Soft Matter Physics

01.  Fundamentals I

• traditional academic disciplines
  
• modern specializations and combinations
• characteristics of soft matter
• major topics
• theoretical methodologies
• experimental techniques
  

• van der Waals bond
• ionic bond
• metallic bond
  
• covalent bond
• hydrogen bond

• polar and non-polar molecules
• hydrophobic, hydrophilic, amphiphilic attributes
  
• enthalpic and entropic effects

• elastic constants: shear modulus, bulk modulus, Young modulus [pln20]
• elastic energy of deformation [pln63] 
  
• elasticity of hard and soft matter
  
• linear (elastic or viscous) response to shear stress [pln21]
  
• nonlinear viscous behavior (shear thinning/thickening, Bingham fluid) [pln22]
  
• dimensionless parameters: Deborah, Weissenberg, Peclet numbers [pln91] *
  
• probing viscoelasticity: stress relaxation, creep, rotation, oscillation
  
• simple model of viscoelasticity [pln23]
  
• measuring viscosity and shear modulus [pex16]
  
• Young modulus for generalized Lennard-Jones potential [pex15] *
  
• Arrhenius behavior of viscosity of water [pex17] *
  

• thermotropic versus lyotropic
• hierarchical (molecules versus molecular aggregates) [tsl50]
  
• orientational versus translational [tsl51]
  
• entropy driven
• polydispersity
• polymorphism
  

• characteristic attributes
  
• glass-forming systems
  
• relaxation time and viscosity (Vogel-Fulcher law)
• volume and entropy versus temperature
• glass transition in polystyrene [pex18]
• entropy from heat capacity of glass [pex19] *
  

02.  Fundamental II

• Helmholtz and Gibbs free energies of solutions [pln26] *
  
• homogeneous state vs phase-separated state [pln27]
  
• osmotic pressure [pln28]
  
• chemical potential [pln29] *
  
• dilute solutions [pln30]
  
• two-phase coexistence [pln31]
• lattice mean-field model free-energy density [pln32]
  
• phase diagram of mixing-unmixing transition [psl4]
  
• stability - metastability - instability [pln33]  
• osmotic pressure in two-component fluid system [pex48]
  
• chemical potential in two-component system [pex46] 
  
• phase diagram of two-component fluid [pex47] 
  
• water solubility of hydrocarbon [pex45] 
• osmotic weight lifting [pex49]  
  
• spinodal decomposition process [pln34]
  
• kinetics of spinodal decomposition [psl5] 
• solution of linearized Cahn-Hilliard equation [pex20]  
  
• nucleation and growth of domains [pln35]
  

• Gibbs free energy near freezing/melting [pln36]
  
• homogeneous vs heterogeneous nucleation [pln37]
  
• catalytic freezing of spherical cap [pex21]
  
• advancing font of solidification [pln38]
  

03.  Colloids I

What are colloids? [pln3] *

• classification
• shapes and sizes
• sols, gels, clays, foams
  
• emulsions
• stability
• interactions
• agents of aggregation and dispersion
  

• historical importance, milestones [nln63]
  
• relevant time scales (collision, relaxation, observation) [nln64]
  
• Einstein's theory [nln65]
  
• Smoluchowski equation [nln66]
  
• Einstein's fluctuation-dissipation relation [nln67]
  
• Langevin's theory (ballistic regime and diffusive regime) [nln71]
• particles with shapes [pln40] 
  

Colloids versus grains

• colloidal regime on Earth and in space [pex22] 
  

Interaction forces

• adhesive forces derived from van der Waals interactions [pln42]
  
• adhesive force between flat colloidal surfaces [pex23] 
  
• adhesive force between spherical colloids (Derjaguin approximation) [pex24] 
  
• electrostatic double-layer forces adjacent to ionized colloidal surface
  
• Stern-layer of counter-ions
• diffuse layers of co-ions and counter ions [pex25] 
  

Electro-kinetic effects

• electrophoresis
• streaming current
• electro-osmosis
• zeta potential [psl8]
  

Charge stabilization

• repulsion between ionic double layers versus VDW attraction [pln43]
  
• colloidal stability, flocculation, and coagulation [pex26] 
  

Steric stabilization [pln44]

• grafted polymer chains
• osmotic pressure [tln26] 
  
• entropic pressure
  
• brush elasticity
• bridging flocculation
• regulation of flocculation/coagulation

Colloids with attractive coupling

• depletion interaction
• depletion interaction potential between spherical colloids [pex27] 
  
• ordering from weak short-range attraction
• ordering from strong short-range attraction
• crystallization of hard-sphere colloids
• spherical aggregates of colloids [pex50] 
  

Flow in dispersions at low and high concentrations

04.  Polymers I

• variety -- structure -- architecture -- conformations [pln45] * 
  
• polydispersity index
• biopolymers [pln41]
  
• rheology of viscoelastic polymers [psl7]
  
• extensional rheometry of polymers
• effectiveness of centrifugation [pln46]
• polymer solutions [pln47]
  
• polymer blends [pln48] 
  
• phase separation in polymer solution [pex51] *
  
• phase separation in polymer blend [pex52] 
  
• interface width in phase-separated polymer blend [pex58] 
  

05.  Polymers II

• sources of entropy
• sources of enthalpy
• conformations: coil, globule, helix
• measures of polymer size

Freely jointed chain (FJC) [pln50] 

• random walk
  
• force-extension characteristics
  
• FJC model: force-extension characteristics, entropy, and heat capacity [pex53] 
  
• discretized FJC model: force-extension characteristics [pex54] 
  
• discretized FJC model: entropy and heat capacity [pex55] 
  
• binomial, Poisson, and Gaussian distributions [nln8]
  

Persistence length and Kuhn segment length [pln51]

• persistence length of ideal polymer chain [pex28]
• Kuhn segment length of ideal polymer chain  [pex29] 
  
• ideal polymer with fixed valence angle I: mean-square end-to-end distance [pex30]
  
• ideal polymer chain with fixed valence angle II: persistence length and Kuhn segment length [pex31]
• ideal polymer chain: flexibility from rigid constraints [pex32]
  
• polymer chain with energetically favored internal rotation angle [pex33] [pex34] 

Long-range self-interaction and interaction with solvent

• Flory argument
• good, poor, and theta solvents
• concentration regimes (dilute, semi-dilute, melt)
• criteria for polymer detection

06.  Polymers III

Polymer viscoelasticity

• creep compliance and stress relaxation [pln52]
  
• linear response and superposition principle
• zero shear viscosity
• polymer creep compliance: linear response [pex35]
• polymer stress relaxation: linear response [pex36] 
  
• relaxation modulus of polymer melt [pln53]
• time regimes: glassy - rubbery - viscous
• characteristic dependences on degree of polymerization [psl9] 
  

• semi-crystalline state [pln54]
  
• hierarchical structure (chain-folding, lamellae, spherulites) [psl10]
• lateral versus linear lamellar growth [pln55]
  
• criteria for lateral growth (minimum stem length, temperature window)
  
• velocity of lateral growth
• conditions for fastest lateral growth [pex37] * 
  

• chemical gels [psl11]
  
• physical gels [psl12]
• rubber elasticity [pln64]
• elasticity of balloon during inflation [pex60]
  
• polymer gel [pln65] 
  
• polymer gel free-energy density of mixing [pex14]
• swelling equilibrium of polymer gel [pex13] [pex12] 
  
• polymer gel compressed uniaxially [pex11] 
  
• percolation threshold and gel fraction
  
• percolation on Bethe lattice [pex38], [nex40]   
  

07.  Liquid crystals I

Introduction [pln79]

• common liquid crystal phases [tsl51]
  
• birefringence of nematic phase [pln73]  
• nematic ordering detected via polarized optical microscopy [pex2]  
  
• anisotropic flow behavior of nematics [pln83]
  

Phase transition between isotropic liquid and nematic liquid-crystal phase

• Maier-Saupe theory for nematic ordering [pln74]
  
• orientation function
• agents of nematic ordering
  
• nematic order parameter
• enthalpy and entropy associated with orientational disorder
• nematic order parameter [pln80] 
  
• attributes of nematic order parameter [pex1] 
  
• Maier-Saupe theory I: variational problem [pex43]
  
• Maier-Saupe theory II: free energy, entropy, order parameter [pex44]
  
• Maier-Saupe theory III: first-order phase transition [pex5]
  
• lyotropic transition to nematic phase (Onsager theory simplified) [pln75]
• multicritical NAC point [pln81]
  
• stages of positional ordering [pln82]
  

• boundary effects: splay, twist, bend [psl16]
  
• topological defects: disclinations [psl17]

• anisotropic dielectric response [pln76] 
  
• Fréedericksz transition in LCD [pln77] 
  

08.  Amphiphiles I

Introduction [pln57]  

• hydrophilic and hydrophobic ends
• headgroups: polar, anionic, cationic, zwitterionic
• hierarchical structures and phases [tsl50]  
  
• configurational entropy of water (dynamic network of H-bonds)
  
• hydrophobic interaction between polar and non-polar molecules
  
• amphiphilic reduction of surface tension
• lipids [pln59]
  
• detergency [psl13]
• surface tension and interfacial tension [pln60]
  

• critical aggregation concentration
• aggregation of amphiphiles [psl14]
• packing parameters (geometric argument)
  
• normal versus inverse structures
  
• self-assembly as predicted by geometric argument) [pex39]
• critical micelle concentration (CMC)
  
• spherical micelles and CMC [pex40]
  
• cylindrical micelles and CMC [pex41]
• critical aggregation of bilayers [pex42]
  
• spherical aggregates of colloids [pex50] 
• stability of shapes against thermal fluctuations
• hierarchical ordering at high concentrations [psl15]
• self-assembly in polymers [pln58] 
  
• lamellar spacing in micro-phase-separated diblock polymer melt [pex59]

09.  Ionic soft matter I

Introduction [pln61]

• examples: colloids, polymers, surfactants
• dissociation equilibrium: pK, pH
• control parameters: pH, salinity, electric field,...
• interaction between dissociated groups: Bjeruum length.

• charge neutrality condition
• Donnan equilibrium: effect of salinity [pln62]
  
• Donnan equilibrium between ionic polymer and solvent [pex56]
  
• poly-electrolyte gel [pln66] 
• charge density profile near interface [pln67]
  
• polyelectrolyte gel: double layer of charges at interface [pex57]
  
• poly-electrolyte gel: profiles of ion densities [pex10] 
  
• Poisson-Boltzmann equation for profile of electric potential [pln68]
• electric potential near thin layer of bound charge [pex9] 
  
• electric potential near interface to poly-electrolyte gel [pex8] [pex7] 
  
• Solution of Poisson-Boltzmann equation via Fourier Transform [pln69]
  
• Layer of bound charge of exponential profile and variable thickness [pex6]
• ion densities near charged surface [pln70]
• electric force between parallel plates [pln71] [pln72] [pln78] 
  
• electric potential between charged plates immersed in electrolyte [pex4] 
• electric force between charged plates immersed in electrolyte [pex3] 
  

10.  Microfluidics I

• mass flux [pln85] *
  
• momentum flux [pln86] *
  
• energy flux [pln87] *
  
• divergence of stress tensor [pex61] *
  
• scaled Navier-Stokes equation and the Reynolds number [pex62] *
• viscous friction under simplified conditions [pex63] *
  

  Elementary fluid flow

• Mechanical equilibrium [pln90]
• Flow down incline [pln??]
• 
  

11.  Biological soft matter I: proteins and peptides

Coil-helix transformation

• Zimm-Bragg model (coil pseudo-vacuum)
  
• Zimm-Bragg inside out (helix pseudo-vacuum)
  
• Zimm-Bragg generalized (coil segments with entropy)
• scenario with real transition
  

12.  Biological soft matter II: DNA

• structure of DNA [pln39] *
  
• DNA interaction with fluid medium [pln88] *
  
• DNA melting [pln89] *
  
• unzipping
  

Melting

Unzipping

A.  Glossary of soft-matter physics terms [pln2] *

B.  Tables, maps, and images

C.  Statistically interacting particles with shapes

• fermions [pln4] *
  
• bosons [pln5] *
  
• cargo, economy, business, first [pln6] *
  
• semions (fractional statistics) [pln7] *
  
• particles in orbitals of different energies [pln8] *
  
• distinguishable particles in shared orbitals (compacts) [pln9] *
  
• hosts and caps [pln10] *
  
• hosts, hybrids, and caps [pln11] *
  
• hosts and tags [pln12] *
  
• hosts, hybrids, and tags [pln13] *
  
• statistically interacting particles (generic case) [pln14] *
  

• configurational entropy [pln15] *
  
• partition function [pln16] (2) *
  
• population density of single species [pln17] *
  

• jammed granular matter
• DNA under tension and torque
• polymer mushrooms and brushes
• liquid crystal columnar phase
• protein coil and helix conformations
• colloidal density profile due to gravity or centrifuge
  
• colloidal depletion interaction
  

Some relevant textbooks and monographs

• R. A. L. Jones: Soft condensed matter. Oxford University Press 2002.
• I. W. Hamley: Introduction to soft matter. Wiley, New York 2007.
• M. Daoud and C. E. Williams (Eds.): Soft matter physics. Springer, New York 1999.
• W. Hu and A.-C. Shi (Eds.): Understanding soft condensed matter via modeling and computation. World Scientific, Singapore 2011.
• A. V. Finkelstein and O. P. Ptitsyn: Protein physics. Academic Press, New York 2002.
• M. Doi: Soft matter physics. Oxford University Press 2013.
• T. A. Witten: Structured fluids -- polymers, colloids, surfactants. Oxford University Press 2004.
  
• P. Nelson: Biological physics. Freeman, New York 2004.
• A. Y. Grosberg and A. R. Khokhlov: Statistical physics of macromolecules. AIP Press, New York 1994.
• Henrik Bruus: Theoretical microfluidics. Oxford University Press 2008.
• L.S. Hirst: Fundamentals of soft matter science. CRC Press, London 2013.
• J. V. Selinger: Introduction to the theory of soft matter. Springer, New York 2016.
• M. Kleman and O. D. Lavrentovich: Soft matter physics. Springer, New York 2003.
• I. Teraoka: Polymer solutions -- an introduction to physical properties. Wiley Interscience, New York 2002.
• Jan Kierfeld: Theorie weicher und biologischer Materie. Lecture notes, Technische Universität Dortmund 2009.