Lamellar peaks widths

There are two widths to the lamellar peak, the axial width in scans parallel to the fiber-axis and the transverse width in scans perpendicular to the fiber-axis. The axial width of the peak in longitudinal scans (Figure 2) is used to evaluate the coherence length or height of the lamellar stack (IJ using the Scherrer equation"... 

The transverse width of the lamellar peak in azimuthal scans (Figure 4) is used to calculate the size of die lamellae in the equatorial plane using the above Scherrer equation. Alternatively, the intensity distribution in Figure 4 can be plotted as a Guinier plot (Figure S), and the slope of this curve is used to evaluate the diameter of the lamellae according to the equation... 

Variations in the Axial Widths of the Lamellar Peak with x... 

If all the lamellar stacks are p fectly oriented parallel to the fiber-axis, then the lamellar peak would be streak or a layer line of constant axial widdL But in a typical SAS pattern, the width of the layer line increases with the distance from the meridian, as shown In Figure 6. Whole body rotation of the lamellar stack (misorientation) causes the width Azj of the layer line to increase with the distance fit)m the meridian. The rate of such increase in the width is determined by the average angle that the lamellar stack makes with the fiber-axis. This orientation angle O) of the lamellar stacks is calculated using the expression... 

Two new parametets for describing the SAS data from semictystalline polymers are introduced. These are the ellipticity of the trace of the lamellar peak-maxima, and the orientation parameter determined from the increase in the longitudinal width of the lamellar peak with the distance from the meridional axis. These two parameters along with Ae lamellar spacing, tilt-angle of the lamellar plane, the diameter and the coherence length of the lamellar stack, and the lamellar intensity completely describe the SAS data from oriented semiciystalline polymers. These parameters can be obtained by fitting the 2-D SAS from uniaxially oriented semicrystalline polymers in elliptical coordinates. 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

In all our linewidth studies the width of the central peak was measured—i.e., the linewidth obeying Equation lib. In Ref. 45 we reported 23Na linewidth studies on a lamellar mesophase containing egg-yolk lecithin. The effect of cholesterol on the linewidth was investigated, and we found that with increasing cholesterol content in the phospholipid bilayers a marked reduction in the linewidth was observed. In accordance with similar investigations for simple soap-alcohol-water lamellar mesophases (42, 43) this is interpreted as a partial release of... 

In the SSL, the structure (Figs. 40,41b) always is characterized by two length scales e.g. in the lamellar structure we have the period of the lamella D, and the width 5 of the interface between the blocks. Of course, the period D experimentally is deduced from the position of the Bragg peaks (observation of higher order Bragg reflections elucidates the type of ordered phase, of course, and the... 

This equation shows that the heights of the successive peaks decrease as n 4. From Equation (5.136) we have already seen that in the ideal lamellar structure the area under the peak varies as n 2. Combination of these two results suggests that the width of the peak increases as n2 in the present variable thickness model. 

Ideal Lamellar System of Two Phases with Variation in the Interlamellar Space Because the autocorrelation part remains the same, in this case the only consequence is an enlargement in the width of the peak due to the closer correlations (Fig. 19.11b). Additionally, the position of the maximum provides the periodicity, which denotes the most probable spacing. 

The distance between the two separated peaks in the 0018 profile for both samples is twice as large as that in the 009 profile, indicating that the same value of half-width can be obtained from each refl hon. For PTeOX-105, the area undo- the higha-angle component (open circles) is smaller than that under the lower-angle component (filled circles), whereas for PTeOX-81, the reverse is the case. Thus, it may be considered that in the PTeOX-105 samjde the amount of lamellar crystallites is larger than that of fibrillar crystallites, and the reverse is so for the PTeQX-81 sample. 

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