Weak forces acting on molecules govern a vast range of physical, chemical, and biological phenomena. To date, it has not been possible to measure these forces directly because force-sensing methods at the nanoscale have lacked the resolution to resolve ultraweak forces at the scale of single molecules deep within complex materials. Here, we solve this challenge by demonstrating singlemolecule force sensing with engineered light-emitting molecules and reporting forces as small as one trillionth of a Newton.
Colloidal gels are a prototypical example of a heterogeneous network solid whose complex properties are governed by thermally-activated dynamics. In this Letter we experimentally establish the connection between the intermittent dynamics of individual particles and their local connectivity. We interpret our experiments with a model that describes single-particle dynamics based on highly cooperative thermal debonding. The model, in quantitative agreement with experiments, provides a microscopic picture for the structural origin of dynamical heterogeneity in colloidal gels and sheds new light on the link between structure and the complex mechanics of these heterogeneous solids.Attractive interactions can drive a dilute colloidal suspension towards a solid state formed by a samplespanning and mechanically-rigid particle network [1,2]. These colloidal gels are non-equilibrium solids, kinetically arrested en route to their equilibrium state of solidliquid coexistence [3]. Such particle gels are characterized by strong heterogeneity in their local connectivity, mesoscopic structure and their dynamics and mechanics [4][5][6][7]. The microstructure and internal dynamics of colloidal gels can be directly observed with microscopy techniques at the single-particle level. As a consequence, it forms an interesting testing ground to explore the complex and length-scale dependent mechanics of heterogeneous solids. Colloidal gels derive their mechanical rigidity from physically bonded gel strands and nodes that form a percolating elastic network. The linear elasticity of gels is governed by the mechanics of the network architecture and its thermal fluctuations [8,9]. By contrast, the gradual aging of gels to a denser state [1,10] and their non-linear response to applied stresses [11,12], is governed by events occuring at the the much smaller length scale of individual particles. Since the bonds between the particles are typically weak, single particles can debond from strands in the gel by thermally-activated bond breaking [13]. On longer time scales, this result in the gradual restructuration of the gel network, causing it to coarsen, age and relax internal stresses that are built up during gelation [14]. Moreover, thermal-activation at the single particle level plays a crucial role in processes of fatigue that preempt stress-induced failure of the gel network [11]. To date, quantitative descriptions of these thermally-activated phenomena have relied on mean-field approximations [13]. Yet, the inhomogeneity in local coordination that is intrinsic to gels, must play a large role in the intermittent debonding dynamics that are at the origin of this complex non-linear behavior. As a result, linking the structure of colloidal gels to their non-linear mechanics has remained challenging, in particular as the relationship between local connectivity and thermallyactivated dynamics of single particles is not clearly established.In this letter we explore the connection between the local connectivity and intermittent bonding-debonding dy...
The repeated loading of a solid leads to microstructural damage that ultimately results in catastrophic material failure. While posing a major threat to the stability of virtually all materials, the microscopic origins of fatigue, especially for soft solids, remain elusive. Here we explore fatigue in colloidal gels as prototypical inhomogeneous soft solids by combining experiments and computer simulations. Our results reveal how mechanical loading leads to irreversible strand stretching, which builds slack into the network that softens the solid at small strains and causes strain hardening at larger deformations. We thus find that microscopic plasticity governs fatigue at much larger scales. This gives rise to a new picture of fatigue in soft thermal solids and calls for new theoretical descriptions of soft gel mechanics in which local plasticity is taken into account.
Many biological materials consist of sparse networks of disordered fibres, embedded in a soft elastic matrix. The interplay between rigid and soft elements in such composite networks leads to mechanical properties that can go far beyond the sum of those of the constituents. Here we present lattice-based simulations to unravel the microscopic origins of this mechanical synergy. We show that the competition between fibre stretching and bending and elastic deformations of the matrix gives rise to distinct mechanical regimes, with phase transitions between them that are characterized by critical behaviour and diverging strain fluctuations and with different mechanisms leading to mechanical enhancement. Many materials, ranging from textiles and paper to connective tissue and the cytoskeleton of living cells, have a microscopic structure that consists of crosslinked fibres. Theoretical progress in the last decades has led to a detailed understanding of the physics of such fibre networks [1]. Because stiff fibres resist not only stretching, but also bending, the mechanical behaviour of fibre networks differs significantly from that of networks of flexible polymers. Different mechanical regimes can be observed: at high densities fibre networks deform affinely and the elasticity is governed by fibre stretching, while at lower densities there is a crossover to a non-affine, bending-dominated regime [2][3][4][5][6].Although experiments on model networks give support to the existence of different mechanical regimes [7][8][9], the current theories fall short in describing real biomaterials. An important reason for this is that natural materials are almost without exception composite materials that consist of mixtures of elements of different rigidity: the cytoskeleton is a complex network of (partially bundled) actin filaments, intermediate filaments, and microtubules [10]; the extracellular matrix consists of stiff collagen fibres in a matrix of more flexible polymers [11]; and also many synthetic high-performance materials are composites of soft and rigid fibres [12][13][14][15][16]. It is clear that the collective non-affine deformation modes that characterize the mechanics of sparse fibre networks must be hindered significantly by the presence of an elastic matrix [17][18][19][20][21], but a fundamental understanding of how this interplay affects the mechanical properties of composites has remained elusive.Here we use numerical simulations to study the mechanics of disordered composite networks, consisting of crosslinked fibres embedded in a soft elastic matrix. Both the fibres and the polymers that constitute the background matrix are arranged on a 2D triangular lattice with lattice spacing l 0 , as shown in Fig. 1. The effects of connectivity are explored by randomly removing segments of the fibre network with a probability 1 − p, so that the average connectivity equals z = 6p. Sequences of contiguous colinear fibre segments are treated as elastic rods, characterized by a stretch modulus µ 1 and a bending modulus κ 1 ....
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