The evaluation of the small-angle scattering of lamellar two-phase systems by means of interface distribution functions

Ruland, W.

doi:10.1007/bf01536457

Cited by 330 publications

(271 citation statements)

References 22 publications

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“…Here λ is the wavelength of radiation, and 2θ is the scattering angle. In the historical context, the CDF is an extension to Ruland's interface distribution function (IDF) 41 to the multidimensional case or, in a different view, the Laplacian of Vonk's multidimensional correlation function. Further to the right, the top row shows the data recorded during the dynamic experiment.…”

Section: Saxs Data Evaluationmentioning

confidence: 99%

Tensile tests of polypropylene monitored by SAXS. Comparing the stretch‐hold technique to the dynamic technique

Stribeck

Nöchel

Funari³

et al. 2008

J Polym Sci B Polym Phys

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Advanced instrumentation at synchrotron beamlines facilitates considerable reduction of the exposure required for the recording of low-noise small-angle X-ray scattering (SAXS) patterns. Concerning the monitoring of tensile tests on polymer materials by SAXS means that change-over from the stretch-hold technique to more practical dynamic straining is possible, although the strain rate is still by a factor of 100 lower than that relevant in industry and service. As hard-elastic polypropylene (PP) is tested, considerably different scattering patterns are recorded after switching to the dynamic technique. Even though during exposure the elongation is no longer constant when applying the dynamic technique, the images collected in stretch-hold technique appear much more blurred. The observed immediate relaxation of nanostructure induced by stopping the extensometer is analyzed by means of the multidimensional chord distribution function (CDF): The extension of the crystalline lamellae is increasing. Their thicknesses are becoming non-uniform. The range of order is shortening. Cross-hatched lamellae are formed.

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Section: Saxs Data Evaluationmentioning

confidence: 99%

Tensile tests of polypropylene monitored by SAXS. Comparing the stretch‐hold technique to the dynamic technique

Stribeck

Nöchel

Funari³

et al. 2008

J Polym Sci B Polym Phys

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“…Kxatky camera data were quantitatively evaluated using the method of interface distribution analysis (Ruland, 1977) and a generalized model for stacking statistics (Stribeck, 1993). After subtraction of the apparent background the measured intensity in absolute units, l~(s)/V, is transformed into an 'interference function', Gid(S), of the ideal two-phase system…”

Section: Evaluation Of Discrete Scattering Neglecting Void Scatteringmentioning

confidence: 99%

Studying the Microstructure of Unaged and Aged PVDF by Small- and Wide-Angle X-ray Scattering

Stribeck¹,

Buchner²

1997

J Appl Cryst

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A layer from plasticized poly(vinylidene fluoride) (PVDF) was aged by exposing one of its faces to an aggressive fluid at elevated temperature and pressure. From visual inspection the aged material appeared not to be homogeneous. Therefore, samples from three distinguishable regions were compared with a sample cut from the virgin material by studying their small-and wide-angle X-ray scattering (SAXS and WAXS). The results show that plasticizer has vanished from the aged material, the crystalline layer thickness distribution has narrowed, amorphous lamellae are collapsed and voids have been created. Within the aged material the number of voids varies: there are more at the inner surface and fewer at the outer surface beneath the rods of a supporting metal grid. Based on the results of this study and theoretical considerations, a method for the quantitative description of the ageing process is proposed, which only requires a simple kind of SAXS measurement.

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“…The Lorentz-corrected SAXS profile can be analyzed by onedimensional correlation function analysis (Goderis et al, 1999;Lee et al, , 2003Strobl & Schneider, 1980;Vonk & Kortleve, 1967) and/ or interface distribution function analysis (Ruland, 1977;Albrecht & Strobl, 1996;Verma et al, 1996;Santa Cruz et al, 1991;Xia et al, 2001) in order to determine the morphological parameters. Both of these approaches were considered for analyzing the SAXS data of our study.…”

Section: Resultsmentioning

confidence: 99%

Synchrotron X-ray scattering studies on the structural evolution of microbial poly(3-hydroxybutyrate)

Heo¹,

Yoon²,

Jin³

et al. 2007

J Appl Cryst

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The crystallization behavior of microbially synthesized poly(3-hydroxybutyrate) was studied in detail using time-resolved small-angle X-ray scattering. This polyester was found to undergo primary crystallization as well as secondary crystallization. In the primary crystallization, the thicknesses of the lamellar crystals were sensitive to the crystallization temperature, but no thickening was observed throughout the entire crystallization at a given temperature. The thickness of the lamellar crystals in the polyester was always larger than that of the amorphous layers. Secondary crystallization favorably occurred during the later stage of isothermal crystallization in competition with the continuous primary crystallization, forming secondary crystals in amorphous regions, in particular in the amorphous layers between the primarily formed lamellar crystal stacks. Compared to the primarily formed lamellar crystals, the secondary crystals had short-range-ordered structures of smaller size, a broader size distribution, and a lower electron density.

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The evaluation of the small-angle scattering of lamellar two-phase systems by means of interface distribution functions

Cited by 330 publications

References 22 publications

Tensile tests of polypropylene monitored by SAXS. Comparing the stretch‐hold technique to the dynamic technique

Tensile tests of polypropylene monitored by SAXS. Comparing the stretch‐hold technique to the dynamic technique

Studying the Microstructure of Unaged and Aged PVDF by Small- and Wide-Angle X-ray Scattering

Synchrotron X-ray scattering studies on the structural evolution of microbial poly(3-hydroxybutyrate)

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