Lamella thickness distribution

This is the expression giving the scattering intensity I q) in terms of the lamellae thickness distributions. The above derivation is based on the one given by Hosemann and Bagchi.35... 

To make the discussion more concrete, we now assume the lamella thickness distributions to be Gaussian, so that... 

Fig. 29 Lamella thickness distribution of different TREF fractions of copolymers obtained from different catalysts (Phillips, Cat-C2, and S-2 catalysts)...

Two techniques have been used a) the simple measurement of the sample length and b) the DSC method for determination of melting behaviour and calculation of the lamellae thickness distribution (LTD) as a measure of the macromolecular structure. The details on the technique and the calculation are given elsewhere (1)... 

Figure 1 SAXS-determined lamella thickness distribution for iPP nucleated with EOl (a-phase) and E3B (p-phase) as a function of the nucleating agent content.

The average lamellae thickness distribution may be described quantitatively by small angle X-ray diffraction (SAXS), or indirectly by differential scanning calorimetry (DSC). According to the Bragg relation, the SAXS measurements permit the determination of the structure units with dimension of some hundreds angstrom (lnm = lO m = lOA). The... 

Figure 3.7 Lamella thickness distribution of different fractions of (A) PE-1 and (B) PE-2.

A modd-free analysis approach of the stacking statistics of tmdecorated lamdlar two-phase systems is given by Ruland s interface distribution function (IDF), which consists of a superposition of first- and higher-order (i.e., spanning multiple lamellae) lamella thickness distributions. Since the IDF is equivalent to a second-order derivative of a ID autoconelation function, the requirements for the data quality are quite high for this method to produce significant results. 

One of the benefits of direct TEM observation is its possible accounting of the thickness of the crystalline and amorphous layers separately. The distributions of thickness for amorphous and crystalline layers are plotted in Figure 8.40 Both crystalline and amorphous thickness distribution curves have their individual maxima, whose positions are independent of prior polymer concentration. The peak top is always located at 9 nm for crystalline layer and 1.5 nm for the amorphous one. Their SAXS profiles are compared in Figure 9.40 The long periods lie in the constant position at around 0.75°, which corresponds to 11.5 nm thickness, independent of prior polymer concentration. As the lamellar thickness obtained by SAXS is the sum of thicknesses of the crystalline and amorphous phases, the average thickness of lamellae measured by TEM coincides with that by SAXS. Therefore, the morphologies seem to be independent of polymer concentration. 

Within a BPE with a distribution of branches, there will be a distribution of lamella thickness. This will result in a broad melting range. BPE with a bimodal distribution of branches will have a bimodal distribution of lamella thickness and a corresponding melting temperature range. When two polyethylenes are blended, assuming they are miscible, they will cocrystallize only where they have common MSL. Some molecular segments in each BPE will crystallize independently of... 

Note The equilibrium melting temperature (tJJ,) of copolymers depends on the molecular weight, sequence distribution and counit content. The T, value is determined by two commonly used techniques the Hoffman-Weeks plot and the Thompson-Gibbs plot. Tire application of the Hoffman-Weeks method to determine the tJ, of a copolymer is unreliable (see reference 43). The more reliable method is to use the Tliompson-Gibbs relationship of Tm as a function of lamellar thickness, provided a large range of lamella thickness can be obtained. Considerable disagreement exists between different authors on the exact value of transition that can be identified for fhe copolymers. Consequently, values tabulated in this table must be used cautiously. See references (39, 43, and 44) for detailed discussions. 

DSC is another tool giving access to the lamellar thickness distribution. Based on the form of the DSC melting curve, the average distribution of the lamellae thickness may be determined. This procedure is based on the assumption that the melting temperature is related to the thickness L of a crystalline lamella, by the Thomson-Gibbs relationship [8] ... 

Keywords chain fold crystal growth, lamella, lamellar thickness distribution, nucleation, secondary crystallization, etching, lamellae detection, small angle X-ray scattering (SAXS), differential scanning calorimetry (DSC), optical microscopy, spherulite, morphology, electron microscopy. 

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