Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userElasticity of disordered binary crystals
159
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The chemical and structural disorder impedes the study of the elasticity of such solid solutions, since standard procedures like potential expansions cannot be applied. We present a generalization of a density-functional based approach recently developed for one-component crystals to multi-component crystals. It yields expressions for the elastic constants valid in solid solutions with arbitrary amounts of point defects and up to the melting temperature. Further, both acoustic and optical phonon eigenfrequencies can be computed in linear response from the equilibrium particle densities and established classical density functionals. As a proof of principle, dispersion relations are computed for two different binary crystals: A random fcc crystal as an example for a substitutional, and a disordered sodium chloride structure as an example of an interstitial solid solution. In cases where one of the components couples only weakly to the others, the dispersion relations develop characteristic signatures. The acoustic branches become flat in much of the first Brillouin zone, and a crossover between acoustic and optic branches takes place at a wavelength which can far exceed the lattice spacing.*
rate research
Read More
We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.
It has become clear in recent years that the simple uniform wormlike chain model needs to be modified in order to account for more complex behavior which has been observed experimentally in some important biopolymers. For example, the large flexibility of short ds-DNA has been attributed to kink or hinge defects. In this paper, we calculate analytically, within the weak bending approximation, the force-extension relation of a wormlike chain with a permanent hinge defect along its contour. The defect is characterized by its bending energy (which can be zero, in the completely flexible case) and its position along the polymer contour. Besides the bending rigidity of the chain, these are the only parameters which describe our model. We show that a hinge defect causes a significant increase in the differential tensile compliance of a pre-stressed chain. In the small force limit, a hinge defect significantly increases the entropic elasticity. Our results apply to any pair of semiflexible segments connected by a hinge. As such, they may also be relevant to cytoskeletal filaments (F-actin, microtubules), where one may treat the cross-link connecting two filaments as a hinge defect.
In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this paper, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active odder elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with anti-ferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state -- an array of lines on an incompressible, free-standing film of chiral active fluid with a preferred normal direction -- is generically unstable. However, this instability can be tuned in easily realisable experimental settings, when the film is either on a substrate or in an ambient fluid.
We evaluate the effective Hamiltonian governing, at the optically resolved scale, the elastic properties of micro-manipulated membranes. We identify floppy, entropic-tense and stretched-tense regimes, representing different behaviors of the effective area-elasticity of the membrane. The corresponding effective tension depends on the microscopic parameters (total area, bending rigidity) and on the optically visible area, which is controlled by the imposed external constraints. We successfully compare our predictions with recent data on micropipette experiments.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
