Soft Matter

Wim van Saarloos is professor emeritus of theoretical physics at the Lorentz Institute at Leiden University. Vincenzo Vitelli is professor of physics at the University of Chicago. Zorana Zeravcic is associate professor of physics in the Gulliver Laboratory at ESPCI Paris.

"A beautiful introduction to the field of soft matter, with a nice conversational and unassuming writing style. . . . [T]he book is a joy to read, with much to offer for new students interested in soft matter and researchers in the field alike."---Suraj Shankar, American Journal of Physics

• List of FiguresPrefaceIntroduction: The Challenges, Relevance, and Fun of Soft MatterI.1 Inspiration from an exampleI.2 Our view of soft matter and our approachI.2.1 Our approach in this bookI.2.2 The hydrodynamic perspectiveI.2.3 A field relevant to societyI.3 Outline of the book and how to use itI GROUNDWORK: FROM CLASSIC RESULTS TO SOFT MATTER TODAY1 Fluid Dynamics1.1 The relevance and attractiveness of a continuum description of fluids1.2 Hydrodynamics as a balance equation of fluid elements1.3 Derivation of the equations1.3.1 The material or convective derivative1.3.2 Separating out the various components of flow1.3.3 Conservation of mass1.3.4 Conservation of momentum1.3.5 Conservation of energy1.4 Once more: Reflections on the underlying picture1.5 The dissipative terms: Onsager reciprocity relations1.6 The stress tensor and heat current for a Newtonian fluid1.6.1 Stress tensor and heat current1.6.2 The resulting hydrodynamic equations1.6.3 Heat diffusion equation1.7 Sound waves1.7.1 The equation for sound propagation1.7.2 Analysis of the equation with damping1.8 When can we treat a flow as incompressible?1.9 The Navier-Stokes equations1.10 The dimensions of physical quantities, dimensionless numbers, and similarity1.10.1 Dimensions of physical quantities1.10.2 The Reynolds number1.10.3 Dimensionless numbers and similarity1.11 From small to large Reynolds numbers1.11.1 Low Reynolds number hydrodynamics1.11.2 Intermediate Reynolds numbers1.11.3 Very large Reynolds numbers1.12 Lubrication approximation for thin film flow1.13 Contact angle, coffee stains, and Marangoni flow1.13.1 Contact angle and wetting1.13.2 Coffee stains resulting from enhanced evaporation at the rim of a droplet1.13.3 Marangoni convection1.14 Bubble oscillations1.15 Droplets1.16 What have we learned1.17 Box 1: Key dimensionless parameters1.18 Problems2 Elasticity2.1 Elasticity: A time honored subject with a twist2.2 The strain tensor2.3 The linear stress-strain relation2.4 The Poisson ratio2.5 Frequency-dependent generalization of the shear modulus2.6 A brief foray into elastodynamics2.6.1 Sound waves in solids: Continuum approach2.6.2 Dynamical matrices: Microscopic description of elasticity2.7 Bending is the low-energy deformation of sheets and rods2.7.1 Scaling with thickness: Dimensional analysis2.7.2 Analysis of the strain and energy of a bent sheet2.7.3 Implications2.8 Static shapes and buckling of rods2.8.1 Geometrical quantities for small deflections2.8.2 Buckling of a long rod2.8.3 The general force and torque balance equations for static rods2.8.4 Equations in the small deflection approximation2.9 Auxetics: Metamaterials with negative Poisson ratio2.10 Packings of particles jammed together: Beyond standard elastic behavior2.10.1 The jamming phase diagram2.10.2 Counting argument for frictionless spheres2.10.3 Scaling of the ratio of elastic constants2.10.4 Excess of low-frequency modes2.10.5 The crossover length scale2.10.6 Jammed packings versus disordered crystals2.10.7 Toward designer granular matter2.11 Dislocations and defect-mediated melting2.12 Topological mechanics2.12.1 Topological waves2.12.2 Topological zero-energy modes2.13 What have we learned2.14 Box 2: Summary of Landau theory2.15 Problems3 Brownian Motion, Thermal Fluctuations, and Diffusion3.1 A matter of scales and description3.2 Langevin equation for Brownian motion3.2.1 Basis of the Langevin equation3.2.2 The Langevin equation3.2.3 Mean square variations of velocity and position: Diffusion3.2.4 The Stokes-Einstein equation for the diffusion coefficient3.2.5 Cutting corners and what we learn from it3.3 The Fokker-Planck equation for the probability distribution3.3.1 The Fokker-Planck equation: Equivalence to a Langevin equation3.3.2 The Fokker-Planck equation for the velocity of the Brownian particle3.3.3 The Fokker-Planck equation for the position of a Brownian particle in an external potential3.3.4 The diffusion equation and its Gaussian solution3.3.5 Self-similarity and self-similar solutions3.3.6 The Kramers problem: Fluctuation-driven escape over a barrier3.4 The master equation3.5 Size matters for diffusion and dispersion of Brownian particles3.5.1 Diffusion3.5.2 Dispersions versus granular media3.6 Probing fluctuations and taking advantage of them as a probe3.6.1 Measuring force constants of biomatter experimentally3.6.2 Directed Brownian motion of molecular motors3.6.3 Bending modulus or surface tension from shape fluctuation measurements3.6.4 Thermal fluctuations in a buckling colloidal chain3.7 Probing soft matter with scattering techniques3.7.1 Essentials of scattering experiments3.7.2 Probing small fluctuations in continuum systems with laser light scattering3.8 What have we learned3.9 Box 3: Calculating thermal averages3.10 ProblemsII SOFT MATTER PHASES4 Colloids4.1 Colloidal dispersions and emulsions4.1.1 Colloids: Fundamental studies4.1.2 Colloids: Application perspective4.2 Colloids as a thermodynamic system with effective interactions4.2.1 Hard core particles: Model system with entropic interactions4.2.2 Colloids tend to attract4.3 Naturally occurring attractive forces between colloids4.3.1 The Van der Waals attraction4.3.2 Depletion interaction4.3.3 Induced attractive interaction due to perturbations of the surrounding medium4.4 Repulsive forces4.4.1 Electrostatic stabilization4.4.2 Steric stabilization by grafting polymers on the surface4.5 Playing with colloids as model systems4.5.1 Colloidal aggregates4.5.2 From spheres, rods, and plates to cubes and beyond4.5.3 The use of colloidal crystals to make optical bandgap materials4.5.4 Colloidal glasses4.5.5 Colloidal motifs as the building blocks of designer matter4.5.6 Colloids as active matter4.6 Non-Newtonian rheology of colloidal dispersions4.6.1 Shear thinning and shear thickening4.6.2 A temporal transition due to competition between aging and rejuvenation4.6.3 Comparison with emulsions4.6.4 Flow of granular media4.7 What have we learned4.8 Problems5 Polymers5.1 The ever-broadening field of polymer science5.2 Polymers: Long chain molecules with many accessible conformations5.3 Ideal chains, excluded volume effects, and the Flory argument5.3.1 The ideal chain model5.3.2 Excluded volume interaction and self-avoiding walks5.3.3 The Flory argument for the excluded volume interaction5.3.4 Taking stock5.4 The wormlike chain model for biopolymers5.4.1 The wormlike chain model and its persistence length5.4.2 Charge effects on the persistence length5.4.3 Why excluded volume effects are small5.4.4 The force-extension curve of the WLC5.5 Polymers in solution5.5.1 The dilute regime5.5.2 From semi-dilute to concentrated solutions5.5.3 Concentrated solutions5.6 Polymer brushes5.7 Flory-Huggins mean-field theory5.7.1 Flory-Huggins approach5.7.2 Flory-Huggins as a mean-field theory5.8 Response of biopolymer networks5.8.1 Biopolymer networks5.8.2 The slack or thermal-fluctuation-induced contraction5.8.3 The stress-strain response of a network5.8.4 Beyond the simple approximation5.9 Reptation and the viscosity of polymer melts5.9.1 The polymer viscosity plays only a limited role in several relevant flow effects5.9.2 Reptation5.10 Non-Newtonian rheology of polymer solutions and melts5.10.1 Importance of polymer stretching effects5.10.2 The dimensionless Weissenberg number5.10.3 The Oldroyd-B and upper convected Maxwell model for polymer rheology5.10.4 Polymer flow instabilities due to hoop stresses5.11 What have we learned5.12 Problems6 Liquid Crystals6.1 Liquid crystals as mesophases6.1.1 A bewildering variety of liquid crystal phases6.1.2 Molecular liquid crystals versus colloidal liquid crystal phases6.1.3 The power of coarse-graining in the spirit of Landau6.1.4 The director field n?6.2 Landau–de Gennes approach to the isotropic-nematic transition6.3 Frank energy expression for the nematic director field6.3.1 The Frank free energy6.3.2 Splay, twist, and bend distortions6.3.3 Boundary conditions6.4 Analysis of equilibrium solutions6.5 Switching the director with a field: The Fréedericksz transition and LCDs6.5.1 The Fréedericksz transition6.5.2 Liquid crystal displays6.6 Topological defects in the director orientation6.6.1 Defects in the director field6.6.2 Visualization of defects in thin samples between crossed polarizers6.6.3 Interaction of defects in two dimensions6.7 Nematohydrodynamics based on non-equilibrium thermodynamics6.8 Playing with the molecular shape6.9 Opportunities and challenges at interfaces with other fields6.9.1 Biological liquid crystals6.9.2 Liquid crystals in droplets and other confined geometries6.9.3 Colloidal liquid crystals and beyond6.9.4 Mesophases of lipid molecules relevant to pharmaceutics, cosmetics, and food6.9.5 Epithelial cells die and disappear near +½ defects6.10 Renormalization group analysis of the defect unbinding transition6.10.1 Statistical mechanics of a gas of Coulomb charges6.10.2 The idea behind the RG calculation: Screening6.10.3 Setting up the RG calculation6.10.4 How to derive the renormalization group flow relations6.10.5 Critical scaling6.11 What have we learned6.12 Problems7 Interfaces, Surfaces, and Membranes7.1 Fluid interfaces7.2 Helfrich free energy for membranes7.3 Virus shapes and buckling transitions in spherical shells7.4 Crumpling of membranes and sheets7.4.1 A crumpling transition in thermal systems?7.4.2 Athermal crumpling by compression7.5 A soft matter realization of the one-dimensional KPZ equation7.6 What have we learned7.7 ProblemsIII ADVANCED TOPICS8 Pattern Formation out of Equilibrium8.1 Spontaneous pattern formation resulting from instabilities8.2 Gearing up for studying patterns in spatially extended systems8.2.1 The pitchfork bifurcation of dynamical systems8.2.2 The Swift-Hohenberg model equation8.2.3 Supercritical versus subcritical transitions8.3 Inspiration: Rayleigh-Bénard convection and Turing patterns8.3.1 The Rayleigh-Bénard instability8.3.2 Turing instabilities8.4 Three types of linear instabilities8.5 Amplitude equations for stationary type I instabilities8.5.1 Inspiration from a simple perturbative calculation for the Swift-Hohenberg equation8.5.2 Amplitude equation in one dimension for ?q real8.5.3 Two-dimensional patterns8.6 Dynamics just above a type II instability8.7 Amplitude equations for oscillatory type I instabilities8.7.1 Amplitude equations for one-dimensional traveling waves8.7.2 Dominant structures: Sources and sinks8.7.3 What about two and higher dimensions?8.8 Amplitude equations for type III instabilities8.9 Taking stock on pattern formation and the amplitude description8.9.1 Box 4: Summary of insights from amplitude equation approach8.9.2 Pattern selection?8.10 Excitable media8.10.1 The basic mechanism of excitable media8.10.2 Excitable waves in chemical systems, nerves, and beyond8.11 What have we learned8.12 Problems9 Active Matter9.1 Hydrodynamic theories of active matter9.2 Flocking9.2.1 The Vicsek model9.2.2 Flocking and the Mermin-Wagner theorem9.2.3 Toner-Tu theory9.3 Motility-induced phase separation9.3.1 Active Brownian particles9.3.2 The mechanism behind the instability9.4 Bacterial suspensions9.5 Active nematics9.5.1 Active nemato-hydrodynamics9.5.2 Transition to chaos and topological defects9.5.3 Self-propulsion of topological defects9.6 Active solids9.6.1 Moving and self-propelled solids9.6.2 Odd elasticity9.6.3 Odd elastodynamics9.7 Chiral active fluids9.7.1 Hydrodynamics of self-spinning particles9.7.2 Odd viscosity9.8 Nonreciprocal phase transitions9.8.1 Chiral phases in nonreciprocal active matter9.8.2 Nonreciprocal pattern formation: A case study9.8.3 Exceptional points and parity-breaking bifurcations9.8.4 Exceptional points-induced instabilities9.9 Applications to biological problems9.9.1 Active gels9.9.2 Active matter effects during morphogenesis9.9.3 Tissue mechanics and vertex models9.10 What have we learned9.11 ProblemsIV PERSPECTIVE: NEW FRONTIERS OF SOFT MATTER10 From Designing Matter to Mimicking Life10.1 Designer matter10.1.1 What we mean by designer matter10.1.2 Basic concepts and definitions10.1.3 Examples10.2 Memory formation in matter10.2.1 Types of memories in matter10.2.2 Examples10.3 Artificial intelligence10.3.1 Types of machine learning10.3.2 Neural network architectures10.3.3 Examples10.4 Artificial life10.4.1 What do we mean by artificial life?10.4.2 Additional concepts and glossary10.4.3 ExamplesAppendix: Notation and Symbols UsedNotesBibliographyImage CreditsIndex