Christian Santangelo - Academia.edu (original) (raw)
Papers by Christian Santangelo
Physical Review E, 2017
We study the influence of particle size asymmetry on structural evolution of randomly jammed bina... more We study the influence of particle size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere/small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small sphere composition, f. Our simulations reveal that at high values of ratio α of large to small sphere radii, (α ≥ αc ≈ 5.75) evolution of structural properties such as packing density, fraction of jammed spheres and contact statistics with f exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures α → ∞ by the Furnas model, but occurring for finite values range of α above a critical value, αc ≈ 5.75. The existence of a sharp transition from small-to large-f values for α ≥ αc can be attributed to the existence of a sub-jamming transition of small spheres within the interstices of jammed large spheres along the line of compositions f sub (α). We argue that the critical value of finite size asymmetry αc ≃ 5.75 is consistent with the geometric criterion for the transmission of small sphere contacts between neighboring tetrahedrally close packed interstices of large spheres, facilitating a cooperative sub-jamming transition of small spheres confined within the disjoint volumes.
Materials Horizons, 2017
The capillary assembly of stimulus-responsive hydrogel particles with programmed multipolar inter... more The capillary assembly of stimulus-responsive hydrogel particles with programmed multipolar interactions defined by their prescribed three-dimensional (3D) shapes is demonstrated.
Condensed Matter Physics, 2005
We compute the free energy for two rows of localized adsorption sites embedded in a two dimension... more We compute the free energy for two rows of localized adsorption sites embedded in a two dimensional one-component plasma with neutralizing background density ρ. The interaction energy between the adsorption sites is repulsive. We also compute the average occupation number of the adsorption sites and compare it to the result for a single row of sites. The exact result indicates that the discretization does not induce charge asymmetry and no attractive forces occur.
Journal of Computer-Aided Materials Design, 2007
The free energy of inserting a protein into a membrane is determined by considering the variation... more The free energy of inserting a protein into a membrane is determined by considering the variation in the spectrum of thermal fluctuations in response to the presence of a rigid inclusion. Both numerically and through a simple analytical approximation, we find that the primary effect of fluctuations is to reduce the effective surface tension, hampering the insertion at low surface tension. Our results, which should also be relevant for membrane pores, suggest (in contrast to classical nucleation theory) that a finite surface tension is necessary to facilitate the opening of a pore.
Nature materials, Jan 31, 2015
Elastic sheets offer a path to encapsulating a droplet of one fluid in another that is different ... more Elastic sheets offer a path to encapsulating a droplet of one fluid in another that is different from that of traditional molecular or particulate surfactants. In wrappings of fluids by sheets of moderate thickness with petals designed to curl into closed shapes, capillarity balances bending forces. Here, we show that, by using much thinner sheets, the constraints of this balance can be lifted to access a regime of high sheet bendability that brings three major advantages: ultrathin sheets automatically achieve optimally efficient shapes that maximize the enclosed volume of liquid for a fixed area of sheet; interfacial energies and mechanical properties of the sheet are irrelevant within this regime, thus allowing for further functionality; and complete coverage of the fluid can be achieved without special sheet designs. We propose and validate a general geometric model that captures the entire range of this new class of wrapped and partially wrapped shapes.
We consider the non-local elastic problem of a closed thin filament settling under gravity in a f... more We consider the non-local elastic problem of a closed thin filament settling under gravity in a fluid at zero Reynolds number. The filament is modeled as an inextensible chain, with no bending or twist rigidity. Although the equations admit rigid motions of the chain, there are no stable trajectories. We explore whether a stable envelope may exist around a recirculating blob and tail arrangement.
Physical Review E, 2014
A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by foldi... more A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how to incorporate film weight, selfadhesion and energy dissipation.
Under certain kinetic conditions, the dynamics of solid surfaces is governed by surface diffusion... more Under certain kinetic conditions, the dynamics of solid surfaces is governed by surface diffusion processes. This type of dynamics is relevant, for example, in high-temperature sintering processes, and in the coarsening of nanoporous metals coated by catalytic elements. For compact surfaces, the fixed points of this dynamics are surfaces of constant mean curvature (CMC). It is thus natural to ask
Soft Matter, 2014
We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the... more We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified.
Soft Matter, 2013
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure tha... more A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to structures with a chiral seam known as a 'line slip' phase, neither of which are stable for isotropic particles in equilibrium on flat surfaces. In this study, we use molecular dynamics simulations to find the steady-state structure of spherical particles with shortrange repulsion and long-range attraction far below the melting temperature. We vary the range of attraction using the Lennard-Jones and Morse potentials and find that a shorter-range attraction favors the line-slip. We develop a simple model based only on geometry and bond energy to predict when the crystal or line-slip phases should appear, and find reasonable agreement with the simulations. The simplicity of this model allows us to understand the influence of the commensurability constraint, an understanding that might be extended into the more general problem of self-assembling particles in strongly confined spaces.
Soft Matter, 2013
Figure SI1. Anisotropically swelled multistrips show a slight degree of buckling around the axis ... more Figure SI1. Anisotropically swelled multistrips show a slight degree of buckling around the axis parallel to the interfaces. Laser scanning confocal microscope images (top: plan-view section, bottom: cross-section) reveal that the degree of buckling is modest.
Soft Matter, 2009
Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" po... more Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a level surface analysis of the periodic structures of soft-sphere aggregates to study stable morphologies for all clustering potentials. We develop a systematic approach to the thermodynamics of mesophase assembly in the low-temperature, strong-segregation and predict a generic sequence of phases including lamella, hexagonal-columnar and body-center cubic phases, as well as the associated inverse structures. We discuss the finite-temperature corrections to strong segregation theory in terms of Sommerfeld-like expansion and how these corrections affect the thermodynamic stability of bicontinuous mesophase structures, such as gyroid. Finally, we explore the opposite limit of weakly-segregated particles, and predict the generic stability of a bicontinuous cluster morphology within the mean-field phase diagram.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
Considerations of rotational invariance in one-dimensionally modulated systems such as smectics-A... more Considerations of rotational invariance in one-dimensionally modulated systems such as smectics-A, necessitate nonlinearities in the free energy. The presence of these nonlinearities is critical for determining the layer configurations around defects. We generalize our recent construction for finding exact minima of an approximate nonlinear free energy to the full, rotationally invariant smectic free energy. Our construction exhibits the detailed connection between mean curvature, Gaussian curvature and layer spacing. For layers without Gaussian curvature, we reduce the Euler–Lagrange equation to an equation governing the evolution of a surface. As an example, we determine the layer profile and free energy of an edge dislocation.
Physical Review Letters, 2012
An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a q... more An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady stress field, validate our assumptions with numerical experiments, and pose new questions about the spatially developing motions of thin objects.
Physical Review Letters, 2010
Physical Review Letters, 1996
Physical Review E, 2006
By decomposing the Coulomb interaction into a long distance component appropriate for meanfield t... more By decomposing the Coulomb interaction into a long distance component appropriate for meanfield theory, and a nonmean-field short distance component, we compute the counterion density near a charged surface for all values of the counterion coupling parameter. A modified strong-coupling expansion that is manifestly finite at all coupling strengths is used to treat the short distance component. We find a nonperturbative correction related to the lateral counterion correlations that modifies the density at intermediate coupling.
Physical Review E, 2008
Describing the diffusion of particles through crowded, confined environments with which they can ... more Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system, and find excellent agreement with our analytic results.
Journal of Statistical Mechanics: Theory and Experiment, 2012
The densest packings of N unit squares in a torus are studied using analytical methods as well as... more The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a family of "gapped bricklayer" Bravais lattice solutions with density N/(N + 1); and some surprising non-Bravais lattice configurations, including lattices of holes as well as a configuration for N = 23 in which not all squares share the same orientation. The entropy of some of these configurations and the frequency and orientation of density-one solutions as N → ∞ are discussed.
Physical Review E, 2017
We study the influence of particle size asymmetry on structural evolution of randomly jammed bina... more We study the influence of particle size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere/small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small sphere composition, f. Our simulations reveal that at high values of ratio α of large to small sphere radii, (α ≥ αc ≈ 5.75) evolution of structural properties such as packing density, fraction of jammed spheres and contact statistics with f exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures α → ∞ by the Furnas model, but occurring for finite values range of α above a critical value, αc ≈ 5.75. The existence of a sharp transition from small-to large-f values for α ≥ αc can be attributed to the existence of a sub-jamming transition of small spheres within the interstices of jammed large spheres along the line of compositions f sub (α). We argue that the critical value of finite size asymmetry αc ≃ 5.75 is consistent with the geometric criterion for the transmission of small sphere contacts between neighboring tetrahedrally close packed interstices of large spheres, facilitating a cooperative sub-jamming transition of small spheres confined within the disjoint volumes.
Materials Horizons, 2017
The capillary assembly of stimulus-responsive hydrogel particles with programmed multipolar inter... more The capillary assembly of stimulus-responsive hydrogel particles with programmed multipolar interactions defined by their prescribed three-dimensional (3D) shapes is demonstrated.
Condensed Matter Physics, 2005
We compute the free energy for two rows of localized adsorption sites embedded in a two dimension... more We compute the free energy for two rows of localized adsorption sites embedded in a two dimensional one-component plasma with neutralizing background density ρ. The interaction energy between the adsorption sites is repulsive. We also compute the average occupation number of the adsorption sites and compare it to the result for a single row of sites. The exact result indicates that the discretization does not induce charge asymmetry and no attractive forces occur.
Journal of Computer-Aided Materials Design, 2007
The free energy of inserting a protein into a membrane is determined by considering the variation... more The free energy of inserting a protein into a membrane is determined by considering the variation in the spectrum of thermal fluctuations in response to the presence of a rigid inclusion. Both numerically and through a simple analytical approximation, we find that the primary effect of fluctuations is to reduce the effective surface tension, hampering the insertion at low surface tension. Our results, which should also be relevant for membrane pores, suggest (in contrast to classical nucleation theory) that a finite surface tension is necessary to facilitate the opening of a pore.
Nature materials, Jan 31, 2015
Elastic sheets offer a path to encapsulating a droplet of one fluid in another that is different ... more Elastic sheets offer a path to encapsulating a droplet of one fluid in another that is different from that of traditional molecular or particulate surfactants. In wrappings of fluids by sheets of moderate thickness with petals designed to curl into closed shapes, capillarity balances bending forces. Here, we show that, by using much thinner sheets, the constraints of this balance can be lifted to access a regime of high sheet bendability that brings three major advantages: ultrathin sheets automatically achieve optimally efficient shapes that maximize the enclosed volume of liquid for a fixed area of sheet; interfacial energies and mechanical properties of the sheet are irrelevant within this regime, thus allowing for further functionality; and complete coverage of the fluid can be achieved without special sheet designs. We propose and validate a general geometric model that captures the entire range of this new class of wrapped and partially wrapped shapes.
We consider the non-local elastic problem of a closed thin filament settling under gravity in a f... more We consider the non-local elastic problem of a closed thin filament settling under gravity in a fluid at zero Reynolds number. The filament is modeled as an inextensible chain, with no bending or twist rigidity. Although the equations admit rigid motions of the chain, there are no stable trajectories. We explore whether a stable envelope may exist around a recirculating blob and tail arrangement.
Physical Review E, 2014
A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by foldi... more A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how to incorporate film weight, selfadhesion and energy dissipation.
Under certain kinetic conditions, the dynamics of solid surfaces is governed by surface diffusion... more Under certain kinetic conditions, the dynamics of solid surfaces is governed by surface diffusion processes. This type of dynamics is relevant, for example, in high-temperature sintering processes, and in the coarsening of nanoporous metals coated by catalytic elements. For compact surfaces, the fixed points of this dynamics are surfaces of constant mean curvature (CMC). It is thus natural to ask
Soft Matter, 2014
We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the... more We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified.
Soft Matter, 2013
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure tha... more A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to structures with a chiral seam known as a 'line slip' phase, neither of which are stable for isotropic particles in equilibrium on flat surfaces. In this study, we use molecular dynamics simulations to find the steady-state structure of spherical particles with shortrange repulsion and long-range attraction far below the melting temperature. We vary the range of attraction using the Lennard-Jones and Morse potentials and find that a shorter-range attraction favors the line-slip. We develop a simple model based only on geometry and bond energy to predict when the crystal or line-slip phases should appear, and find reasonable agreement with the simulations. The simplicity of this model allows us to understand the influence of the commensurability constraint, an understanding that might be extended into the more general problem of self-assembling particles in strongly confined spaces.
Soft Matter, 2013
Figure SI1. Anisotropically swelled multistrips show a slight degree of buckling around the axis ... more Figure SI1. Anisotropically swelled multistrips show a slight degree of buckling around the axis parallel to the interfaces. Laser scanning confocal microscope images (top: plan-view section, bottom: cross-section) reveal that the degree of buckling is modest.
Soft Matter, 2009
Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" po... more Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a level surface analysis of the periodic structures of soft-sphere aggregates to study stable morphologies for all clustering potentials. We develop a systematic approach to the thermodynamics of mesophase assembly in the low-temperature, strong-segregation and predict a generic sequence of phases including lamella, hexagonal-columnar and body-center cubic phases, as well as the associated inverse structures. We discuss the finite-temperature corrections to strong segregation theory in terms of Sommerfeld-like expansion and how these corrections affect the thermodynamic stability of bicontinuous mesophase structures, such as gyroid. Finally, we explore the opposite limit of weakly-segregated particles, and predict the generic stability of a bicontinuous cluster morphology within the mean-field phase diagram.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
Considerations of rotational invariance in one-dimensionally modulated systems such as smectics-A... more Considerations of rotational invariance in one-dimensionally modulated systems such as smectics-A, necessitate nonlinearities in the free energy. The presence of these nonlinearities is critical for determining the layer configurations around defects. We generalize our recent construction for finding exact minima of an approximate nonlinear free energy to the full, rotationally invariant smectic free energy. Our construction exhibits the detailed connection between mean curvature, Gaussian curvature and layer spacing. For layers without Gaussian curvature, we reduce the Euler–Lagrange equation to an equation governing the evolution of a surface. As an example, we determine the layer profile and free energy of an edge dislocation.
Physical Review Letters, 2012
An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a q... more An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady stress field, validate our assumptions with numerical experiments, and pose new questions about the spatially developing motions of thin objects.
Physical Review Letters, 2010
Physical Review Letters, 1996
Physical Review E, 2006
By decomposing the Coulomb interaction into a long distance component appropriate for meanfield t... more By decomposing the Coulomb interaction into a long distance component appropriate for meanfield theory, and a nonmean-field short distance component, we compute the counterion density near a charged surface for all values of the counterion coupling parameter. A modified strong-coupling expansion that is manifestly finite at all coupling strengths is used to treat the short distance component. We find a nonperturbative correction related to the lateral counterion correlations that modifies the density at intermediate coupling.
Physical Review E, 2008
Describing the diffusion of particles through crowded, confined environments with which they can ... more Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system, and find excellent agreement with our analytic results.
Journal of Statistical Mechanics: Theory and Experiment, 2012
The densest packings of N unit squares in a torus are studied using analytical methods as well as... more The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a family of "gapped bricklayer" Bravais lattice solutions with density N/(N + 1); and some surprising non-Bravais lattice configurations, including lattices of holes as well as a configuration for N = 23 in which not all squares share the same orientation. The entropy of some of these configurations and the frequency and orientation of density-one solutions as N → ∞ are discussed.