Physics 850, Soft Condensed Matter Physics (Fall05)
Prof. A. Dinsmore, UMass Amherst Physics Department
(Last taught in Fall05)

Physics 850, Soft Condensed Matter Physics, presents a graduate-level overview of current topics in the field.

[] height = 100 [yogurt, 10% milk solids] [colloidal crystal]

Soft condensed matter physics is the study of materials that are literally soft and squishy: colloids, emulsions, membranes, polymers, liquid crystals are a few examples. These materials are very common in nature, play a huge role in industry and emerging technology, and are the basis of many biological systems. Soft condensed matter is an old sub-field, but also a fast-growing one owing to recent advances in sample-preparation and measurement techniques, new technological applications, and new problems of biology and statistical physics. The goal of this course is to provide an overview of the theoretical underpinnings of soft condensed matter physics (which includes topics that play an important role in other areas of physics). We focus on four classes of materials: polymers, membranes, droplets, and colloids; the sequence of topics moves in order of 1, 2 and 3-dimensions. Experimental methods are also discussed.

Here is a summary of the lecture topics with links to scanned lecture notes in pdf format. The notes are currently password-protected, but there is a clue to the password on the longin page. I am also happy to send the password on request (e.g. by email).

News: 9/7/07-Notes for Ch 9 and 10 were uploaded.

  1. Introduction. (Notes: 14 pages, 1.4 MB)
    • Examples of soft materials in industry and biology.
    • Foams as a lead-off example of macro properties derived from micro.
    • Atomic- and molecular-scale forces and bonds.
    • Repulsion, entropy, hydrophobicity.
  2. van der Waals Forces. (Notes: 23 pages, 3.4 MB)
    • Keesom, Debye, and London contributions.
    • Mean-field models of media.
    • Measurements; list of Hamaker constants, relationship to surface tension.
    • Derjaguin approximation; interaction between spherical particles (not 1/r^6)
  3. Review of Statistical Mechanics. (Notes; 12 pages, 1.3 MB)
    • Probabilities; Boltzmann distribution, Helmholtz energy, Equipartition theorem.
    • Example of pulling RNA and measuring stiffness of a network (experiments).
  4. Fluctuation-induced forces. (Notes; 11 pages. 2.7 MB)
    • Osmotic pressure
    • Depletion attraction
    • Repulsion between membranes
    • Tension in a polymer
  5. Polymers (1 dimensional materials existing in 3D). (Notes (Part A); 14 pages, 2.3 MB)
    • Part A: Survey of types of polymers.
    • ...Ideal-chain and Freely-jointed chain models.
    • Part B:Worm-like chain (Kratky-Porod) model. (Notes (Part B); 10 pages, 1.6 MB)
    • ...The spectrum of fluctuations and the stiffness of a single polymer.
  6. Friction in Fluids: the Langevin Equation of motion of a particle in fluid. (Notes; 10 pages, 1.8 MB)
    • Viscosity and a simple model for its value; terminal velocity; sedimentation.
    • The mean-square displacement, Fluctuation-dissipation theorem.
  7. The Diffusion Equation. (Notes 21 pages, 3.4 MB)
    • A free particle; an ink spot; diffusion to capture, etc.
    • Particle-hopping model; Fick's law; diffusion with drift.
    • Experimental methods: Dynamic light scattering and the correlation function.
    • An aside: Measuring interactions: terminal velocity; g(r); Boltzmann method.
  8. Fluid Interfaces (2 dimensional materials existing in 3D). (Notes; 31 pages, 2.7 MB)
    • Surface tension, surfactants and Pickering emulsions.
    • Consequences of a surface tension: LaPlace pressure, Jurin's Law, the Rayleigh instability, the Young-Dupre law and wetting, the shape of a meniscus: the equation of capillarity. Forces among interfacial inclusions (the 'Cheerios Effect').
    • Assembly of particles at liquid interfaces
  9. Lipid Bilayer Membranes. (Notes; 17 pages, 1.4 MB)
    • Overview of vesicles and cell membranes.
    • The Helfrich model and bending modulus
    • The spectrum of thermal fluctuations; roughness of a membrane at finite temperature.
    • Vesicles.
  10. Electrostatics in Solution (3D). (Notes; 25 pages, 3.6 MB)
    • Poisson-Boltzmann theory and Debye length
    • Inter-particle forces, pH.
  11. Structure in 3D.
    • Packing spheres in 3D: Close-packing geometry; minimum contact #.
    • Long- and short-range order and frustration.
    • Liquid crystalline meso-phases.
  12. Phase separation.
    • Phenomenological models for hard spheres,
    • Flory Huggins theory for polymers.
    • Binodals and spinodals.
  13. Random aggregation and fractals.
    • DLA and DLCA.
    • (Unfortunately, I have not found time for phase transitions in 2D: KTHNY theory and disclinations)
  14. Fluid Dynamics. (Notes; 20 pages, 1.1 MB)
    • The Navier-Stokes equation for an isotropic fluid.
    • Reynolds Number, Re.
    • laminar flow, Poiseuille flow, lubrication.
  15. Continuum Elasticity and Viscoelasticity. (Notes on elasticity; 24 pages, 1.2 MB; Notes on microrheology; 7 pages, 0.36 MB))
    • Elasticity: stress, strain and the modulus.
    • Thermal displacements in 1D, 2D and 3D lattices (for polymers, membranes and 3D solids)
    • The loss modulus; viscoelasticity; frequency dependence of the modulus
    • Microrheology: G*(?) from the mean-square displacement.

Here is deGenne's description of soft matter (from a Nobel lecture, reprinted in Rev. Modern Phys.).

A. Dinsmore, 9/2007