Non-affine lattice dynamics of disordered solids

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

Unifying model for random matrix theory in arbitrary space dimensions.

A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the eigenvalue spectrum of this model in different limits of space dimension d, and for arbitrary values of the lattice coordination number Z, are shown and discussed. As a function of these two parameters (and their ratio Z/d), the most studied models in random matrix theory (Erdos-Renyi graphs, effective medium, and replicas) can be reproduced in the various limits of block dimensionality d. Remarkably, the Marchenko-Pastur spectral density (which is recovered by replica calculations for the Laplacian matrix) is reproduced exactly in the limit of infinite size of the blocks, or d→∞, which clarifies the physical meaning of space dimension in these models. We feel that the approximate results for d=3 provided by our method may have many potential applications in the future, from the vibrational spectrum of glasses and elastic networks to wave localization, disordered conductors, random resistor networks, and random walks

Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids.

The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios

Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids

The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios

Adsorption Free Energy Predicts Amyloid Protein Nucleation Rates

Primary nucleation is the fundamental event that initiates the conversion of proteins from their normal physiological forms into pathological amyloid aggregates associated with the onset and development of disorders including systemic amyloidosis, as well as the neurodegenerative conditions Alzheimer\u27s and Parkinson\u27s diseases. It has become apparent that the presence of surfaces can dramatically modulate nucleation. However, the underlying physico-chemical parameters governing this process have been challenging to elucidate, with interfaces in some cases having been found to accelerate aggregation, while in others they can inhibit the kinetics of this process. Here, we show through kinetic analysis that for three different fibril-forming proteins, interfaces affect the aggregation reaction mainly through modulating the primary nucleation step. Moreover, we show through direct measurements of the Gibbs free energy of adsorption, combined with theory and coarse-grained computer simulations, that overall nucleation rates are suppressed at high and at low surface interaction strengths, but significantly enhanced at intermediate strengths, and we verify these regimes experimentally. Taken together, these results provide a quantitative description of the fundamental process which triggers amyloid formation and shed light on the key factors that control this process

Ethanol Controls the Self-Assembly and Mesoscopic Properties of Human Insulin Amyloid Spherulites.

Protein self-assembly into amyloid fibrils or highly hierarchical superstructures is closely linked to neurodegenerative pathologies as Alzheimer's and Parkinson's diseases. Moreover, protein assemblies also emerged as building blocks for bioinspired nanostructured materials. In both the above mentioned fields, the main challenge is to control the growth and properties of the final protein structure. This relies on a more fundamental understanding of how interactions between proteins can determine structures and functions of biomolecular aggregates. Here, we identify a striking effect of the hydration of the single human insulin molecule and solvent properties in controlling hydrophobicity/hydrophilicity, structures, and morphologies of a superstructure named spherulite, observed in connection to Alzheimer's disease. Depending on the presence of ethanol, such structures can incorporate fluorescent molecules with different physicochemical features and span a range of mechanical properties and morphologies. A theoretical model providing a thorough comprehension of the experimental data is developed, highlighting a direct connection between the intimate physical protein-protein interactions, the growth, and the properties of the self-assembled superstructures. Our findings indicate structural variability as a general property for amyloid-like aggregates and not limited to fibrils. This knowledge is pivotal not only for developing effective strategies against pathological amyloids but also for providing a platform to design highly tunable biomaterials, alternative to elongated protein fibrils

Self-replication of Aβ₄₂ aggregates occurs on small and isolated fibril sites

Self-replication of amyloid fibrils via secondary nucleation is an intriguing physicochemical phenomenon in which existing fibrils catalyse the formation of their own copies. The molecular events behind this fibril surface-mediated process remain largely inaccessible to current structural and imaging techniques. Using statistical mechanics, computer modelling, and chemical kinetics, we show that the catalytic structure of the fibril surface can be inferred from the aggregation behaviour in the presence and absence of a fibril-binding inhibitor. We apply our approach to the case of Alzheimer’s Aβ₄₂ amyloid fibrils formed in the presence of proSP-C Brichos inhibitors. We find that self-replication of Aβ₄₂ fibrils occurs on small catalytic sites on the fibril surface, which are far apart from each other, and each of which can be covered by a single Brichos inhibitor

Adsorption free energy predicts amyloid protein nucleation rates.

Primary nucleation is the fundamental event that initiates the conversion of proteins from their normal physiological forms into pathological amyloid aggregates associated with the onset and development of disorders including systemic amyloidosis, as well as the neurodegenerative conditions Alzheimer's and Parkinson's diseases. It has become apparent that the presence of surfaces can dramatically modulate nucleation. However, the underlying physicochemical parameters governing this process have been challenging to elucidate, with interfaces in some cases having been found to accelerate aggregation, while in others they can inhibit the kinetics of this process. Here we show through kinetic analysis that for three different fibril-forming proteins, interfaces affect the aggregation reaction mainly through modulating the primary nucleation step. Moreover, we show through direct measurements of the Gibbs free energy of adsorption, combined with theory and coarse-grained computer simulations, that overall nucleation rates are suppressed at high and at low surface interaction strengths but significantly enhanced at intermediate strengths, and we verify these regimes experimentally. Taken together, these results provide a quantitative description of the fundamental process which triggers amyloid formation and shed light on the key factors that control this process