NS-TP458M3.8 ECTSQ2EnglishMaster
Theory of Soft and Active Matter
FaculteitFaculty of Science
NiveauMaster
Studiejaar2026-2027
Beschrijving
Course goals
Upon successfully completing the course, the student
1. Understands the concepts of direct and total correlation functions and Density Functional Theory for inhomogeneous fluids and can calculate functional derivatives to construct Euler-Lagrange equations. The student can solve these equations for a few specific cases and can perform bifurcation analysis of symmetry-breaking transitions for a few cases. They also understand the relation between DFT and the Ornstein-Zernike equation.
2. Can work with the solutions of the Percus-Yevick equation for hard spheres, can employ thermodynamic perturbation theory about a hard-sphere reference system, and understand the relation with exact free-energy calculations from computer simulations. They have notion of the crystallization of the hard-sphere system and its relation to colloidal self-assembly.
3. Understands the notion of osmotic pressure and can calculate effective interactions that follow from tracing out the solvent degrees of freedom in the “osmotic ensemble,” which is used to describe extremely asymmetric solvent-solute mixtures of small molecules (say H2O) and larger species (DNA, nanoparticles, colloids, etc.).
4. Understands the role and the structure of electric double layers and dissolved ions for applications in e.g. supercapacitors for energy storage, blue energy harvesting, water desalination, and the action potential in neurons. Can solve the (linearized) Poisson-Nernst-Planck-Stokes equations to understand basic electrokinetic transport phenomena such as electro-osmosis and streaming currents, as well as in self-propulsion.
5. Has an appreciation for the role of topological defects in liquid crystals. The student can also perform calculations thereon using Oseen-Frank theory for elastic deformations of the nematic director in simple geometries.
6. Is familiar with basic concepts in active matter, including self-propulsion, the Vicsek model, Active Brownian particles, and motility-induced phase separation. The student can compute the mean-squared displacement of a single active particle and can understand the origin of a hydrodynamic description of swarming/flocking.
7. Is familiar and can derive transport equations with dynamic DFT. They understand classical nucleation theory and can perform calculations using this formalism. They can also understand the coarsening mechanics of spinodal decomposition using the Cahn-Hilliard description.
Content
Course content
The course Theory of Soft and Active Matter formalizes and extends upon the concepts introduced in the course Fundamentals of Soft Matter, which is a prerequisite to this module. These extensions prepare the student for ongoing (theoretical) soft-matter research, and theoretically unify several concepts introduced in the preceding course Fundamentals of Soft Matter.
The framework of Density Functional Theory (DFT) will be covered in greater detail. This is a variational formulation of statistical physics that simultaneously and coherently describes not only the thermodynamics (phase diagrams, equations of state, surface tension, adsorption, capacity), but also the structure (density profiles, radial distribution function, structure factor) of strongly interacting many-body systems. Using DFT we will derive the Ornstein-Zernike equation, study symmetry-breaking phase transitions in terms of a bifurcation analysis, and explicitly derive a few classical effective interactions (DLVO, depletion) between self-assembling colloidal nanoparticles.
Special topics on liquid crystals include Frank and/or Landau-De Gennes theory for elasticity and topological defects in nematic liquid crystals.
In this course we will also discuss dynamic DFT (DDFT), Cahn-Hilliard theory, and the Poisson-Nernst-Planck-Stokes formalism, which enable you to elucidate non-equilibrium phenomena such as electrokinetic transport (blue energy, H2 production, water desalination), active self-propelling particles (bacteria, Vicsek model, artificial swimmers, motility-induced phase separation), nucleation and growth, as well as spinodal decomposition.
Active participation to the problem class is a prerequisite for access to the exam.
The course Theory of Soft and Active Matter formalizes and extends upon the concepts introduced in the course Fundamentals of Soft Matter, which is a prerequisite to this module. These extensions prepare the student for ongoing (theoretical) soft-matter research, and theoretically unify several concepts introduced in the preceding course Fundamentals of Soft Matter.
The framework of Density Functional Theory (DFT) will be covered in greater detail. This is a variational formulation of statistical physics that simultaneously and coherently describes not only the thermodynamics (phase diagrams, equations of state, surface tension, adsorption, capacity), but also the structure (density profiles, radial distribution function, structure factor) of strongly interacting many-body systems. Using DFT we will derive the Ornstein-Zernike equation, study symmetry-breaking phase transitions in terms of a bifurcation analysis, and explicitly derive a few classical effective interactions (DLVO, depletion) between self-assembling colloidal nanoparticles.
Special topics on liquid crystals include Frank and/or Landau-De Gennes theory for elasticity and topological defects in nematic liquid crystals.
In this course we will also discuss dynamic DFT (DDFT), Cahn-Hilliard theory, and the Poisson-Nernst-Planck-Stokes formalism, which enable you to elucidate non-equilibrium phenomena such as electrokinetic transport (blue energy, H2 production, water desalination), active self-propelling particles (bacteria, Vicsek model, artificial swimmers, motility-induced phase separation), nucleation and growth, as well as spinodal decomposition.
Active participation to the problem class is a prerequisite for access to the exam.
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