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A new small-angle X-ray scattering model for polymer spherulites with a limited lateral size of the lamellar crystals

机译:一种新的小角度X射线散射模型用于层状晶体侧面尺寸有限的聚合物球晶

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摘要

As is well known, polymers commonly form lamellar crystals, and these assemble further into lamellar stacks and spherulites during quiescent crystallization. Fifty years ago, Vonk and Kortleve constructed the classical small-angle X-ray scattering theory (SAXS) for a lamellar system, in which it was assumed that the lamellar stack had an infinite lateral size [Vonk & Kortleve (1967), Kolloid Z. Z. Polym. >220, 19–24]. Under this assumption, only crystal planes satisfying the Bragg condition can form strong scattering, and the scattering from the lamellar stack arises from the difference between the scattering intensities in the amorphous and crystalline layers, induced by the incident X-ray beam. This assumption is now deemed unreasonable. In a real polymer spherulite, the lamellar crystal commonly has dimensions of only a few hundred nanometres. At such a limited lateral size, lamellar stacks in a broad orientation have similar scattering, so interference between these lamellar stacks must be considered. Scattering from lamellar stacks parallel to the incident X-ray beam also needs to be considered when total reflection occurs. In this study, various scattering contributions from lamellar stacks in a spherulite are determined. It is found that, for a limited lateral size, the scattering induced by the incident X-ray beam is not the main origin of SAXS. It forms double peaks, which are not observed in real scattering because of destructive interference between the lamellar stacks. The scattering induced by the evanescent wave is the main origin. It can form a similar interference pattern to that observed in a real SAXS measurement: a Guinier region in the small-q range, a signal region in the intermediate-q range and a Porod region in the high-q range. It is estimated that, to avoid destructive interference, the lateral size needs to be greater than 11 µm, which cannot be satisfied in a real lamellar system. Therefore, SAXS in a real polymer system arises largely from the scattering induced by the evanescent wave. Evidence for the existence of the evanescent wave was identified in the scattering of isotactic polypropyl­ene. This study corrects a long-term misunderstanding of SAXS in a polymer lamellar system.
机译:众所周知,聚合物通常形成层状晶体,并且在静态结晶期间这些聚合物进一步组装成层状堆叠和球晶。五十年前,Vonk和Kortleve为层状体系构建了经典的小角度X射线散射理论(SAXS),其中假设层状叠层具有无限的横向尺寸[Vonk&Kortleve(1967),Kolloid ZZ Polym。 > 220 ,19-24]。在这种假设下,只有满足布拉格条件的晶面才能形成强散射,而层状堆叠的散射是由入射X射线束引起的非晶层和晶体层中散射强度之间的差异引起的。现在认为该假设是不合理的。在真正的聚合物球晶中,层状晶体的尺寸通常只有几百纳米。在这样有限的横向尺寸下,在宽方向上的层状堆叠具有相似的散射,因此必须考虑这些层状堆叠之间的干扰。当发生全反射时,还需要考虑平行于入射X射线束的层状堆栈的散射。在这项研究中,确定了球晶中层状叠层的各种散射贡献。已经发现,对于有限的横向尺寸,由入射X射线束引起的散射不是SAXS的主要来源。它形成双峰,由于层状叠层之间的相消干涉,在实际散射中未观察到。 van逝波引起的散射是主要来源。它可以形成类似于在实际SAXS测量中观察到的干涉图:小q范围内的Guinier区域,中q范围内的信号区域和高q范围内的Porod区域。据估计,为了避免破坏性干扰,横向尺寸必须大于11μm,这在实际的层状系统中是无法满足的。因此,实际聚合物系统中的SAXS很大程度上是由van逝波引起的散射引起的。在等规聚丙烯的散射中发现了e逝波的存在的证据。这项研究纠正了对聚合物层状系统中SAXS的长期误解。

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