Reports: AC7
47321-AC7 Computational and Topological Modeling of Mesophase Carbon Composites
Carbonaceous mesophases (CMs) based on petroleum and synthetic pitches are discotic nematic liquid crystals used in the manufacture of high performance carbon fiber-carbon (C/C) composites. The structure underlying their high performance is determined by the texture within the carbonaceous mesophase matrix, including the orientation , density and type of topological defects, and fiber-matrix interfacial structure.
Understanding the principles of texture generation in CM matrices due to the presence of the embedded fibers and processing flows is essential in developing science-based manufacturing processes. Texture generation in CMs is well described by liquid crystal surface science, defect physics and rheology. Furthermore, under strong fiber-matrix interface interaction, experiments show that texturing results from the propagation of the embedded fibers’ curvature. Thus, topological methods are also appropriate tools to characterize texturing. Since processing includes mesophase injection flow along the fibers, flow-induced texturing is another critical process. The path to the ultimate understanding and control of texturing processes in C/C composites builds on theory and simulation of: (i) liquid crystal coating fiber flow and injection flow, (ii) liquid crystal fiber wetting models, and (iii) wetting properties of fiber bundles, performed in the previous period of this grant. (i) Theoretical modeling of fiber coating flows based on nematodynamics was performed taking into account the complex geometry of the process and the predictions were integrated with the experimental work of Professor Srinivasarao at the Georgia Institute of Technology.
The experimental results on forced wetting of a liquid crystal( in the isotropic and nematic states) on a polymer fiber under partial wetting conditions revealed that the coating thickness h scales with the capillary number as h ~ Can, with n=0.94 for the nematic state and n=2/3 for the isotropic state. Theory revealed that the scaling renormalization due to liquid crystallinity (n=2/3(isotropic) à n=0.94(nematic) ) is due to interaction between the coating geometry and the viscous anisotropy of the liquid crystal, such that extensional deformation produce shear stresses and shear deformation produce extensional stresses. The theory, in perfect agreement with experiments, predicts that due to this coupling, the power law exponent “n” must be equal to one. (ii) The understanding of anchoring at the mesophase-carbon fiber interface is crucial to the interfacial processes that control texturing as well as adhesion in the post processing stage and is the starting point to describe the mechanics of liquid crystal films on solid substrates. In this project the multiscale Landau-de Gennes equations for nematic liquid crystals are used to describe typical thin film microstructures. This research developed a generalized film tension equation, in terms of interfacial, anchoring, ordering, and gradient energies. Wetting properties of flat thin films were established through the formulation of a generalized model that relates the film spreading parameter to the anchoring and gradient energies. The film model provides quantitative rules to classify them into homogeneous and heterogeneous. Homogeneous thin films of the order a few nanometers are predicted to be organized in a biaxial nematic state across the film. Heterogeneous thick films due to different surface anchoring of the order of 50 nm exhibit orientation gradients. Systematic use of nematostatics leads to a generalized film tension expression and to wetting thresholds. Under complete wetting liquid crystal films of different thicknesses may co-exist since gradient elasticity, surface anchoring energy, and bulk order energy can provide the underlying required constant film tension. The key finding is that orientation gradients in a thick film generates a film tension that can be achieved in a thinner film by anchoring energy and biaxial nematic ordering. These results can be leveraged to improve adhesion between the fiber and the matrix. (iii) Since C/C composites consists of fiber bundles, the wetting properties of the entire bundle has to be characterized. The ability of isotropic liquids to wet a substrate is a function of geometry and curvature, and generally wettability is easiest for fiber bundles and hardest for single fibers, with flat films occupying the intermediate state. The key reason for the wettability of fiber bundles is that the spreading parameter of a fiber bundle of radius R is always negative since wetting always decreases the free energy by a factor of R-nf rf <0, where nf is the number of fibers of radius rf.
The motivation of this research is to establish whether mesophases follow the same geometry-dependent wettability sequence as isotropic liquids. This research developed a model based on the Landau-de Gennes (LdG) liquid crystal theory in conjunction with topological rules for defect formation, that leads to carbonaceous mesophases’ wetting thresholds of carbon sheets, fibers, and fiber bundles. It is found that for typical material properties and fiber radii, from nano to micron ranges, the ability of carbonaceous mesophases to wet carbon substrates decreases from fiber bundles to sheets to single fibers. The critical Harking spreading parameter or wetting threshold for each geometry is expressed in terms of the isotropic liquid result times a resistance factor that encapsulates the resistance of LC gradient elasticity to wetting. It is found that the resistance factor is close to one for both fiber bundles and single fibers and hence the isotropic fluid rules should be reliable when considering mesophases.
