Hierarchical and Fractal Structuring in Polymer Processing

Abstract

The potential of structuring thermoplastic polymers by convection only, using a combination of static mixer elements, which easily produce stratified structures with thousands of layers, and the black box concept that serves to elegantly combine materials in standard co‐extrusion technology is investigated. The aim is to obtain an alternative for routes that try to structure organic matter such as polymers down to submicrometer levels, usually via self‐organization based on phase separation. Structure is characterized by its complexity, here defined by the level of hierarchy. Horizontal stratification, parallel to the surface, is level 0. Vertical stratification connected to horizontal surface layers, is level 1. A series of horizontal stratifications in distinct places vertically connected to the surface layers is level 2. Higher levels of hierarchy finally result in dendritic structures that are fractal. Applications of complex structures with a huge interface and guaranteed cocontinuity throughout the whole cross section of the products are found in, for example, membranes for fuel cells and gas separators, and in miniaturizing electronic and optical devices such as photovoltaic cells.

One‐step creation of hierarchical fractal structures

“…The experimental results obtained in Reference [28] proved that, for non‐Newtonian fluids, a series of mirroring Chen elements gives less optimal interface rotation compared to a series of layering Dentincx elements. Geometry optimization to improve on this aspect would concern the precise corner geometry, as well as the distances between successive rotation elements.…”

“…Feeding the system with more than two layers—see, for example, [ 28 ] —is beneficial in all cases. After exiting a separate feed block of, for example, a symmetric system of nine alternating layers, differences in viscosity and viscoelasticity between the materials forming the layers have been averaged over the channel height.…”

Structuring Hydrogel Cross-Link Density Using Hierarchical Filament 3D Printing

“…When multilayers of these materials are subjected to gradients in the stress, substantial normal stress differences, and abrupt transitions between rotational and extensional flow types, significant distortions arise, and the control and predictability of the structure are lost. In rheologically matched melts, nonaxisymmetric extension engenders elastic instabilities and secondary flows, causing layers to fold, while rotation engenders vorticity which causes layers to coil. , In mismatched melts, these effects are compounded by viscous encapsulation, , which can only be partially overcome by optimizing devices to minimize asymmetry and adding lubricating fluids to promote slip at the wall …”

“…In our geometric approach, hydrogel precursors with different macromer concentrations are fed into custom millifluidic devices. The devices, inspired by some of the geometries used to structure polymeric melts, , advect disparate streams through serpentine splitting, rotation, and recombination elements. In the present work, these elements are used to multiply the incoming 2D concentration field across the cross-sectional area while preserving its relative spacing and orientation.…”

Pea fractionation into functional ingredients : a structural perspective

“…These tools can facilitate the application of lower refined ingredients in foods by providing more insight into the mechanical phenomenon that explain the fraction behaviour. Such repetitive stretching and folding has been demonstrated for polymer melts but also for oil/water emulsions (Hofmann, Bayles, & Vermant, 2021;Schaller, Neerincx, & Meijer, 2017). The application of laminar fractal mixing for food structuring has so far not been discussed.…”