Fourier-transform rheology and printability maps of complex fluids for three-dimensional printing

Abstract

Direct ink writing (DIW) is a three-dimensional (3D) printing technique exploited by researchers working in fields from scaffolds for energy applications to bioprinting. DIW's main strength is that it enables shaping advanced materials, if these materials can be formulated into complex fluids that meet the demands of the printing process. They must be extremely shear thinning soft solids, able to flow through narrow nozzles, recovering their structure upon deposition and retaining the predesigned 3D shape. Formulation design and rheology are critical, but these aspects can be overlooked due to the high specialization required. This work provides insight on the rheology and printability of complex yield-stress fluids through the study of linear and nonlinear behaviors using large-amplitude oscillatory shear rheology. We refine previous protocols and develop tools to understand the behaviors of formulations for DIW. We apply an existing mathematical framework to a library of carbon-based formulations for energy applications. Fourier transform analysis enables quantifying the onset and rising of higher harmonic contributions. Quantitative comparisons between different formulations are established using 3D harmonics maps, stress–strain plots, and material measures of nonlinearities [Fourier and Chebyshev coefficients, elastic moduli (GM′, GL′), and dimensionless index of nonlinearity (S)]. 3D Lissajous plots provide a qualitative alternative to interpretate the yielding transition. We create Ashby-type printability maps to guide formulation design and elucidate that non-printable formulations show distinctive features. This insight on yield-stress fluids for DIW is relevant to other applications and technologies: drilling fluids, gels, colloids, and foods.