Reports: AC7 47321-AC7: Computational and Topological Modeling of Mesophase Carbon Composites

Alejandro Rey, McGill University

Carbon-carbon (c/c) composites are multifunctional structural materials that find wide range of applications in transportations, microelectronics, and aerospace sectors. c/c composites based on carbonaceous mesophase (CM) matrices and carbon fibres are obtain by flowing the nematic CM into an array of carbon fibres. Since nematic liquid crystal with embedded second phases invariably result in the nucleation of topological defects in the mesophase matrix, the c/c structure-material properties relations need to be based on how defects form and organize. Texture generation in CMs is well described by liquid crystal surface science, defect physics and rheology. The path to the ultimate understanding of texturing processes in c/c composites builds on theory and simulation of: (i) LC coating fibre flow, (ii) LC fibre wetting models, (iii) wetting properties of fibre bundles, (iv) geometric optimization of fibre cross-sectional shape, (v) mesophase mixtures. Objectives (i-iii) were completed in the first part of the grant. In particular 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 .The fourth objective seeks to elucidate the role fibre geometry on texturing . It is well known that CM pitches undergo structuring when they flow through square screens and meshes, leaving behind long lived disclination lattices.

Faceted particles, inclusions, and fibres also have the ability to inject disclinations in a controlled fashion. In contrast to circular fibres. for faceted particles, edges also contribute to defect emission and absorption. Texturing due to single faceted particle has been characterized in this grant period. It is found that defects in an aligned nematic mesophase with homeotropic anchoring surrounding a facetted particle include bulk +1/2 disclinations, surface corner disclinations, and disclination strings that join adjoining vertices.

The phase diagram of a typical single faceted particle in terms of temperature as a function of particle size consist of : (I) string defect mode (small particles or large temperatures) (II) mixed surface defect mode ( intermediate sized particles and lower temperature) (III) surface-bulk defect mode ( larger particles and lower temperatures). It is found that for increasing the temperature for a sufficiently large facetted particle, the surface-bulk defect mode is unstable to bulk defect adsorption into the vertices of the particle resulting in the mixed surface defect mode where the charges in the two pair of corners are different. In the mixed surface mode there are no bulk defects, a situation not possible in circular fibers. Further increase in temperature destabilizes the surface defect mode and the string mode emerges, in which a disclination loop joins two adjoining vertices. Corners joined by disclinations form a new mechanisms to couple facetted particles together into strings and rings.

This novel mechanism of string particle formation has been predicted by the Landau de Gennes model. Power law expressions that fit the numerical results provide power correlations to design new textures based on particle faceting. Emission of defects from surfaces and interfaces is a classical mechanism in materials science, and the present work shows another example of this generic behaviour. Adsorption of defects by corners may serve to control the strength of c/c composites, which is affected by the disclination content of the matrix. Since real carbonaceous mesophases from petroleum pitches are polydispersed , predictions from single species model need to be refined. In this work we developed and solved a Maier Saupe model for binary carbonaceous mesophase mixtures characterized by concentration, molecular weight asymmetry, and interaction potential.

Under strong interaction eutectic behaviour arises, indicating the possibility of processing c/c at lower temperatures. The eutectic concentration correspond to a pure species behaviour and the two LCs behaves like a single species. Moving away from the eutectic concentration gives a behaviour that follows the dominant-slaved model. A close form relation between molecular weight asymmetry and molecular interaction indicates the possibility of eutectic behaviour. Examining an experimental phase diagram in conjunction with the found relation allows for the direct calculation of the interaction parameter, which is otherwise difficult to do. By increasing the temperature in a binary mixture of a low and high molecular weight components, it is found that molecular interaction inhibits randomization of the low mass species , which remains in a frustrated nematic state. This frustration is the source of orientation states when subjecting the mixture to external extensional flows.

Carbonaceous mesophases under extensional flow give rise to biaxial ordering below the clearing temperature and oblate uniaxial paranematic ordering above the clearing temperature. These responses form the basis of carbon fibre spinning of petroleum pitches. When introducing a lower molecular weight component, frustration and interaction leads to modification of this standard picture , and the slaved low molar mass species adopts uniaxial states that created new fibre texture morphologies. Theoretical x-ray diffraction and heat capacity models were developed and implemented to verify predictions. Combining geometric facetted fibres with tailored mesophase mixtures has been shown to lead to richer texturing mechanisms of practical utility to processing carbonaceous mesophase petroleum pitches into high performance composites.

 
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