Scattering butterfly” pattern

This simple model predicts that the structure factor will develop a butterfly pattern and grow along an axis that is at 45° with respect to the flow direction, which is parallel to the principal axis of strain in this flow. Since the structure factor is the Fourier transform of the pattern of concentration fluctuations causing the scattering, the model predicts an enhancement of fluctuations perpendicular to the principal axis of strain. 

Step J At the onset of the simple shear flow, the entire gap becomes turbid (photo 2). The maximum of scattered intensity is reached when the overshoot in cr. An, and X occurs. The observed turbidity is then supposed to result from the orientation and the stretching of the micellar network [144,177,191,194], generating concentration fluctuations along the flow direction [257] as suggested by butterfly patterns observed using two-dimensional SALS experiments under shear [157,194], At this time, all the new phase is nucleated but not arranged into a macroscopic band. 

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. 

An alternative explanation of the observed turbidity in PS/DOP solutions has recently been suggested simultaneously by Helfand and Fredrickson [92] and Onuki [93] and argues that the application of flow actually induces enhanced concentration fluctuations, as derived in section 7.1.7. This approach leads to an explicit prediction of the structure factor, once the constitutive equation for the liquid is selected. Complex, butterfly-shaped scattering patterns are predicted, with the wings of the butterfly oriented parallel to the principal strain axes in the flow. Since the structure factor is the Fourier transform of the autocorrelation function of concentration fluctuations, this suggests that the fluctuations grow along directions perpendicular to these axes. 

T. Hashimoto and T. Kume, Butterfly light scattering pattern in shear-enhanced concentration fluctuations in polymer solutions and anomaly at higher shear rates, J. Phys. Soc. Japan, 61, 1839 (1992). 

It has to be noticed that due to the rather short relaxation times used for blends B 20 and B 60, no lozenge or butterfly scattering patterns [29] were observed for our experiments. 

In the SAXS analysis, the flame-like shape is obtained due to the scattering pattern obtained from nanovoids and butterfly shape is originated from scattering of fillers. Nano voids are initiated at a small strain range and grow perpendicular to the stretching direction as the strain attained a higher value. ... 

Wang W, Murthy NS, Grubb DT. Butterfly smaU-angle X-ray scattering patterns in semicrystaUine polymers are double-elliptical. Polymer 2007 48 3393-3399. 

Hrese shear-enhanced concentration fluauations give rise to strong scattered intensity along the x-axis but not much along the z-axis, giving rise to the butterfly-type anisotropic scattering pattern as shown in Figure 15(d) and the contrast... 

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