Because of their high stiffness in the direction of the tubule axis, carbon nanotubules (CNTs) have also been proposed for use as fibers in the next generation of fiber-matrix composite materials. Sometimes adhesion between the two phases of such composites is enhanced by chemically attaching polymer groups that act as "tethers" to the fibers. It is thought that these chemical attachments break at the fiber wall when the composite is deformed rapidly and disentangle from the surrounding matrix when the composite is deformed slowly. In either case, the attached group is crucial to the dissipation of energy that increases the overall resistance of the composite to failure. Recently, researchers at the University of Kentucky have worked to "decorate" the walls of single-wall CNTs with dichlorocarbene. They are currently working to use standard methods to substitute polymer chains in place of the chlorine atoms. The effects of covalent chemical attachments on the mechanical properties of single wall carbon nanotubules have been modeled using classical molecular dynamics simulations with a well-known many-body, reactive empirical bond-order potential for hydrocarbons. The maximum compressive force (buckling force) for both the functionalized and non-functionalized CNTs were calculated. It was found that the average degradation of the buckling force due to covalent chemical attachments is approximately 15%. New simulation results will be presented where the interaction between carbon nanotubes and various polymeric matrices with and without polymer attachments to the tubule walls are investigated. From these simulations, the quantitative effects of chemical functionalization on fiber-matrix adhesion will be determined.