On the determination of the crystalline fraction of polyethylenes from X‐ray diffraction

Abstract

It is demonstrated that the various procedures recommended in the literature for the determination of the crystalline fraction in polyethylene specimens by means of X-ray diffraction lead to consistent results if certain errors made by some of the previous authors are avoided.A simple procedure which is not inferior to other more elaborate ones and does not require corrections for LORENTZ factor, polarization or incoherent radiation is presented.It is easily adaptable for routine work.Attention is drawn to the observed close correlation between crystallinity and line width of the crystalline interferences. ZUSAMMENFASSUNG:Es wird gezeigt, dal3 die verschiedenen in der Literatur empfohlenen Verfahren zur Bestimmmg des kristallinen Anteiles in Polyathylenen auf rontgenographischem Wege zu iibereinstimmenden Ergebnissen fiihren, wenn bestimmte Fehler, die von einigen der friiheren Autoren gemacht worden sind, vermieden werden.Ein einfaches Verfahren wird angegeben, das den sonstigen umsttindlicheren nicht unterlegen ist, keine Korrektur fiir LORENTZ-Faktor, Polarisation und inkoherente Strahlung erfordert und sich leicht fiir einen Routinegebrauch anpassen liiBt.Auf die Beobachtung einer engen Korrelation zwischen Kristallinitat und Lmienbreite der kristallinen Interferenzen wird hingewiesen.

Determining the Degree of Crystallinity in Semicrystalline Materials by means of the Rietveld Analysis

“…It was subsequently computerized (and slightly modified) by Vonk (1973). As in previously developed external X-ray powder diffraction methods (see, for example, Hermans & Weidinger, 1961), the Ruland method requires the separation of the scattering belonging to the crystalline peaks, I~; u, from the global background scattering, l~,i, u. In the Vonk version, this separation is performed mathematically with a computer program in which the scattering pattern of the amorphous phase (which is assumed to be available) is suitably scaled and fitted using the appropriate constants, Ci.…”

A fitting method for the determination of crystallinity by means of X-ray diffraction

“…Usually, the separation line underneath the crystalline peaks is established by drawing smooth curves from tail to tail following the general slope of the continuous scattering (Hermans & Weidinger, 1961;Ruland, 1961). Vonk (1973) has computerized a procedure which allows the separation of the background when the scattering from a pure amorphous sample is known: a number of intervals where crystalline peaks are entirely absent are located; in the remaining intervals the shape of the amorphous curve is multiplied by a scaling factor which varies linearly from its value at the beginning of the interval to that at the end.…”

“…The results so obtained for the degree of crystallinity as well as for the disorder factor are compared with the corresponding values obtained by applying the method of Hermans & Weidinger (1961) and of Ruland (1961) in the version computerized by Vonk (1973). Since the methods of both Hermans & Weidinger and Gehrke & Zachmann were developed in transmission geometry, whereas those of Ruland and Vonk were developed in reflection geometry, both diffraction geometries have been tested for all methods.…”

Crystallization of polymers. Part I : Polydispersed polymers quenched from the liquid state

“…The most accurate crystallinity measurement taking into account the lattice imperfections, leads to a accuracy on x of 5 % or somewhat less in certain cases [26]. In samples crystallized from different melt temperature, with the same quenching rate, we assume that the lattice distortions do not change, the measurement of the ratio Ac/ Aa of the crystalline and amorphous area can be measured with a accuracy of 1 % [27]. We [14][15][16].…”