arXiv subjects

Alain Goriely

Publications and source records attributed to Alain Goriely.

72 records · Page 4Linked to original sources

arXiv2016

Quantum Capacitance Modifies Interionic Interactions in Semiconducting Nanopores

Nanopores made with low dimensional semiconducting materials, such as carbon nanotubes and graphene slit pores, are used in supercapacitors. In theories and simulations of their operation, it is often assumed that such pores screen ion-ion interactions like metallic pores, i.e. that screening leads to an exponential decay of the interaction potential with ion separation. By introducing a quantum capacitance that accounts for the density of states in the material, we show that ion-ion interactions in carbon nanotubes and graphene slit pores actually decay algebraically with ion separation. This result suggests a new avenue of capacitance optimization based on tuning the electronic structure of a pore: a marked enhancement in capacitance might be achieved by developing nanopores made with metallic materials or bulk semimetallic materials.

cond-mat.mtrl-sci↗

arXiv2016

Capacitance-Power-Hysteresis Trilemma in Nanoporous Supercapacitors

Nanoporous supercapacitors are an important player in the field of energy storage that fill the gap between dielectric capacitors and batteries. The key challenge in the development of supercapacitors is the perceived trade-off between capacitance and power delivery. Current efforts to boost the capacitance of nanoporous supercapacitors focus on reducing the pore size so that they can only accommodate a single layer of ions. However, this tight packing compromises the charging dynamics and hence power density. We show via an analytical theory and Monte Carlo simulations that charging is sensitively dependent on the affinity of ions to the pores, and that high capacitances can be obtained for ionophobic pores of widths significantly larger than the ion diameter. Our theory also predicts that charging can be hysteretic with a significant energy loss per cycle for intermediate ionophilicities. We use these observations to explore the parameter regimes in which a capacitance-power-hysteresis trilemma may be avoided.

cond-mat.mtrl-sci↗

arXiv2016

The surprising dynamics of a chain on a pulley: Lift-off and snapping

The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. Here, we consider the dynamics of the chain when one of the weights is removed and, thus, one end is pulled with constant acceleration. This simple change has dramatic consequences for the ensuing motion: at a finite time, the chain `lifts off' from the pulley and the free end subsequently accelerates faster than the end that is pulled. Eventually, the chain undergoes a dramatic reversal of curvature reminiscent of the crack, or snap, of a whip. We combine experiments, numerical simulations, and theoretical arguments to explain key aspects of this dynamical problem.

cond-mat.soft↗

arXiv2016

Design and stability of a family of deployable structures

A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To model this structure and study its stability, we show that the equilibrium equations describing unloaded states can be derived from a variational principle. We then use a novel geometric method to study the stability of the resulting equilibria. As an example we apply the theory to establish the stability of all possible equilibria of the Bristol ladder.

math.CA↗

arXiv2016

Geometric conditions for the positive definiteness of the second variation in one-dimensional problems

Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is, in general, analytically untractable. However, we show here that a global geometric analysis of the phase-plane trajectories associated with the stationary solutions leads to generic conditions for minimality. These results provide a straightforward and direct proof of positive definiteness, or lack thereof, in many important cases. In particular, when applied to mechanical systems, the stability or instability of entire classes of solutions can be obtained effortlessly from their geometry in phase-plane, as illustrated on a problem of a mass hanging from an elastic rod with intrinsic curvature.

math.CA↗

arXiv2016

Growth, collapse, and stalling in a mechanical model for neurite motility

Neurites, the long cellular protrusions that form the routes of the neuronal network are capable to actively extend during early morphogenesis or to regenerate after trauma. To perform this task, they rely on their cytoskeleton for mechanical support. In this paper, we present a three-component active gel model that describes neurites in the three robust mechanical states observed experimentally: collapsed, static, and motile. These states arise from an interplay between the physical forces driven by growth of the microtubule-rich inner core of the neurite and the acto-myosin contractility of its surrounding cortical membrane. In particular, static states appear as a mechanical traction/compression balance of these two parallel structures. The model predicts how the response of a neurite to a towing force depends on the force magnitude and recovers the response of neurites to several drug treatments that modulate the cytoskeleton active and passive properties.

physics.bio-ph↗

arXiv2015

Dynamics of Ion Transport in Ionic Liquids

A gap in understanding the link between continuum theories of ion transport in ionic liquids and the underlying microscopic dynamics has hindered the development of frameworks for transport phenomena in these concentrated electrolytes. Here, we construct a continuum theory for ion transport in ionic liquids by coarse graining a simple exclusion process of interacting particles on a lattice. The resulting dynamical equations can be written as a gradient flow with a mobility matrix that vanishes at high densities. This form of the mobility matrix gives rise to a charging behaviour that is different to the one known for electrolytic solutions, but which agrees qualitatively with the phenomenology observed in experiments and simulations.

cond-mat.soft↗

arXiv2014

Are Room Temperature Ionic Liquids Dilute Electrolytes?

An important question in understanding the structure of ionic liquids is whether ions are truly "free" and mobile which would correspond to a concentrated ionic melt, or are rather "bound" in ion pairs, that is a liquid of ion pairs with a small concentration of free ions. Recent surface force balance experiments from different groups have given conflicting answers to this question. We propose a simple model for the thermodynamics and kinetics of ion pairing in ionic liquids. Our model takes into account screened ion-ion, dipole-dipole and dipole-ion interactions in the mean field limit. The results of this model suggest that almost two thirds of the ions are free at any instant, and ion pairs have a short lifetime comparable to the characteristic timescale for diffusion. These results suggest that there is no particular thermodynamic or kinetic preference for ions residing in pairs. We therefore conclude that ionic liquids are concentrated, rather than dilute, electrolytes.

cond-mat.soft↗

arXiv2014

Influence of constraints on axial growth reduction of cylindrical Li-ion battery electrode particles

Volumetric expansion of silicon anode particles in a lithium-ion battery during charging may lead to the generation of undesirable internal stresses. For a cylindrical particle such growth may also lead to failure by buckling if the expansion is constrained in the axial direction due to other particles or supporting structures. To mitigate this problem, the possibility of reducing axial growth is investigated theoretically by studying simple modifications of the solid cylinder geometry. First, an annular cylinder is considered with lithiation either from the inside or from the outside. In both cases, the reduction of axial growth is not found to be significant. Next, explicit physical constraints are studied by addition of a non-growing elasto-plastic material: first, an outer annular constraint on a solid silicon cylinder, and second a rod-like inner constraint for an annular silicon cylinder. In both cases, it is found that axial growth can be reduced if the yield stress of the constraining material is significantly higher than that of silicon and/or the thickness of the constraint is relatively high. Phase diagrams are presented for both the outer and the inner constraint cases to identify desirable operating zones. Finally, to interpret the phase diagrams and isolate the key physical principles two different simplified models are presented and are shown to recover important qualitative trends of the numerical simulation results.

cond-mat.soft↗

arXiv2014

Unravelling Nanoconfined Films of Ionic Liquids

The confinement of an ionic liquid between charged solid surfaces is treated using an exactly solvable 1D Coulomb gas model. The theory highlights the importance of two dimensionless parameters: the fugacity of the ionic liquid, and the electrostatic interaction energy of ions at closest approach relative to thermal energy, in determining how the disjoining pressure exerted on the walls depends on the geometrical confinement. Our theory reveals that thermodynamic fluctuations play a vital role in the "squeezing out" of charged layers as the confinement is increased. The model shows good qualitative agreement with previous experimental data, with all parameters independently estimated without fitting.

cond-mat.soft↗

arXiv2014

Combining mechanical and chemical effects in the deformation and failure of a cylindrical electrode particle in a Li-ion battery

A general framework to study the mechanical behaviour of a cylindrical silicon anode particle in a lithium ion battery as it undergoes lithiation is presented. The two-way coupling between stress and concentration of lithium in silicon, including the possibility of plastic deformation, is taken into account and two particular cases are considered. First, the cylindrical particle is assumed to be free of surface traction and second, the axial deformation of the cylinder is prevented. In both cases plastic stretches develop through the entire cylinder and not just near the surface as is commonly found in spherical anode particles. It is shown that the stress evolution depends both on the lithiation rate and the external constraints. Furthermore, as the cylinder expands during lithiation it can develop a compressive axial stress large enough to induce buckling, which in turn may lead to mechanical failure. An explicit criterion for swelling-induced buckling obtained as a modification of the classical Euler buckling criterion shows the competition between the stabilising effect of radius increase and the destabilising effect of axial stress.

cond-mat.soft↗

arXiv2014

Controlled topological transitions in thin film phase separation

In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls towards each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.

physics.flu-dyn↗

arXiv2013

Magnetic chains: From self-buckling to self-assembly

Spherical neodymium-iron-boron magnets are perman-ent magnets that can be assembled into a variety of structures due to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings, and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.

cond-mat.soft↗

arXiv2013

The mechanics of a chain or ring of spherical magnets

Strong magnets, such as neodymium-iron-boron magnets, are increasingly being manufactured as spheres. Because of their dipolar characters, these spheres can easily be arranged into long chains that exhibit mechanical properties reminiscent of elastic strings or rods. While simple formulations exist for the energy of a deformed elastic rod, it is not clear whether or not they are also appropriate for a chain of spherical magnets. In this paper, we use discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres. We find that the mechanical properties of a chain of magnets differ significantly from those of an elastic rod: while both magnetic chains and elastic rods support bending by change of local curvature, nonlocal interaction terms also appear in the energy formulation for a magnetic chain. This continuum model for the energy of a chain of magnets is used to analyse small deformations of a circular ring of magnets and hence obtain theoretical predictions for the vibrational modes of a circular ring of magnets. Surprisingly, despite the contribution of nonlocal energy terms, we find that the vibrations of a circular ring of magnets are governed by the same equation that governs the vibrations of a circular elastic ring.

math.CA↗

arXiv2013

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

Euler's celebrated buckling formula gives the critical load $N$ for the buckling of a slender cylindrical column with radius $B$ and length $L$ as \[ N / (π^3 B^2) = (E/4)(B/L)^2, \] where $E$ is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness $(B/L)$ is an infinitesimal quantity. Here we ask the following question: What is the first nonlinear correction in the right hand-side of this equation when terms up to $(B/L)^4$ are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants ---including Poisson's ratio--- all appear in the coefficient of $(B/L)^4$.

cond-mat.soft↗

arXiv2013

Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov-Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics.

cond-mat.soft↗

arXiv2008

Nonlinear Euler buckling

The buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are developed using the exact solution of Wilkes for the linearized problem within the Stroh formalism. Using these methods, the range of validity of the Euler buckling formula and its first nonlinear corrections are obtained for third-order elasticity. The values of the geometric parameters (tube thickness and slenderness) where a transition between buckling and barrelling is observed are also identified.

nlin.SI↗

arXiv2007

Instabilities in elastomers and soft tissues

Biological soft tissues exhibit elastic properties which can be dramatically different from rubber-type materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material responses under loads we compare three different types of instabilities (two in compression, one in extension) in hyperelasticity for various forms of strain energy functions typically used for elastomers and for soft tissues. Surprisingly, we find that the strain-hardening property of soft tissues does not always stabilize the material. In particular we show that the stability analyses for a compressed half-space and for a compressed spherical thick shell can lead to opposite conclusions: a soft tissue material is more stable than an elastomer in the former case and less stable in the latter case.

cond-mat.soft↗