Butterfly pattern

Rabin Y, Bruinsma R (1992) Europhys Lett 20 79. In their scheme the field c, which is coupled to V u via Eq. (4.53), is arbitrary. They assumed that c may be regarded as the deviation 6 of the polymer volume fraction itself. Then Sip and V u are weakly coupled", whereas they are identical in our scheme. Thus a butterfly pattern appears in the form of Eq. (4.56) in their... 

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. 

Distinct butterfly patterns have also been observed when inhomogeneous gels are deformed by uniaxial deformation. The length scales in such systems, however, are usually much smaller that those encountered for polymer solutions subject to flow, and small-angle... 

Lorenz discovered that a wonderful structure emerges if the solution is visualized as a trajectory in phase space. For instance, when x(t) is plotted against z(t), a butterfly pattern appears (Figure 9.3.2). 

Figure 9. Microcavitation in a "butterfly" pattern formed in Epon 828/CTPnBA cured by DMHDA in the two step procedure.

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. 

A clandestinely produced ecstasy tablet. The butterfly pattern was likely created with a tablet press as described here.. Image courtesy of Aaron Brudenell, Tucson Police Department Laboratory. 

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. 

Hre butterfly patterns were observed at various tempera-mres and concentrations and for various solvents such as DOP, tydohexane, and diethyl malonate, which are theta solvents for PS at 35°C, as wdl as dibutyl phthalate and tricresyl phosphate, which are good solvents for PS. The patterns were also observed for semidilute solutions of polyethylene with paraflin as the solvent (athermal solution) and for sheared colloidal srrspensions. They are thus quite general for sheared dynamically asymmetric systems. The butterfly pattern was also formd for PS/PVME mixtures by Mani et and Gerard et and for other polymer mixtures. ... 

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