Lamellar reflection

Generally, lipids forming lamellar phase by themselves, form lamellar lipoplexes in most of these cases, lipids forming Hn phase by themselves tend to form Hn phase lipoplexes. Notable exceptions to this rule are the lipids forming cubic phase. Their lipoplexes do not retain the cubic symmetry and form either lamellar or inverted hexagonal phase [20, 24], The lamellar repeat period of the lipoplexes is typically 1.5 nm higher than that of the pure lipid phases, as a result of DNA intercalation between the lipid bilayers. In addition to the sharp lamellar reflections, a low-intensity diffuse peak is also present in the diffraction patterns (Fig. 23a) [81]. This peak has been ascribed to the in-plane positional correlation of the DNA strands arranged between the lipid lamellae [19, 63, 64, 82], Its position is dependent on the lipid-DNA ratio. The presence of DNA between the bilayers has been verified by the electron density profiles of the lipoplexes [16, 62-64] (Fig. 23b). 

DNA arranges into rectangular superlattice in the low-temperature gel phase of saturated cationic lipids [83, 84]. This is evidenced by two or three diffuse reflections in addition to the set of lamellar reflections these are attributed to DNA ordering both within the layer and across the lipid bilayers, from one DNA layer to another. These reflections index on a centered rectangular lattice. Noteworthy, DNA does not affect the gel-liquid crystalline transition temperatures of the lipoplexes [16, 19, 84]. This transition is associated with loss of the DNA inter-lamellar correlation. 

Fig.9. Scattering patterns obtained for a PE-PVCH diblock (Mn=15 kg mol 1,/PE=0.52) at room temperature [ 17]. a SAXS pattern. The sharp first-order lamellar reflection is at q = 0.035 A"1 b WAXS pattern. Four 110 reflections are apparent at 20(CuKa)=2r, and two equatorial 200 reflections at 20(CuKa)=24°. The X-ray beam was incident perpendicular to the shear direction and to the lamellar normal (i.e. along the perpendicular direction in Fig. 10)...

Fig. 5. Progress of the pressure-induced L. /L phase transition in hydrated phosphatidyiethanolamine monitored by time-resolved X-ray diffraction. Included in the figure is the changing scattered X-ray intensity in the (001) lamellar reflection, pressure and in-sample temperature following a 9.64 MPa (96.4 atm, 1400 psi) pressure-jump applied in the load and unloading directions. The data clearly illustrate a recurring limitation in many of these measurements, namely, the control of the transition by heat flux into and out of the sample. This is shown in the load curve. However, heat flow need not always be a limitation as is evident in the unload curve. (Unpublished observations, M. Caf-frey and A. Mencke)...

A) Small-angle X-ray diffraction intensity contour map of first-order and second-order lamellar reflections observed on heating fully hydrated dipahnitoylphosphatidycholine. (B)... 

The lamellar reflections in small-angle scattering patterns from polymer fibers are often spread onto a curve symmetrical about the fiber axis. These are usually referred to as two-or four-point patterns, the latter sometimes resembling the butterfly pattern frequently found in light scattering. We recently showed that these 2-D patterns could be best analyzed if we describe die intensity distribution in elliptical coordinates because the intensity maxima of the lamellar reflections from oriented polymers fall on an elliptical curve. We now present new analysis to support this assertion. We will also discuss die physical basis for some of the features in the SAXS pattern in terms of misorientation of the lamellar stacks, deformation of the lamellae, and possible correlation between the lamellar spacing and the orientation of the lamellae. 

The SAXS pattern from the fiber used to illustrate the analyses here is shown in Figure 1. The two features obvious in the data are the lamellar reflections and the equatorial streak. Less obvious is an interfibrillar interference peak along the equator at about 50 A. We will here focus only on the lamellar reflections. The various parameters determined by analyzing the data in Figure 1 are listed in Table 1 and are further elaborated below. 

Table I. Characteristics that describe the lamellar reflections (Figures 2-8)...

A longitudinal slice (i.e., parallel to the fiber axis z-axis) through the lamellar reflections showing the lamellar peaks. 

Azimuthal scan (slice parallel to the equatorial plane x-axis) through the lamellar reflections for calculating the tilt-angle of the lamellar planes. 

The lamellar reflections are not flat, but are curved i.e., there is a continuous shift in the z-position of the maxima (z ) in the lamellar peaks as a function of x (Figure 1) Because of this curvature, the two-dimensional (2-D) data could not be fitted in Cartesian coordinates. But they are not curved enough to be a circle, hence the polar coordinates ordinarily used in analyzing the wide-angle x-ray diffraction patterns cannot be used either. It appears that the description in elliptical coordinates provides the best fit to the data. This feature of the scattering curve will be analyzed in detail in this paper. 

Guinier plot of the intensity of the lamellar reflection measured as function of x. 12.5... 

Variations in the axial-width of the lamellar reflections with x. 

The parameters in Table I fully account for the various features of the lamellar reflections. Many of these have been used in the past. We have introduced two additional parameters, misorientation of the lamellar stacks P and ellipticity e. These parameters can be derived from a least-squares fit to 2-D data, which is best carried out in elliptical coordinates. The ellipticity is clearly seen in the vs. tan < (Figure 8). Brandt and Ruland have found a similar characteristics in their SAXS pattern from deformed microdomain structures of block copolymers. As we pointed out in our earlier publication, a wide variety of SAS patterns found in the literature can be simulated in elliptical coordinates. 

Lamellar structures or domains in oriented samples Lamellar or domain spacing Lamellar or domain thickness and diameter Tilt angle of the lamellae Misorientation Position of the interference peak along the meridian or the minor axis of the elliptical trajectory of the lamellar reflection Extent of the reflection in meridional and equatorial directions Angular separation of the lamellar reflections across the meridian in 4-point patterns Variation in the meridional width with distance from the meridional axis... 

FIG. 4 Lamellar reflections in the XRD spectra of HDTABr/n-pentanol/water system before and after addition of Na-montmorillonite. (IX amount of surfactant corresponding to the cec of the montmorillonite 3. IX, 4.3X, 6.5X amount of surfactant corresponding to 3.1, 4.3, 6.5 times the value of cec. The basal distances are denoted in the figure.)... 

FIG. 6 Lamellar reflections of HDTABr/w-pentanol/water and HDTABr/n-pentanol/ silver nanosol systems. (The basal distances are denoted in the figure.)... 

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