Anomalous dynamics of interstitial dopants in soft crystals

The dynamics of interstitial dopants governs the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically-stabilised BCC crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localised and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: i) the instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and ii) elastic interactions cause strong dopant-dopant interactions even at low doping fractions. These results illustrate how describing non-classical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopant-dopant interactions into account.Comment: 16 pages, 14 figures. Includes Supplementary Informatio

Stress management in composite biopolymer networks

Living tissues show an extraordinary adaptiveness to strain, which is crucial for their proper biological functioning. The physical origin of this mechanical behaviour has been widely investigated using reconstituted networks of collagen fibres, the principal load-bearing component of tissues. However, collagen fibres in tissues are embedded in a soft hydrated polysaccharide matrix which generates substantial internal stresses whose effect on tissue mechanics is unknown. Here, by combining mechanical measurements and computer simulations, we show that networks composed of collagen fibres and a hyaluronan matrix exhibit synergistic mechanics characterized by an enhanced stiffness and delayed strain-stiffening. We demonstrate that the polysaccharide matrix has a dual effect on the composite response involving both internal stress and elastic reinforcement. Our findings elucidate how tissues can tune their strain-sensitivity over a wide range and provide a novel design principle for synthetic materials with programmable mechanical properties

Microscopic insights into the failure of elastic double networks

The toughness of a polymer material can increase significantly if two networks are combined into one material. This toughening effect is a consequence of a transition from a brittle to a ductile failure response. Although this transition and the accompanying toughening effect have been demonstrated in hydrogels first, the concept has been proven effective in elastomers and in macroscopic composites as well. This suggests that the transition is not caused by a specific molecular architecture, but rather by a general physical principle related to the mechanical interplay between two interpenetrating networks. Here we employ theory and computer simulations, inspired by this general principle, to investigate how disorder controls the brittle-to-ductile transition both at the macroscopic and the microscopic level. A random spring network model featuring two different spring types, enables us to study the joined effect of initial disorder and network-induced stress heterogeneity on this transition. We reveal that a mechanical force balance gives a good description of the brittle-to-ductile transition. In addition, the inclusion of disorder in the spring model predicts four different failure regimes along the brittle-to-ductile response in agreement with experimental findings. Finally, we show that the network structure can result in stress concentration, diffuse damage and loss of percolation depending on the failure regime. This work thus provides a framework for the design and optimization of double network materials and underlines the importance of network structure in the toughness of polymer materials.Comment: main text: 18 pages, 9 figures. Supplemental material: 5 pages, 6 figure

Crosslinker mobility governs fracture behavior of catch-bonded networks

While most chemical bonds weaken under the action of mechanical force (called slip bond behavior), nature has developed bonds that do the opposite: their lifetime increases as force is applied. While such catch bonds have been studied quite extensively at the single molecule level and in adhesive contacts, recent work has shown that they are also abundantly present as crosslinkers in the actin cytoskeleton. However, their role and the mechanism by which they operate in these networks have remained unclear. Here, we present computer simulations that show how polymer networks crosslinked with either slip or catch bonds respond to mechanical stress. Our results reveal that catch bonding may be required to protect dynamic networks against fracture, in particular for mobile linkers that can diffuse freely after unbinding. While mobile slip bonds lead to networks that are very weak at high stresses, mobile catch bonds accumulate in high stress regions and thereby stabilize cracks, leading to a more ductile fracture behavior. This allows cells to combine structural adaptivity at low stresses with mechanical stability at high stresses

Correlations, fluctuations and stability of a finite-size network of coupled oscillators

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model.Comment: 25 pages (2 column), 12 figures, modifications for resubmissio

Reading Merleau-Ponty: Cognitive science, pathology and transcendental phenomenology

This thesis explores the evolution of the way the Phenomenology of Perception is read for the purpose of determining its relevance to cognitive science. It looks at the ways in which the descriptions of phenomena are taken to converge with connectionist and enactivist accounts (the "psychological" aspect of this reading) and the way Merleau-Ponty's criticisms of intellectualism end empiricism are treated as effective responses to the philosophical foundations of cognitivism. The analysis reveals a general assumption that Merleau-Ponty's thought is compatible with a broadly naturalistic approach to cognition. This assumption has its roots in the belief that Merleau-Ponty's proximity to the existential tradition is incompatible with a commitment to a genuine transcendental philosophical standpoint. I argue that this suspicion is unfounded, and that it neglects the internal structure of the Phenomenology. Merleau-Ponty's criticism of classical forms of transcendental philosophy is not a rejection of that tradition, but instead prompts his unorthodox use of pathological case-studies. For Merleau-Ponty, this engagement with pathology constitutes a kind of transcendental strategy, a strategy that is much closer to Husserl's later work than is commonly acknowledged. The thesis also demonstrates a different mode of engagement with cognitive science, through a critical encounter with John Haugeland's transcendental account of the perception of objects. Confronting his account with the phenomenon of anorexia, I challenge him to differentiate his notion of an existential commitment from the anorexic's pathological over-commitment to a particular body image. Merleau-Ponty's account does not suffer from the same problems as Haugeland's because transcendence is not construed in terms of independence, but in terms of the fecundity and inexhaustibility of the sensible. I attempt to articulate Merleau-Ponty's own notion of a pre-personal commitment through the metaphor of invitation and show how this commitment and the Husserlian notion of open intersubjectivity can shed light on the anorexic's predicament

Dealing with stress : elasticity and fracture of soft network materials

Fracture of materials is both undesirable and unavoidable; therefore, there is great interest in methods to either forecast or control the fracture process of a material. To develop these methods, a deep understanding of the microscopic fracture process is needed covering the entire process from the scission of the first atomic bond to catastrophic failure of the entire material. In this thesis we study the microscopic fracture processes in soft network materials, ranging from elastomers, like rubber, to biological fibre networks, like collagen. Due to their disordered network structure, these materials can undergo large deformations prior to the damage accumulation process, in contrast to stiff materials, like concrete, where deformation is negligible. Here we investigate the implications of these large deformations on the elastic response and the fracture process of soft network materials. Specifically, we investigate the role of the network structure on elasticity and fracture via highly coarse grained models, wherein the network structure plays a central role. To cover the whole range of soft network materials ranging from soft brittle to soft ductile, we model both single network materials and composite networks materials where two or more networks are combined.In Chapter 2 we introduce the simplest model to study fracture in networks that can undergo large deformations: the athermal central-force elastic model. In this two-dimensional model the network structure is simplified to a graph consisting of linear springs and nodes and its equilibrium configuration is found by an energy minimization procedure. Although the elastic contributions in these networks only comes from the elements, rearrangements at the network level have a significant impact on the mechanical and fracture response. We also use our model to explain the role of network structure in the fracture response of disordered collagen networks, revealing that the athermal central-force elastic model can be a helpful tool in understanding the microscopic fracture response of real soft network materials.In the athermal model, the effect of thermal fluctuations and other time related processes, such as relaxation, are neglected. However, many soft network materials are actually highly sensitive to thermal fluctuations. To study the effect of these fluctuations we embed our central-force elastic model in a Langevin dynamics environment in Chapter 3, introducing both thermal fluctuations and an implicit solvent. We find that temperature has two seemingly opposing effects on network fracture. Entropic effects homogenize stress with respect to the athermal simulation. However, the stochastic nature of the thermal fluctuations also allows rupture of bonds that are on average not overstretched, which can be understood as a destabilizing effect.In Chapter 4 we shift our attention to composite networks, by investigating the linear and non-linear response of collagen networks embedded in a matrix of crosslinked hyaluronan polysaccharides, the two main component of the extracellular matrix, the network structure that supports the cells in our body. The presence of two networks results in an enhancement in the linear modulus due to a competition between their preferred modes of local deformation. Another intriguing experimental finding is that upon crosslinking the hyaluronan, a negative normal stress arises, indicative of a tendency to compress. We find that the hyaluronan network pulls on the collagen fibres, which causes a delay in the onset of strain-stiffening. We have been able to capture both the enhanced linear modulus and the delayed strain stiffening by expanding the central-force elastic model, describing the composite as a subisostatic network with bending interactions between neighbouring bonds, representing the collagen network, which is coupled to a homogeneous soft network, representing the hyaluronan matrix.In Chapter 5 we shift our focus to the fracture response of double networks, inspired by the significantly enhanced fracture response found in double network elastomers, hydrogels, and macroscopic materials. All these materials show that the response of an initially brittle network, also called the sacrificial network, can be shifted to a seemingly ductile response by embedding it in a significantly softer matrix network. We explore this transition from brittle to ductile behaviour by expanding upon the idea that the location of the brittle-to-ductile transition is governed by a force balance between the two networks. We locate the transition from brittle to ductile in a two-spring model, a multi-spring model and a random spring network model (another variant of the central-force elastic model) and find that in all models the location of the brittle-to-ductile transition can be predicted even when disorder is included in the latter two models. A detailed study of the network model reveals that also the development of the microscopic fracture response can be understood with respect to this brittle-to-ductile transition.In Chapter 6 we also study the fracture response of a double network via a coarse grained model, but now we use a three-dimensional model that specifically targets polymer double networks. We explicitly model the polymers as a string of particles, so that each bond represents a Kuhn length. We find that our networks behave similar to the experimental systems, and we can even rescale the initial mechanical response following a procedure proposed in literature for elastomers and hydrogels. We find that the damage response of our networks takes place in two steps. At first bond scission is governed by the first network, while after the yield strain interactions between the two networks dominate bond scission. This fracture mechanism, and the associated evolution of microscopic damage deviates significantly from the affine predictions for the damage response, where network structure is not considered. Overall, this research demonstrates that redistribution of stress over the network plays an important role in the damage response of polymer networks.In the general discussion we reflect on our findings and present a microscopic picture of fracture in soft network materials. Furthermore, we discuss a strategy to explore fracture processes that span a range of time scales, such as delayed fracture. Finally, we discuss our findings in the context of continuum elasticity and provide an outlook for future research into fracture of soft network materials