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Cursus: NS-TP453M
NS-TP453M
Soft condensed matter theory
Cursus informatie
CursuscodeNS-TP453M
Studiepunten (EC)7,5
Cursusdoelen
  1. has good working knowledge of thermodynamics and classical Gibbs ensembles, can calculate thermodynamic properties of non-ideal gases from the virial expansion and has a basic understanding of pair correlations and the structure factor of gases, liquids, and crystals
  2. understands the Ornstein-Zernike equation and its application to hard-sphere fluids, and can calculate macroscopic properties of classical many-body systems from thermodynamic perturbation theory
  3. knows concepts and theories of surface tension, adsorption, and capillary waves
  4. understands the concept of effective interactions in the osmotic ensemble, understands the basics of classical density functional theory, and is aware of its relations to the virial expansion and the Ornstein-Zernike equation
  5. knows the concepts of electrostatic double layers and ionic screening, and can do calculations within Poisson-Boltzmann and Debye-Hückel theory for charged particles or surfaces in electrolytes
  6. knows scaling properties of ideal and self-avoiding polymer chains and can calculate the universal scaling exponents in the semi-dilute regime of polymer solutions
  7. has a basic knowledge of the structure and properties of liquid crystalline states of matter, can derive Onsager’s theory for nematic liquid crystals and work with it
  8. has basic knowledge of nonequilibrium and hydrodynamic phenomena such as shear flow and electrokinetics
Inhoud
Soft matter consists of mesoscopic objects such as colloidal particles, polymer chains, or macromolecules, which are often suspended in a liquid medium, often with addional ions. Traditional examples of such systems are blood, mud, hairgel, yoghurt, or paint, but more recent examples include liquid crystals, photonic bandgap materials, DNA in the living cell, and e-ink.The traditional picture of these systems a "dirty chemical soup" is no longer true due to spectacular advances in chemical synthesis and microscopy, resulting in clean and well-defined model systems that can be studied in great detail experimentally. In this course we will discuss the phenomenology of this systems from a theoretical perspective, with a focus on e.g. phase transitions, structure, spontaneous ordering, medium-induced effective interactions, Brownian dynamics. We will develop the theory to interpret, describe and predict physical properties of these systems. A short initial crash-course on classical statistical mechanics (thermodynamic potentials, Legendre transforms, ensembles, partition functions, etc.) will be extended to describe interacting many-body systems (virial expansion, distribution functions, Ornstein-Zernike theory, thermodynamic perturbation theory, van der Waals theory, critical exponents, hard-sphere crystallisation, and density functional theory). Further extensions to describe ionic liquids and colloidal suspensions will be discussed (Debye-Hueckel theory, screening, Poisson-Boltzmann theory, DLVO theory, effective many-body interactions, depletion effect due added polymers, charge renormalization). Also liquid crystals (nematic, smectic, columnar phases, Onsager theory), polymers (random walks, theta collapse, flexibility, persistence length,scaling concepts), interfacial phenomena (adsorption, wetting, surface tension, capillary waves, density profiles, droplets), and (hydro-)dynamic effects (Brownian motion, Langevin equation, dynamic density functional theory) will be covered.
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