hours.

AFM Measurements and Annealing of Single Crystals
Characterization of the morphology and thermal behaviour of the single crystals was performed by atomic force microscopy 45 (AFM, JPK Instruments, Germany). The microscope was equipped with a high-temperature heating stage accessory, controlling the temperature of the sample, allowing to perform in-situ experiments at elevated temperatures. Figure 1a illustrates a typical temperature protocol used in this study for the in-situ 50 AFM experiments. By conducting in-situ AFM measurements during annealing of the samples, it was possible to observe, in addition to changes in morphology at the chosen annealing temperature, also changes in the phase-signal of the tappingmode AFM. This phase-signal reflects viscoelastic properties of 55 the sample and thus allowed to distinguish between crystalline and molten regions. However, the relatively high annealing temperatures caused stickiness between the AFM-tip and the molten polymers and made measurements more complex. In addition, due to the required scanning velocities, it was often 60 difficult to obtain high-resolution in-situ images with a low noise level. Thus, some high-resolution AFM images of the 65 morphology evolution after annealing at increasing temperature (Ta) and for prolonged times were performed ex-situ at room temperature. For ex-situ experiments, the single crystals were annealed first on a Linkam THMS 600 hot stage (Linkam Scientific Instruments, Tadworth, UK) under nitrogen atmosphere 70 at a desired temperature for a chosen time (mostly 20 minutes). The sample was subsequently cooled to room temperature and investigated by AFM. The sample was further annealed on the Linkam hot stage at a slightly higher temperature and reexamined by AFM. This procedure was repeated several times. 75 However, at room temperature the molten polymers recrystallized and the AFM phase-signal was not able to distinguish them from the crystalline regions existing at elevated Ta. Thus, after a temperature protocol as the one shown in Figure 1b including a quench to room temperature, AFM measurements could only visualize the morphology obtained after the annealing process but could not indicate the amount of molten polymers and their distribution within the single crystal.  In Figure 2, we show a sequence of in-situ AFM height images of a truncated lozenge-shaped polyethylene single crystal of PE1, taken after different annealing steps. At each temperature, the sample was kept for 20 min, followed by a 20 temperature increase of a maximum of a few degrees (see also Figure 1a). Up to an annealing temperature (Ta) of ca. 122 °C, the crystal morphology almost did not change. Only the crystal periphery became periodically modulated. Notches, bounded by a thickened rim, appeared along the edges of the crystal. These 25 localized changes reflect modulations of stability favoured by the higher mobility of the polymer chains located at the edges of the crystals, i.e., the most unstable parts of crystal. There, reorganization of thermodynamic meta-stable states towards more stable states occurred first. 30 Upon annealing at Ta > 122 °C, thickened parts became more prominent and grew from the periphery of the crystal in the direction towards the interior of the crystal. The resulting branches progressively carved regularly spaced valleys into the single crystal. Eventually, the branches reached the centre of the 35 crystal, i.e. the initial nucleation site. When heating slightly above 130°C, valleys were refilled by molten polymers. However, the memory of the branched patterns still existed as the branches re-appeared upon cooling (see also Figure 3). Only after heating above ca. 135°C, all memory of a crystalline pattern was 40 lost. It is worth noting that annealing the crystal by jumping right away to temperatures above ca. 130°C caused the formation of "Swiss-cheese"-like patterns rather than branches. Thus, slowly removing less perfect crystalline regions by providing enough time for re-organisation within the crystal seems to be required to 45 generate periodic patterns formed within a single crystal.

Results and Discussion
In addition to identifying local morphological changes, we also determined the mean height of the crystal, recorded during annealing. These mean values allowed a direct comparison with results frequently obtained via averaging techniques like X-ray 50 scattering 34,47 . As shown in the histogram of Figure 2f, taken from the recorded AFM images, a sequence of stages can be identified, consistent with previous observations 21 . For the early stages (low Ta and/or short annealing times (ta)), the mean height of the crystal (its lamellar thickness (ld)) did not change much. 55 Nonetheless, even at such early stages, the morphology already started to change at the crystal periphery. At progressively higher Ta, or after prolonged annealing, a stage of local melting and significant reorganization followed (Figure 2(c+d)), causing a shoulder to appear at higher thickness values and evolving into a 60 peak in the height histogram. With increasing Ta, this new peak, which is typically attributed to lamellar thickening 29, 31, 58, 59 , slowly shifted to higher values of ld. In combination with the direct space observation by AFM, we can conclude that the lamellar thickening process was accompanied by the formation of 65 a regular pattern within the single crystal. For Ta > 130 °C, the height distribution became rather broad, related to the simultaneous melting of large parts of the crystal and thickening of the remaining parts, the branches.  The size of the scale bar is always 500 nm. 80 Using the phase-signal of tapping mode AFM, it is possible to visualize differences in viscoelastic properties within an annealed single crystal. Under the imaging conditions used here, the contrast visible in the phase images reflects crystalline (light colours) and molten (dark colours) areas. As can be seen in Figure 3a, the AFM phase images indicated that in the course of the appearance of the branches, they carved regularly spaced valleys into the single crystal which were partially filled by molten polymers as indicated by the change in the phase signal (the dark colour of the phase signal is indicating molten 10 polymers).
The short waiting time of 10 min at Ta = 124 °C did not allow for the formation of branched structures within the whole crystal. After raising the temperature to 128 °C, only the thickened parts, i.e. the parts forming the branched morphology, 15 exhibited a solid-like response in the AFM phase-signal. At even higher temperatures, such as 132 °C (Figure 3c), the branched structure seemed to disappear. Under the chosen imaging conditions, it was not visible anymore in the AFM phase-signal. However, when increasing the tapping force 60,61 , it became clear 20 that branches still existed but were "hidden" under a layer of molten polymers. In addition, upon quenching to room temperature, the branched structure became clearly visible (compare Figs. 3f and 3i).
Upon cooling, all molten polymers re-attached to the 25 remaining branches, making them visible again in the AFM topography images. A series of high resolution AFM high images of PE1 single crystals were taken at room temperature after annealing at various Ta (see Figure 3g-3i). When annealing at temperatures lower than 128 °C, the morphological evolution of 30 the annealing-induced branched pattern was obviously very similar to what was demonstrated in the above in-situ AFM images (compare Figures 2b + 2c and 3b and 3e). Crack-like structures could be seen both in the central region and at the crystal edges after annealing at 128 °C. As shown in the AFM 35 height image (Figure 3h), the cracks formed a branched pattern. In addition, the lamellar thickness within such single crystals increased upon annealing. Upon quenching the sample to room temperature, recrystallisation of polymers from the partially molten state in 40 between the branches contributed to the morphological changes. This became particularly visible for annealing temperatures above 128 °C. It can be deduced by comparison of Figures 3d -3f with Figures 3g -3i that re-crystallisation of the molten polymers was guided by the crystalline branched pattern. 45 Besides varying Ta, we also varied ta while keeping Ta constant. For example, at Ta = 125 °C, the morphological evolution of one solution-grown faceted crystal is shown in Figure 4a. Already after ta = 2 min, numerous notches formed along the crystal edges. With increasing ta, these notches 50 penetrated further towards the centre of the crystal. Elongated branches formed in each sector of the initial crystal, all of them pointing preferentially towards the centre (i.e. the nucleation site) of the crystal. As shown in the height histogram of Figure 4b, a second broad peak emerged at the expense of the initial peak. The 55 comparison of Figures 2 and 4 reveals a kind of time-temperature superposition. Interestingly, the value of the periodic spacing () of the branches increased with ta, reflected by a decrease in number of branches per unit length. This evolution of (ta) followed the same trend as the mean crystal thickness (ld) ( Figure   60 4c), consistent with previous scattering experiments 34  In order to demonstrate the generality of our approach, we have repeated analogous experiments for a variety of PE molecules of high molecular weight, including commercial products (see Experimental Section). For all samples, we grew single crystals having the shape of a truncated lozenge. Applying The initial lamellar thickness (ld0) depends on the growth rate, which, in turn, can be controlled by crystallization temperature Tc. 35,62 In addition, the thickness (ld) of a crystalline lamella can vary during growth in the regions behind the growth front or during post-growth annealing stages. In Figure 6, we 5 demonstrate that λ also depends on Tc. This suggests that a relation between λ and ld0 (or ld) exists. As has been shown previously, 34, 58 lamellar thickening 15 induced by annealing is a complex process involving (1) a molecular diffusion process of the detached/molten molecules to more stable, thicker crystalline regions, (2) attachment and incorporation of molecules into these regions, followed by (3) further improvement of stability by removing even more folds 20 and disappearance of less stable regions. Consequently, as shown in Figures 2-6, annealing temperature and time have a crucial influence on the evolution of morphology and lamellar thickness (ld) during/after growth. The rate of such annealing-induced changes depended on the initial degree of order and the 25 morphology of the single crystal, mainly determined by the crystallization temperature.
To shed some light on the origin of annealing-induced branched patterns, we searched for relations between the conditions under which the faceted polymer single crystals were 30 grown and the periodic patterns observed after annealing. For various annealing procedures and crystallization conditions, we analysed a series of single crystals and compared the evolution of  with the accompanying changes in the parameters ld0 (see Figure 7a) or ld (see Figure 7a). The results are summarized in 35 Figure 7, from which we can draw the following conclusions.  was found to be much smaller than the size of the faceted crystals and only about ten times larger than ld. As shown in Figure 4, for constant Ta, λ increased approximately with log(ta). Because ld also increased with log(ta), a clear relation between λ and ld was 40 found. Single crystals prepared at increasing Tc showed an increase in ld0. As shown in Figure 7b for annealing times increasing with Tc, λ also increased with Tc, giving rise to an approximately linear relation between λ and ld0. A more complex behaviour was found when keeping ta constant (20 minutes) and 45 varying Ta (from 115 to 130 °C). At low Ta, λ increased rapidly with ld. But at high Ta, λ increased only slowly with ld. At low annealing temperatures (from ca. 115 to 120 °C), changes in morphology could only be observed for crystals grown at low Tc. At such conditions, λ was found to be small, i.e., the distances 50 between branches were short, allowing for relatively efficient transport of polymer chains between branches. Thus, a coarsening of λ was observed even for short annealing times. For thicker lamellar crystals, higher temperatures and longer times were required to allow for the annealing-induced changes in 55 morphology to become visible. changes of lamellar thickness (ld) and the changes of λ. All crystals were similar in lateral size, obtained by adjusting tc. Only one parameter (either ta, Tc or Ta, respectively) was varied for each of the three data sets. Annealing and crystallization conditions are represented as: (Ta | ta | Tc | tc). 75

Conclusions
Using solution grown polymer single crystals of polyethylene, one of the simplest and most widely studied polymers, we have been able to change the morphology of faceted crystals by annealing. Under the here applied low-5 temperature and long-lasting annealing conditions, we were able to unveil a rather regularly branched pattern within a polymer single crystal which we tentatively relate to variations in the degree of thermal stability. Upon annealing, the less stable regions, characterized by a lower melting temperature, were 10 redistributed between the more stable regions. The branches, which emerged after annealing, all had similar width and were preferentially oriented towards the centre, the initial nucleation site. Like the thickness of the lamellar crystal, the observed period of the branches depended on the crystallization conditions 15 of the starting crystals but also on the conditions of subsequent annealing. Although within experimental error no regions of different lamellar thickness could be identified within as-grown single crystals, we speculate that such regions of differing degrees of thermal stability existed. These observed annealing- 20 induced morphological changes from a faceted to a branched pattern within polymer single crystals may provide an instructive approach for studying differences in organization and thermal stability created within polymer single crystals in the course of growth. 25

Textual abstract
Faceted polymer single crystals have been transformed into periodically 45 branched patterns by applying a slow annealing procedure.