Layer line

In addition to the reciprocal relationship between the helix pitch and layer line spacing, Figure 18.14 illustrates the reciprocal relationship between the orientation of the arms of the cross and the angle of climb of the helix as the helix becomes steeper the arms of the cross become more horizontal. 

Figure 18.14 The diffraction pattern of helices in fiber crystallites can be simulated by the diffraction pattern of a single slit with the shape of a sine curve (representing the projection of a helix). Two such simulations are given in (a) and (b), with the helix shown to the left of its diffraction pattern. The spacing between the layer lines is inversely related to the helix pitch, P and the angle of the cross arms in the diffraction pattern is related to the angle of climb of the helix, 6. The helix in (b) has a smaller pitch and angle of climb than the helix in (a). (Courtesy of W. Fuller.)...

The x-ray diffractograms of those three samples are shown in Fig. 12. The lower pattern corresponds to the quenched sample where only the mesophase is present (the layer line, appearing at lower angles is not shown). The other two diagrams corresponding to the annealed samples present several sharp diffraction peaks, which... 

The cell layer lining blood vessels. It is now well established that endothelial cells not only maintain a non-thrombogenic surface in the blood vessels, but also... 

At one extreme, one has the structural models of perfect crystals, which have long-range positional order for all the atoms (apart thermal motion). A diffraction experiment on a set of such crystals oriented in one direction (corresponding, in most real cases of polymeric materials, to an oriented fiber) would result in a pattern of sharp reflections organized in layer lines. 

In the first case, there is only partial instead of complete long-range three-dimensional order. Fiber spectrum features are diffuse haloes (besides sharp reflections) on the layer lines. 

As an example of the second case, we may have conformationally disordered chains, but long-range order in the positions of the chain axes (condis crystals [5]). Fiber spectrum features are the occurrence of sharp reflections on the equator only and diffuse reflections on the other layer lines. 

Data from oscillation photographs of bixbyite show a to be a multiple of 4.68 A (Table I). The Polanyi layer-line relation applied to photographs with [4 00] as rotation axis showed that this multiple must be 2, giving a unit with... 

These reflections are from the first, second, and third layer lines of the same photograph as that from which the data of Table I were obtained, so that intercomparisons between Tables I and V may be made. 

The third category, shown in Fig. 2d, results when all of the long molecules or microcrystallites are aligned along the fiber axis, but they aggregate with little lateral ordering. This assembly, called an oriented fiber, diffracts to produce a series of layer lines that are perpendicular to the fiber axis. The intensity is nonuni-... 

Fig. 2. (continued)—(d) an aggregate of microcrystallites whose long axes are parallel, but randomly oriented (left), diffracts to produce a series of layer lines (right) and (e) a polycrystalline and preferentially oriented specimen (left) diffracts to give Bragg reflections on layer lines (right). The meridional reflection on the fourth layer line indicates 4-fold helix symmetry. 

Figure 8. (Continued). As described above, the packing of myosin molecules into the thick filament is such that a layer of heads is seen every 14.3 nm, and this reflection is thought to derive from this packing. Off the meridian the 42.9 nm myosin based layer line is shown. This arises from the helical pitch of the thick filament, due to the way in which the myosin molecules pack into the filament. The helical pitch is 42.9 nm. c) Meridional reflections from actin. Actin based layer lines can be seen at 35.5 nm, 5.9 nm and 5.1 nm (1st, 6th, and 7th layer lines)and they all arise from the various helical repeats along the thin filament. Only the 35.5 nm layer line is shown here.The 5.9 nm and 5.1 nm layer lines arise from the monomeric repeat. The 35.5 nm layer line arises from the long pitch helical repeat and is roughly equivalent to seven actin monomers. A meridional spot at 2.8 nm can also be seen, d) The equatorial reflections, 1,0 and 1,1 which arise from the spacings between crystal planes seen in cross section of muscle.

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