Fractal Structuring in Polymer Processing

Abstract

For a multitude of high‐end applications such as photovoltaics and membranes for fuel cells or gas separation, creating large internal surfaces via fractal structuring during polymer processing can result in unique possibilities for enhancing performance. Structuring is possible even in processing techniques like injection molding. Inspired by microfluidic practice, an optimized splitting and recombining static mixer is realized on the parting surface of a mold. Different geometries are used to multiply, rotate, and add stratified structures. After the obvious structuring of a number of parallel layers, attention is focused on layers perpendicular to the product surface. A combination of the two allows complex hierarchical fractal structures to be obtained. A first demonstration of its feasibility is reported.

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

“…To confirm that flows that add layers orthogonal to existing layers are similarly stable, we selectively dyed the cross-section of extruded gels and imaged them using fluorescent microscopy. Cross sections in Figure d are similar in dimension to those reported to viscoelastic, rheologically matched epoxies, but demonstrate significantly less distortion across the layers . The gradients in the fluorescent cross sections reflect the interdiffusion of PEGDA that occurs while the un-cross-linked streams are in contact during their residence in the device.…”

“…In rheologically matched melts, nonaxisymmetric extension engenders elastic instabilities and secondary flows, causing layers to fold, 34 while rotation engenders vorticity which causes layers to coil. 18,35 In mismatched melts, these effects are compounded by viscous encapsulation, 36,37 which can only be partially overcome by optimizing devices to minimize asymmetry 38 and adding lubricating fluids to promote slip at the wall. 39 Viscoplastic, strongly shear-thinning materials, overcome all these processing bottlenecks by the mere virtue of their rheology.…”

“…Cross sections in Figure 2d are similar in dimension to those reported to viscoelastic, rheologically matched epoxies, but demonstrate significantly less distortion across the layers. 35 The gradients in the fluorescent cross sections reflect the interdiffusion of PEGDA that occurs while the un-cross-linked streams are in contact during their residence in the device. Modulating the total flow rate creates a trade-off: reducing the flow rate minimizes the thickness of the boundary layer at the cost of increased residence time within the device.…”

“…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 …”

One‐step creation of hierarchical fractal structures

“…These structures can be easily produced on two advancing surfaces of any device and on any scale, from microfluidic scales [ 13 ] to a two‐component injection molding machine. [ 29 ] Extension to create other fractal hierarchical structures follows from the above presented results. Further examples of how dies that yield similar structures can be designed and realized, once the operator sequence is known, are presented in Appendix D in Supporting Information.…”