Computational Polymer Physics

Spring semester course 327-5102-00L

Teaching Goals

The course offers an introduction to computer simulation methods and their foundations for the physics and material behavior of simple and complex materials and in particular polymeric and anisotropic liquids. The lecture is devised for students which have attended the course 402-0809-00L Introduction to Computational Physics. The goal is to i) introduce theoretical approaches used in soft matter physics, ii) motivate coarse-grained models, and ii) the numerical solution of many body problems for optical, mechanical, or electromagnetic applications.

Summary and Outline

• Theory: equilibrium statistics, nonequilibrium statistics, tensors, nonequilibrium dynamics of anisotropic fluids, partial differential equations
• Models: Phase transitions, dumbbell models, chain models, primitive path models, elongated particle models, connection between different levels of description
• Simulation: Monte Carlo, brownian dynamics, molecular dynamics, smoothed particle dynamics, embedded atoms, structure recognition, optimization

The lecture focuses on particle methods. Techniques such as Monte Carlo, equilibrium, beyond-equilibrium and nonequilibrium molecular dynamics, smoothed particle dynamics, dissipative particle dynamics, Brownian dynamics, embedded atoms, lattice Boltzmann will be introduced and applied. Master equations, Markov processes, Fokker-Planck equations, stochastic differential equations play a major role in the fundamental chapters. Substances: from simple towards structured fluids (gases, polymers, ferrofluids, liquid crystals, glasses, metals). The lectures and exercises will be structured as follows:

Tentative Schedule for the Course

• [Introduction to programming, if needed]
• Cellular Automata (CA), introduction, classification
  Moore models
  Traffic modeling
  Shock waves
  The Q2R Ising Model
• Monte Carlo integration, error estimates, scaling
  Monte Carlo in statistical physics, Quasi Monte Carlo
  Distributed random numbers, methods
  Accretion
  The Ballistic Deposition Model
  Diffusion limited aggregation (DLA) model
  Fractal dimensions, polymers
• Random walk, theory, applications
  Monte Carlo simulation for the random walk
  Freely rotating polymers
  Wormlike polymers
  Self-avoiding walk (SAW)
  Slithering Snake, Pivot, Enriched samples algorithms
  Flory type theory for polymers
  Exactly solvable semiflexible spin chain model
• Master equation, introduction, applications
  Stationary solution of the Master equation
  Detailed balance
  Coupled equations for moments
  Metropolis Monte Carlo (MC)
  Thermostatted 1D harmonic oscillator via Metropolis MC
  Lennard-Jones system via Metropolis MC
  Gaussian integrals
• Ising model and Phase transitions
  Metropolis MC algorithm for the 2D Ising model
  Finite size effects
  Phase transitions & percolation
  Percolation theory in the Ising Model
  Q-Potts model and foams
  Random site percolation model
• [Lattice gases, method, simulation and applications]
  [Lattice-Boltzmann, method, simulation and applications]
• Multiscale dynamics
  Molecular dynamics, implementation, applications
  Mesoscopic interaction potentials
  Finite difference methods
  Einstein frequency and configurational temperature
  Periodic boundary conditions
  Temperature control
  Lees-Edwards boundary conditions
• Beyond-equilibrium molecular dynamics
  Long-range forces
  White and colored noise
  Random vector with given mean and covariance
  Whitening a random vector
  Brownian dynamics, theory and simulation
  Langevin equations
• Rouse model for polymer solutions
  Reptation models for polymer melts
  Primitive and shortest path methods
  Flow channel, flow birefringence
  Dendronized polymers, simulations, experiments, applications
• Kramers process
  Brownian dynamics of a FENE dumbbell
  Smoothed particle dynamics, soft fluid particles
  Dissipative particle dynamics
• Ferrofluids, ferromagnetic chains, theory, simulation, applications
  Magnetorheological fluids, simulation methods
  Liquid crystals, theoretical approaches, simulation, experiments
  Liquid crystalline polymers, theoretical approaches, simulations, experiments
  Frank-Ericksen elasticity, theories, experiments
• Wormlike micelles, living polymers, theory and simulation
  Plasticity, metals, embedded atoms simulations
  Delaunay triangulation and Voronoi diagram

Script

A script, exercises, sample codes and other supplementary material will be available online. The latest version of the script is available here »»

Slides from the lecture

• cpp_CA_MCintro (MK)
• cpp_OneStepProcess_AND_MetropolisMC (MK)
• cpp_MC_application_AND_KMC (MK)
• cpp_PolymerChains_MC_Flory_SCF (MK)
• cpp_MD_NEMD_introduction (MK)
• cpp_MDapplications (PI)
• cpp_FPEandBD (PI)
• cpp_BDcomplexfluids (PI)
• cpp_LCPs.pdf (PI)
• cpp_FENEmodels_AND_ShortestPath (MK)
• cpp_FP_complexfluids (MK)
• cpp_SoftSolid_And_Networks (MK)
• cpp_Addon_JanusChainModel (MK)
• cpp_Addon_KineticTheory_Gas_LC (MK)

Exercises

• Analytical exercises
• Program codes to be submitted through the online documentation center »»

Literature

• M.P. Allen, D.J. Tildesley, Computer simulation of liquids (Clarendon Press, Oxford, 2000)
• Mathematica »»
• MatLab »»
• M. Rubinstein, R.H. Colby, Polymer physics (Oxford, 2003)
• H. Risken, The Fokker-Planck equation (Springer, Berlin, 1989).
• S. Hess, M. Kröger, P. Fischer, Einfache und disperse Flüssigkeiten, in: Bergmann-Schaefer, Band 5 (de Gruyter, Berlin, 2005).
• J. Honerkamp, Stochastische dynamische Systeme (VCH, Weinheim, 1990)
• H.C. Öttinger, Stochastic processes in polymeric fluids (Springer, Berlin, 1996) »»
• C.W. Gardiner, Handbook of stochastic methods (Springer, Berlin, 1985).
• M. Karttunen, I. Vattulainen, A. Lukkarinen (Eds.), Novel methods in soft matter simulations (Springer, Berlin, 2004).
• R.J. Gaylord, P.R. Wellin, Computer Simulations with Mathematica (Springer, Berlin, 1995).
• M. Kröger, Models for polymeric and anisotropic liquids (Springer, Berlin, 2005) »»

Lecturer(s)

• Emanuela Del Gado »»

Potential Guest Lecturers

• Patrick Ilg »»
• Martin Kröger »»

Teaching Assistant

• N.N.

Time and Location

• Lectures: Fridays, 13:45 - 15:15, HCI F 8
• Computer pool: Fridays, 15:45 - 17:40, HCI D 451

Remarks

• The course is held simultaneously with two corresponding lectures building on the above-mentioned ‘Introduction to Computational Physics’: Computational Statistical Physics, 402-0812-00L (2L, 2E, 8 CP) by Prof. H.J. Herrmann (D-BAUG), and Computational Quantum Physics, 402-0810-00L (2L, 2E, 8 CP) by Prof. M. Troyer/Dr. P. De Forcrand.(D-PHYS).
• This course is part of the area of specialization Materials Modeling and Simulation of the master degree program in Materials Science, it is an elective course in Mathematics, Physics, Computer Science, and an elective course of the batchelor and master degree programs in Computer Science. Some of the methods presented in Introduction to computational physics will be taken for granted.
• Credit points: 4