Soft Matter at the Thermal Scale

Colloids, Polymers, Liquid Crystals, Membranes and Phase Separation in 12 chapters — from “Brownian particles, sedimentation and the hard-sphere fluid” to “Spinodal decomposition and coarsening”.

Chapters

  1. Brownian particles, sedimentation and the hard-sphere fluid
    • Perrin's grains and colloidal length and time scales
    • Sedimentation equilibrium and the gravitational length
    • The osmotic equation of state of a dispersion
    • The second virial coefficient from the pair potential
    • The hard-sphere equation of state and its test
    • The hard-sphere freezing transition as a free-volume effect
    • The colloidal glass and the limits of equilibrium
    • Problems
  2. Forces between colloids and the stability of a dispersion
    • Clay, salt and the van der Waals bond
    • The Derjaguin approximation and van der Waals attraction
    • The Poisson-Boltzmann equation for a salt solution
    • The Debye screening length
    • The double-layer repulsion between two spheres
    • The DLVO potential and its barrier
    • The critical coagulation concentration
    • The stability ratio and steric stabilisation
    • The depletion attraction
    • Depletion-driven phase separation
    • What the DLVO potential settles and leaves open
    • Problems
  3. The size and shape of a polymer chain
    • Polystyrene sizes against the random walk
    • The freely jointed chain and the Gaussian chain
    • Bond angles, rotations and the Kuhn length
    • The worm-like chain and its persistence length
    • The radius of gyration and the Guinier law
    • The excluded volume parameter from the pair integral
    • The Flory argument and the Flory exponent
    • The theta condition and the collapsed globule
    • Ideal chains in a melt
    • Problems
  4. Polymer solutions and blends
    • Cloudy blends and the ideal entropy of mixing
    • The Flory-Huggins entropy of mixing on a lattice
    • The Flory-Huggins parameter and the energy of contact
    • The Flory-Huggins free energy and its shapes
    • The osmotic pressure of a polymer solution
    • The overlap concentration and the semidilute correlation length
    • Thermodynamic stability of a mixture
    • The binodal and the spinodal
    • The critical point of a polymer mixture
    • The immiscibility of polymer blends
    • Problems
  5. Rubber elasticity, swelling and gelation
    • Treloar's curve and the entropic spring
    • The affine network model
    • The stress-strain law of rubber
    • The Mooney-Rivlin form and finite extensibility
    • Thermoelastic inversion and the energy fraction
    • Network swelling in a good solvent
    • The gel point of a branching reaction
    • Gelation as percolation
    • The modulus of a gel
    • Problems
  6. Polymer dynamics and viscoelasticity
    • Bouncing putty and the modulus of a gel
    • The Maxwell model of a viscoelastic liquid
    • The Boltzmann superposition principle
    • The complex modulus in oscillatory shear
    • The Rouse model of an unentangled chain
    • The Zimm model in dilute solution
    • Entanglement and the rubbery plateau
    • Reptation in a tube
    • Time-temperature superposition
    • The critical gel
    • Problems
  7. Nematic order and the isotropic-nematic transition
    • The nematic phase between crossed polarisers
    • The director and the nematic order parameter
    • The order tensor
    • Birefringence as a measure of order
    • The Onsager transition of hard rods
    • Maier-Saupe mean-field theory
    • The Landau-de Gennes free energy
    • Pretransitional order in the isotropic phase
    • Problems
  8. Frank elasticity, defects and smectic layers
    • Threads where the director breaks
    • Splay, twist, bend and the Frank free energy
    • The Freedericksz transition
    • The twisted nematic display
    • Disclinations and their energy
    • Reading disclinations in the Schlieren texture
    • The cholesteric helix and its colours
    • Smectic layer order
    • The smectic penetration length
    • Problems
  9. Amphiphiles and self-assembly
    • The CMC of a soap solution
    • The hydrophobic effect
    • The closed-association model of micelles
    • The critical micelle concentration
    • The aggregation number and its measurement
    • The packing parameter
    • Micelle shapes from spheres to bilayers
    • The lyotropic nematic of rod-like micelles
    • Lyotropic liquid-crystalline phases
    • The bilayer edge energy
    • Problems
  10. Membranes, fluctuations and soft matter in biology
    • The flicker of a red blood cell
    • The elastic moduli of a fluid bilayer
    • The Helfrich bending energy
    • Bending rigidity from bilayer thickness
    • Vesicle closure and the smallest vesicle
    • The undulation spectrum and flicker
    • The Helfrich steric repulsion between membranes
    • DNA as a worm-like chain
    • Biomolecular condensates and membrane domains
    • Problems
  11. Nucleation and the lifetime of a metastable phase
    • Supercooled water and a cloud chamber
    • The supersaturation and the metastable region
    • The work of forming a nucleus
    • The critical nucleus and its barrier
    • The Kelvin equation and cloud droplets
    • The nucleation rate and its steepness
    • Heterogeneous nucleation on a surface
    • Nucleation of colloidal crystals
    • The Avrami equation for crystallisation
    • Problems
  12. Spinodal decomposition and coarsening
    • Light scattered by a quenched blend
    • Uphill diffusion inside the spinodal
    • The square-gradient free energy
    • The Cahn-Hilliard equation
    • The fastest-growing wavelength
    • The interfacial width and tension of a blend
    • The spinodal scattering ring
    • Lifshitz-Slyozov coarsening and Ostwald ripening
    • Hydrodynamic coarsening and dynamic scaling
    • Arrested spinodal decomposition and colloidal gels
    • Problems