Santangelo, Christian

Job Title

Associate Professor, Department of Physics

Last Name

Santangelo

First Name

Christian

Discipline

Physics

Expertise

Soft Condensed Matter Theory

Show all metadata

Search Results

Now showing 1 - 7 of 7

Open Access
Smooth Cascade of Wrinkles at the Edge of a Floating Elastic Film
(2010-01) Huang, J; Davidovitch, B; Santangelo, C; Russell, T; Menon, N
An ultrathin polymer sheet floating on a fluid forms a periodic pattern of parallel wrinkles when subjected to uniaxial compression. The wave number of the wrinkle pattern increases sharply near the fluid meniscus where the translational symmetry of this one-dimensional corrugated profile is broken. We show that the observed multiscale morphology is controlled by a new “softness” number that quantifies the relative strength of capillary forces at the edge and the rigidity of the bulk pattern. We discover a new elastic cascade by which the wrinkling pattern in the bulk is smoothly matched to the fine structure at the edge by a discrete series of higher Fourier modes.
Open Access
Mesophases of soft-sphere aggregates
(2009-01) Shin, H; Grason, G; Santangelo, Christian
Soft spheres interacting via a hard core and a 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.
Open Access
Buckling thin disks and ribbons with non-Euclidean metrics
(2009-01) Santangelo, Christian
I consider the problem of a thin membrane on which a metric has been prescribed, for example by lithographically controlling the local swelling properties of a polymer thin film. While any amount of swelling can be accommodated locally, geometry prohibits the existence of a global strain-free configuration. To study this geometrical frustration, I introduce a perturbative approach. I compute the optimal shape of an annular, thin ribbon as a function of its width. The topological constraint of closing the ribbon determines a relationship between the mean curvature and the number of wrinkles that prevents a complete relaxation of the compression strain induced by swelling and buckles the ribbon out of the plane. These results are then applied to thin, buckled disks, where the expansion works surprisingly well. I identify a critical radius above which the disk in-plane strain cannot be relaxed completely.
Open Access
Membrane morphology induced by anisotropic proteins
(2010-01) Akabori, Kiyotaka; Santangelo, Christian
There are a great many proteins that localize to and collectively generate curvature in biological fluid membranes. We study changes in the topology of fluid membranes due to the presence of highly anisotropic, curvature-inducing proteins. Generically, we find a surprisingly rich phase diagram with phases of both positive and negative Gaussian curvature. As a concrete example modeled on experiments, we find that a lamellar phase in a negative Gaussian curvature regime exhibits a propensity to form screw dislocations of definite burgers scalar but of both chirality. The induced curvature depends strongly on the membrane rigidity, suggesting membrane composition can be a factor regulating membrane sculpting to to curvature-inducing proteins.
Open Access
Minimal resonances in annular non-Euclidean strips
(2010-01) Chen, B; Santangelo, Christian
Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of “conical” closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. We derive and test a surprising resonance condition for strips with minimal bending energy along the strip center line to exist.
Open Access
Diffusion and binding of finite-size particles in confined geometries
(2008-01) Henle, M; DiDonna, B; Santangelo, Christian; Gopinathan, A
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.
Open Access
Extrinsic curvature, geometric optics, and lamellar order on curved substrates
(2009-01) Kamien, R; Nelson, D; Santangelo, Christian; Vitelli, V
When thermal energies are weak, two-dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We present broad design principles to engineer the geometry of the underlying substrate so that a desired lamellar pattern can be obtained by self-assembly. Two distinct physical effects are identified as key factors that contribute to the interaction between the shape of the underlying surface and the resulting lamellar morphology. The first is a local ordering field for the direction of each individual layer, which tends to minimize its curvature with respect to the three-dimensional embedding. The second is a nonlocal effect controlled by the intrinsic geometry of the surface that forces the normals to the (nearly incompressible) layers to lie on geodesics, leading to caustic formation as in optics. As a result, different surface morphologies with predominantly positive or negative Gaussian curvature can act as converging or diverging lenses, respectively. By combining these ingredients, as one would with different optical elements, complex lamellar morphologies can be obtained. This smectic optometry enables the manipulation of lamellar configurations for the design of materials.