This thesis provides a study of different aspects of the mechanical and vibrational properties of disordered and amorphous solids. Resorting to the theoretical framework of non-affine lattice dynamics the attention is focused on the analysis of disordered networks and lattices which serve as tractable model systems for real materials. Firstly, we discuss the static elastic response and the vibrational spectra of defective fcc crystals. The connection to different types of microstructural disorder in the form of bond-depletion and vacancies is described within the context of the inversion symmetry breaking of the local particle configurations. We identify the fluctuations of the local inversion symmetry breaking, which is directly linked to the non-affinity of the disordered solid, as the source of different scalings behaviours of the position of the boson peak. Furthermore, we describe the elastic heterogeneities occurring in a bond-depleted two- dimensional lattice with long-range interactions. The dependence of the concomitant correlations of the local elastic moduli are studied in detail in terms of the interaction range and the degree of disorder. An analytical scaling relation is derived for the radial part of the elastic correlations in the affine limit. Subsequently, we provide an argument for the change of the angular symmetry of the elastic correlation function which was observed in simulations and experiments on glasses and colloids, respectively. Moving to the dynamical behaviour of disordered solids, a framework is developed based on the kernel polynomial method for the approximate computation of the non- affine correlator of displacement fields which is the key requirement to describe the linear viscoelastic response of the system within the quasi-static non-affine formalism. This approach is then extended to the case of multicomponent polymer melts and validated against molecular dynamics simulations at low non-zero temperatures. We also consider the dynamical behaviour of metallic glasses in terms of its shear elasticity and viscosity. A theoretical scheme is suggested which links the repulsive strength of the interatomic potential to the viscoelasticity and fragility in metallic glasses in the quasi-affine limit.

The proton exchange membrane (PEM) is a key component in proton exchange membrane fuel cells (PEMFCs). During standard fuel cell operation, the PEM degrades due to cyclic hygrothermal loads, resulting in performance loss or total failure. Improvement of current PEM materials and development of cheaper, more durable materials is essential to the commercialization of PEMFC technology, which may provide an attractive alternative energy source for transportation. This dissertation investigates a new PEM material which is a blend of sulfonated perfluorocyclobutane (PFCB) and polyvinylidene fluoride (PVDF). Hereafter referred to as PFCB/PVDF, this polymer blend was developed by General Motors Company™ as a potential replacement for the current benchmark PEM, the DuPont™ product Nafion®. The PFCB/PVDF blend is less costly to manufacture than standard PEM materials and investigations into its long-term mechanical durability are ongoing. Specifically, this document discusses the experimental and analytical work performed in the material characterization, constitutive expression development, and implementation of that expression into uniaxial and biaxial finite element geometries. Extension of the model to time-varying temperature and moisture conditions is also explored. The uniaxial finite element model uses a non-linear viscoelastic viscoplastic (NLVE-VP) constitutive expression with parameters determined from uniaxial creep and recovery experiments at a single environmental condition. Validation tests show that this model accurately predicts results from uniaxial tension experiments, such as stress relaxation, force ramp, and multistep creep and recovery, to stresses of 8 MPa and strains approaching 15%, which is the maximum hygrothermal strain expected in an operating fuel cell. The biaxial finite element model combines the NLVE-VP constitutive expression with the geometry of a pressure-loaded blister experiment, which better approximates fuel cell membrane constraints. Results from the biaxial model are compared to experimental results. The model accurately predicts strain in the blister test but predicts stresses that differ from those estimated from blister curvature. Additionally, it is found that both the non-linear viscoelastic and viscoplastic parameters are functions of the operating environment. Future experimental work is needed to characterize that dependence before the constitutive model is used to simulate the response of the PFCB/PVDF blend to fuel cell operating conditions. / Ph. D.

Polypropylene (PP) and ethylene-co-octene copolymer (EOC) blends were prepared at various component ratios and reinforced with silica nanoparticles (SiO2). Strategies to improve filler dispersion involved the grafting of a silane coupling agent on the PP matrix, the addition of a maleated PP (PP-g-MA) as a compatibilizer and the use of hydrophobic silica nanoparticles. These approaches resulted in a fine dispersion of the nanoparticles within the PP phase and induced a reduction of the size of the EOC domains, due to a barrier effect. Tensile and flexural properties were significantly increased, whereas ductility and impact properties were not affected. These enhancements are attributed to the favourable microstructure of the blends, featuring a segregated microstructure, and to the improved interfacial adhesion between the functionalized polymer matrix and the surface of the nanoparticles. The microstructure and rheology of model melt compounded EOC-based nanocomposites were investigated. Functionalization of the polyolefin matrix was accomplished through silane grafting, or addition of a maleated EOC (EOC-g-MA) compatibilizer. Various grades of unmodified SiO2 having different specific surface areas (SSA), as well as a surface-modified grade were added to the EOC matrix at various loadings. The formation of covalent and hydrogen bonds between the silanol groups and the functionalized polymer generated strong polymer/filler (P/F) interactions, resulting in improved filler dispersion. Bound polymer characterization revealed that in the compatibilized materials, the amount of polymer physically attached to the nanoparticles was higher than in the non-compatibilized samples. In the absence of a compatibilizer, larger SiO2 aggregates formed upon increasing SSA because of increased probability of hydrogen bonding between the particles. The increased propensity for aggregation was revealed by time sweeps as well as by the increased strain sensitivity in stress sweeps. On the contrary, the compatibilized composites exhibited a stable response and a higher critical strain for the onset of non-linearity, indicative of stronger adhesion between the fillers and the matrix. Superposition of oscillatory and creep/recovery experiments revealed that the viscoelastic properties in the terminal region were influenced substantially by the state of dispersion of the nanoparticles. In the absence of a compatibilizer, substantial enhancements in the linear viscoelastic (LVE) functions were noted and an increasing SSA resulted in more significant deviations from terminal flow. On the contrary, the SSA of the particles had no effect on the viscoelastic and mechanical properties of the compatibilized composites. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2011-04-18 15:17:52.471

Collagen is the most abundant protein in mammals and has special mechanical behavior that enables it to play an important role in the structural integrity of many tissues, e.g., skin, tendon, bone, cartilage and blood vessels. The mechanical properties of collagen are governed by hierarchical mechanisms in different length-scales from molecule to tissue level. Currently, there is no multi-scale model that can predict the mechanical properties of collagen at macroscopic length scales from the behavior of microstructural elements at smaller length scales. This dissertation aimed at developing a multi-scale model using a bottom-up approach to predict the elastic and viscoelastic behaviors of collagen at length scales spanning from nano to microscale. Creep simulations were performed using steered molecular dynamics (SMD) method on collagen molecules, cross-link, and micro-fibrils with various lengths. A micro-fibril is considered as a combination of two collagen molecules connected by a cross-link. The strain time histories for force levels in the range of 10 to 4000 pN were characterized using quasilinear viscoelastic models. These models were utilized to make a reduced model of a micro-fibril and the reduced models, in turn, were combined to make a model of a fibril up to 300 micrometers in length. The micro-fibril and fibril models were validated with available experimental measurements. Hydrogen bonds rupture and formation of collagen molecule played a central role in its viscoelastic behavior and were used to estimate the creep growth rate. The propagation of force wave in the molecule was shown to be an important factor in providing the time-dependent properties of the fibrils. This propagation was modeled with delay elements and this allowed reducing the micro-fibril model to only three degrees of freedom. In conclusion, the results confirmed that the combination of molecular dynamics simulations and viscoelastic theory could be successfully utilized to investigate the viscoelastic behavior of collagen at small scales. The model reported in this dissertation, lays the groundwork for future studies on collagen, particularly in elucidating how each particular level of hierarchy affects the overall tissue behavior. / Mechanical Engineering