Lamellar thickness in semicrystalline polymers as a result of the competition between crystal growth and intracrystalline chain dynamics


 The non-equilibrium thickness of lamellar crystals in semicrystalline polymers varies largely between different polymer systems and depends on the crystallization temperature Tc. There is currently no consensus on the mechanism of thickness selection. Previous work has highlighted the decisive role of intracrystalline chain dynamics (ICD) in special cases, but a systematic dependence of lamellar thickness on relevant timescales such as that of ICD and stem attachment has not yet been established. Studying the morphology by small-angle X-ray scattering and the two timescales by NMR methods and polarization microscopy, we here present data on poly(oxymethylene), a case with comparably slow ICD. It fills the gap between previously studied cases of absent and fast ICD, enabling us to establish for the first time a quantitative dependence of lamellar thickness on the competition between the noted timescales.


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The characteristic morphological feature of semicrystalline polymers crystallized from the 14 melt is a nanoscopic two-phase structure of thin lamellar crystals separated by disordered 15 amorphous layers, which contain the entanglements retained during crystallization. This 16 morphology is to a large extent responsible for the advantageous mechanical properties of 17 semicrystalline polymers 1 . It has been a classical question in polymer physics, which factors 18 control the thickness of the crystalline layers resulting in a number of crystallization models 19 without reaching final consensus 2,3 .

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Most crystallization models start from the assumption that the semicrystalline morphol-21 ogy is a non-equilibrium structure, which is experimentally supported by the observation of 22 a melting point depression that depends on thermal history, specifically the crystallization 23 conditions. Structurally the melting point depression is explained by a finite crystal thick-24 ness 1 . In consequence, for a given crystallization temperature T c there is a minimal stable 25 crystal thickness. To explain the selection of a relatively well-defined crystal thickness during 26 crystallization, a second criterion defining an upper limit for the thickness is required. At 27 this point the assumptions made by different models diverge. The classical approach as-28 sumes that the crystal thickness is kinetically selected. The crystals with the thickness that 29 grow the fastest, dominate 4-8 , and once a stable crystal has formed, it is assumed that no 30 further structural changes will take place. Multistage models on the other hand assume that 31 crystal growth happens in several stages and is coupled to crystal reorganization processes. 32 Different mechanisms have been suggested -without reaching final agreement-to limit reor-33 ganization to a certain thickness, as thickness dependent stability of different crystal phases 9 34 or mesophases 10,11 or thickness dependent intracrystalline chain dynamics 3,12,13 . All these lization showed that indeed, for PEO the ICD is so fast that it can cause reorganization 69 over a very small nanometre-sized reorganization zone directly behind the growth front and 70 practically simultaneously with crystal growth 20 . From these results we concluded that in 71 crystal-mobile polymers the morphology is controlled by a minimum value of the amorphous 72 thickness related to the entanglement density in the amorphous regions.

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In order to enable a more quantitative description of the above-mentioned competition 74 between crystal growth and ICD we introduced three parameters describing the typical 75 timescales. As depicted in Figure 1(A) below, we describe the timescale of crystallization 76 by the layer crystallization time τ lc , the time during which the crystal grows on average by 77 one molecular layer. τ c and τ stem on the other hand are the characteristic timescales of the 78 ICD. Here τ c is the so-called jump correlation time as probed by NMR, i.e. the average 79 time between two helical defect jumps, whereas τ stem represents the time, during which a 80 defect diffuses over a distance equal to the crystal thickness d c by successive helical jumps.

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Our previous experiments on PCL and PEO correspond to the cases of non-existing (or very 82 slow) and very fast ICD, i.e. τ c ≫ τ lc and τ c ≪ τ lc respectively. τ c is measured on the 83 fully crystallized sample. As we cannot exclude that the ICD is faster directly behind the 84 growth front, the measured τ c is an upper estimate for the relevant parameter, but this does 85 not harm the arguments in general.

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Here, we present a set of experiments designed as a critical test of the hypothesized 87 competition between crystal growth and ICD by extending previous our studies to a poly- assuming a typical intermolecular distance of about 5 A. µ was measured by optical mi-103 croscopy. Figure 1 (B) shows µ as a function of T c for POM130 and POM212 (cf. Table 1).

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Corresponding data for PCL and PEO were already published and can be found in the SI.

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Previous investigations suggested that POM belongs to the class of crystal-mobile poly-106 mers, and that its intracrystalline chain dynamics (ICD) is much slower than in PEO 16 .
E a and τ 0 were determined for different T c s and both molecular weights. Exemplary results 115 are shown in Figure 1(C), the full set of resulting values are listed in Table S1 in the SI. As Here we assumed a random walk of N = τ stem / τ c steps of size ∆z c . The squared distance (1). τ c is the average residence time between two helical jumps calculated with eq. (2) and the values given in the SI. τ stem denotes the time during which a chain in the crystal diffuses over a distance equal to the lamellar thickness d c , estimated by eq.(3). τ c can be considered as lower and τ stem as an upper limit of the timescale of crystal reorganization enabled by the α c -relaxation. For PCL the solid line shows the NMR detection limit for τ c due to a possibly undetectably slow α c -relaxation. 35 for PEO τ lc is lying well above τ c for the whole temperature range and even becomes   Figure 3: Structure parameters during isothermal crystallization from the melt as a function of the crystallization time obtained by SAXS. For each sample system the isothermal crystallization was performed for a high (∼ 20 K) and a low (∼ 5 K) supercooling ∆T . The arrow represents the expected influence of α c -relaxation according to Figure 2. Rhs y-axis: time-dependent Porod parameter P (grey) normalized to 1 at the end of primary crystallization process (dotted line). Lhs y-axis: time-dependent long period L (black), amorphous thickness d a (blue) and crystalline thickness d c (red). σ c/a are shown as "error bars". For PEO the scale of the y-axis is increased roughly by factor 2. 177 In comparison, POM shows strong structural changes with time for both T c . For the lower 178 crystallization temperature these changes mostly take place after the primary crystallization. 179 We observe not only an increase in d c and a decrease in d a , but also a decreasing distribution with the higher T c shows that d c depends much more strongly on T c than in case of PCL. bly slow α c -relaxation. 16 The sample characteristics are given in Table 1. For each sam-  isothermal crystallization experiments at different crystallization temperatures T c .

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The data were analyzed using a quantitative approach based on modeling the interface     Therefore, we can safely ignore spin diffusion. See also the SI ( Figure S1). can be demonstrated directly as we follow the thickening process at the higher crystallization 428 temperature. Figure 6 shows the Porod parameter P and lamellar thickness d c as resulting