Polarized small-angle light scattering from gels estimated in terms of a statistical approach

Abstract

To analyze polarized light scattering patterns from gels, an approach is proposed to calculate the scattered intensity. In the proposed model system, difference between polar angles of the principal axes of the and elements, which were defined with respect to the axis along the distance between two elements, was given as a correlation of the distance between the two elements. Furthermore, the azimuthal angle, which makes a projection of the principal axis onto a plane perpendicular to the principal axis of the element, was also given as a correlation of the distance between the two elements. The theoretical calculation was carried out for the scattered intensity under Hv and Vv polarization conditions. The general equations proposed for Hv and Vv scattering were based on a statistical approach for polarized light scattering system. The calculated pattern under the Hv polarization condition showed an X-type pattern and was in good agreement with the pattern observed from polymer gels prepared by quenching their solutions to the desired temperatures.

Gelation mechanism of ultra-high-molecular-weight polyethylene (UHMWPE) chains in dispersion solutions containing multiwall carbon nanotubes (MWNTs) analyzed in terms of liquid-liquid phase separation

“…In comparison with the previous results [13][14][15][16], the growth rate of concentration fluctuation R(q) for neat UHMWPE solution became higher, as the concentration increased. This means that R(q) is not closely related to viscosity of the solution but is associated with the coagulation speed of UHMWPE chains to form gels.…”

“…The Hv scattering mode is different from the mode under the gelation process of agarose [14,15], and PVA [11] with a perfectly dark POM photograph. In comparison with the POM photos in Fig.…”

“…Since then, more detailed analysis has been reported for several kinds of polymer. By using successful analysis of the linear theory of spinodal decomposition by Cahn [9,10], Matsuo et al extended to some crystalline polymer solutions such as PVA [11,12], polypropylene [13], agarose [14,15], and polyethylene [16] in order to investigate whether the gelation by the quenching is attributed to the phase separation of solution by the concentration fluctuation.…”

“…On the basis of a series of established results [11][12][13][14][15][16], this paper deals with the admixed effect of multiwall carbon nanotubes (MWNTs) on the gelation/crystallization mechanism of UHMWPE solutions. This is very important to make clear the evidence that well-blended UHMWPE-MWNT composites prepared by gelation/crystallization provide characteristics of high modulus and high electric conductivity.…”

Understandable Unified Description about Diffraction and Scattering of X‐Ray and Visible Light Beams from Soft Matters in Terms of Educational Aspects

“…When there exist many small assemblies with ordered chain arrangement as a function of distance between their chains in polymer film or gel, each assembly can be considered as optical elements, In such a case, H v scattering pattern becomes very weak and the pattern could not be observed on the photo screen of frosted glass (as shown in Figure (a)), since the very weak light scattered from the gels could not pass through the analyzer. The pattern was observed on the sample surface by the reflection from the analyzer, and then photographs were taken using a commercial camera, as shown in Figure (b).…”