Optimal Shapes and Complex Structure in Soft Matter Physics
(This is a copy of the seminar course announcement I designed when I taught this seminar course at the FAU Erlangen-Nuremberg in 2013. Publication date of this post is backdated to 2013)
We will explore the formation of complex structure in soft matter systems, relevant to both synthetic and biological systems, in response to minimisation of relatively simple energy functionals that are often very geometric in their nature. The seminar will give an overview of the systems where such approaches apply, including biological membranes, liquid foams, cellular systems, minimal surfaces, biophotonic crystals, granular materials, etc. Each set of seminar talks (see format description below) will represent some background on the different disciplines, and some hands-on projects, e.g. computational projects using the ‘Surface Evolver’, 3D printing of complex structures or experiments on foams or granular matter.
Course format, location and dates
Seminars will be held Monday 3:30-5pm in SR 01.683
The seminar is conducted in English, and takes place Mondays from 3:30pm to 5pm
Highly-recommended tutorials: Tuesdays and Thursdays from 4-6pm
The seminar will also include regular tutorials (Übungen) that we highly recommend you participate in. We will offer two time-slots for these tutorials, on Tuesdays from 4-6 pm and Thursdays from 2-4pm. The tutorials will be hands-on to make you familiar with numeric methods and experimental techniques and to help you in preparing your own seminar presentations. These tutorials will be held in one of the smaller front rooms of the CIP pool.
Course format
We will deviate slightly from the traditional format of a seminar, in order to spread the work-load more evenly throughout the semester and to maintain livelyness of the programm throughout the semester. Each student will give two talks, each about 20-30 minutes.
The first set of talks, to be given in November or December, shall provide an introduction into the different topics, emphasizing the key problems and aspects of the topic.
The second set of talks, to be given in January or February, shall describe the specific project carried out by the student.
Specific topics may include
Optimal shape of a trefoil knot : The trefoil knot is the simplest knotting of a string, readily occurring in structures throughout the natural science, from DNA with specific function to complex chemical frameworks. The geometry of the trefoil knot in an energy minimising form is shown in the figure. This project explores discretised and analytical forms of this shape, as well as the distribution of curvature over the knotted tube. (References: Pieranski & Przybyl ; Recommended reading: Pieranski’s web page ; Contact person: Myfanwy Evans)
Exotic photonic effects of complex biomaterials : Ordered geometry and chirality of biomaterials often dictates exotic photonics properties. This project explores two biomaterials with related chiral geometry, butterfly wing-scales and human skin, from the perspective of photonics. In the case of the butterfly wings, the photonic effects add to the brilliant green colour to the wing, yet the photonic effect of the translucent outer layer of human skin is still unknown. (Recommended reading: Hyde et al , Evans et al , Saba et al ; Recommended reading: ; Contact person: Myfanwy Evans)
Biophotonics: Strongly angular-dependent reflections of the Blue Morpho butterfly caused by nanostructure : Many butterflies and beetles are known to generate their brilliant coloration through a micro-structure rather than pigmentation. Among the most famous examples is the Morpho rhetenor, a butterfly that is found in South America and generates its iridescent blue color by an effectively two-dimensional micro-structure: Morpho’s wing scales are covered with a lamella structure made of chitin that looks like a Christmas tree when cut and viewed from the side (see scanning electron micrographs in the picture). It has been shown by qualitative argumentation and simulation that this micro-structure with feature size on the order of the wave-length of visible light is responsible for the blue coloration. In this project we calculate the reflection spectrum with a semi-analytical method for a simplified structure model based on a transfer matrix treatment. The aim of this calculation is to obtain a fine grasp on the physics of the scattering process at the Christmas tree structure that induces frequency dependent reflection as a function of the angle of incidence. (this project involves analytical calculations) (References: Vukusic & Shambles , Whittaker & Culshaw , Vukusic et al, Yoshioka & Kinoshita , Siddique et al ; Preparation material: Tutorial Scattering Matrix ; Contact person: Matthias Saba )
Wrinkly skin from complex geometry : The complex 3-dimensional weaving of filaments shown in the Figure describes the arrangement of keratin intermediate filaments in the dead outer layer of mammalian skin. The geometry of the filaments enables a simple but large expansion of the material, readily observed when the skin swells and wrinkles on prolonged exposure to water. This project examines the interaction of geometry and mechanics in the system. (References: Evans et al; Recommended reading: ; Contact person: Myfanwy Evans)
Random Close Packing and Dense Crystals in Granular Materials : Crystalline sphere packs can achieve packing fractions (fraction of space covered by the spheres) of 74%. Yet, when pouring beads in a jar, one observes a fairly strict upper limit for the packing fraction of 64%, first observed by Bernal. This limit is referred to as the random close packing limit. The corresponding configurations are disordered. It is nowadays well known that, somewhat against intuition, ellipsoids can reach higher packing fractions. We will explore the notion of random close packing, in various contexts from biology to the physics of amorphous materials. This topic will include packing experiments of ellipsoidal and spherical lollies and likely some hands-on tomography experiments. (References: van Hecke et al ; Recommended reading: Aste & Weaire ; Contact person: Fabian Schaller )
The role of friction in random packings : Friction is a major determinant of both the maximally achieved packing fractions and the speed of compactification, and is hence of huge relevance for understanding random close packing. We will discuss the role of friction, for example with respect to isostaticity (the number of neighbors required for completely constraining all degrees of freedom of a particle). This project will include some hands-on experiments on custom-fabricated plastic particles. (References: van Hecke et al ; Recommended reading: Aste & Weaire ; Contact person: Fabian Schaller )
Random packings on negatively-curved interfaces: Defects and scars : The densest packing of equal sized disks on an infinite plane is obtained by arranging the disks into a triangular tilling. Similarly, the lowest energy configuration of monodisperse (i.e. equal volume) two dimensional bubbles corresponds to a hexagonal bubble lattice. In both cases the disks and the bubbles occupy the same area on the plane and have the same local environment of six equally-spaced first neighbours which is reproduced all over the plane according to the laws of classical crystallography. However, this ideal organization is no longer possible when the disks are assembled onto curved surfaces. Several natural and man-made mechanical systems can be viewed as two-dimensional curved crystals. Examples include architectural structures, viral shells and colloidosomes (crystals formed by beads self-assembled on water droplets in oil). In such systems most of the constituent particles have six nearest neighbours but in addition distinctive high angle grain boundaries are observed. These consist of disclinations (disks or bubbles with five or seven neighbours) and dislocations (a pair of adjacent five-seven disclinations), which together form complex “scar” like arrangements. Dislocations have been observed in flat 2D foams but disclinations and scars have not. In this project you will conduct simple numerical simulations to the elucidate properties on familiar geometries, such as spheres, and end up with analysing packings of equal-sized disks onto complex negatively curved surfaces, such as triply-periodic minimal surfaces. (This project is best carried out together with the following project, and may involve some 3D printing) (References: Bausch et al , Irvine et al , Cox ; Recommended reading: Bowick & Giomi , Vitelli et al ; Contact person: Adil Mughal )
Random and ordered foams on negatively-curved interfaces: Why do bees build hexagons? : We will explore the shape and structure of random and ordered foams that ‘live’ in negatively curved manifolds, again addressing the question of where and how defects form in the polygonal structure, as a consequence of the Euler formula. The packings of disks in the previous project will be used as a starting point for simulations involving 2D foams which you will investigate using the Surface Evolver package. Furthermore, you may use 3D printing technology to produce a mould into which monodisperse foam will be injected, or onto which the bees could build their honeycombs… (References: Bausch et al , Irvine et al , Cox ; Recommended reading: Bowick & Giomi , Vitelli et al ; Contact person: Adil Mughal )
The shape and feel of random soap froth: geometry determines physical properties : Foams (such as beer foam, shaving foam, polymeric foams) are not only important for our daily life and well-being but are interesting because of their close correlation between geometry and physics. When modelling these structures in the so-called dry-limit, the problem reduces essentially to area-minimisation of a spatial tessellation under the constraint of constant bubble volumes. We will review the Plateau’s laws that govern the structure of liquid foams, discuss the relevance of topological transitions and the relationship between physical stress and geometric structure, particularly for sheared foams. (this project will involve quite a bit of surface evolver simulation and or participation in the coarsening experiments described below) (References: Evans et al , Kraynik et al ; Recommended reading: Weaire & Hutzler ; Contact person: Gerd Schröder-Turk)
Coarsening (or ageing) of liquid foams : Geometry versus topology : Coarsening of liquid foams describes the process whereby cell volumes change due to gas diffusion through the liquid films. Since diffusion occurs as a consequence of pressure differences between neighboring cells, the equivalence of pressure differences across a film with the constant mean curvature of the film implies that coarsening is a geometric problem that can be numerically studied using the Surface Evolver. We will here address the coarsening (or lack thereof) of the Kelvin foam and the Weaire-Phelan foam by surface evolver, and that of a simple model cells called ‘isotropic Plateau polyhedra’. This will clarify the significant differences between 2D and 3D, since in 2D coarsening reduces to a topological problem whereas it is a genuinely geometric problem in 3D. (this project will include experiments with real soap froth and, if possible, high-speed cameras to image equilibration and ageing. (References: Evans et al ; Recommended reading: Weaire & Hutzler ; Contact person: Gerd Schröder-Turk)
Triply-periodic minimal surfaces and the formation of the single Gyroid : Triply-periodic minimal surfaces are fascinating ordered structures that divide space into two intergrown labyrinthine domains. Interestingly, these ordered phases have been observed in various soft matter systems, from lipid to copolymer self-assembly. We will review these structures, describe a very handable model for their description and will simulate a liquid confined to these structures, to provide some insight into the formation of the single Gyroid structure that is found e.g. in some butterfly wing-scales where it acts as a photonic crystals. (this project will include a significant Monte Carlo simulation) (References: Schröder-Turk et al , Almsherqui et al ; Recommended reading: ; Contact person: Gerd Schröder-Turk )
Credit points (“Scheine”)
You can use this module as (Material-)Physikalisches Seminar im Bachelor und Master for modules PS, PS-MAT, PSM-MAT
Preliminary Time table (for winter term WS2013/14)
| 14/Oct | Semester overview and project assignment | |
| 21/Oct | GST | Introduction to the physics of liquid foams (slides) |
| 28/Oct | GST | Introduction to synthetic self-assembly of triply-periodic bicontinuous forms |
| 04/Nov | GST | Introduction to complex negatively-curved nanostructures in biological systems |
| 11/Nov | Student presentations : introduction to field (20+10 minutes) | |
| DJ (MS/GST) | Exotic photonic effects of complex biomaterials | |
| SE (MS/GST) | Biophotonics: Reflections off Morpho butterflies | |
| 18/Nov | No seminar: please use this time to discuss your talks with your supervisors | |
| 25/Nov | Student presentations : introduction to field (20+10 minutes) | |
| SW (FS) | Disordered packings and the random close packing limit | |
| JH (FS) | The role of friction in jamming | |
| 02/Dec | Student presentations : introduction to field (20+10 minutes) | |
| MO (AM) | Random packings on negatively-curved interfaces | |
| PM (AM) | Random and ordered foams on negatively-curved interfaces | |
| 09/Dec | Student presentations : introduction to field (20+10 minutes) | |
| TS (GST) | Stresses in liquid foams | |
| TH (GST) | Diffusive coarsening of liquid foams | |
| JV (MEE) | Optimal shape of a trefoil knot | |
| Colloqium presentation at 5pm in Hörsaal E by eminent foam scientist Denis Weaire (Trinity College Dublin) | ||
| 16/Dec | Student presentations : introduction to field (20+10 minutes) | |
| FS (GST) | Simple fluids confined to complex pores | |
| MK (GST) | Diffusion of chiral molecules in chiral porous materials | |
| 13/Jan | Student presentations : results of projects (30 minutes) | |
| SW (FS) | Granular matter | |
| JH (FS) | Granular matter | |
| PM (AM) | Foams on negatively curved surfaces | |
| 14/Jan | Student presentations : results of projects (30 minutes) Note that this is a Tuesday |
|
| TS (MEE/GST) | Liquid foams | |
| TH (MEE/GST) | Liquid foams | |
| JV (MEE) | Optimal shape of knots | |
| 20/Jan | Student presentations : results of projects (30 minutes) | |
| SE (MS/GST) | Biophotonics | |
| DJ (GST) | Biophotonics | |
| FS(AM/GST) | Confined fluids | |
| 21/Jan | Student presentations : results of projects (30 minutes) Note that this is a Tuesday |
|
| MK (GST) | Chiral molecules in chiral pores | |
| WB (MEE) | Structure of skin | |