Basic Concepts for Simple and Complex Liquids

Abstract

I Thermodynamics, structure and fluctuations 2 A reminder of thermodynamics 36 2.1 State variables and thermodynamic equilibrium 36 2.2 Link with statistical mechanics 42 2.3 Phase coexistence and interfaces 47 2.4 Application 1: scaled particle theory 51 2.5 Application 2: particle insertion 55 2.6 Application 3: critical micellar concentration 57 2.7 Application 4: depletion interactions and solvation forces 62 Further reading 67 3 Equilibrium fluctuations 69 3.1 Gaussian distribution of fluctuations 69 3.2 Density fluctuations in a one-component system 72 3.3 Concentration fluctuations in a mixture 74 3.4 Local order and pair structure 75 3.5 Link with thermodynamics 81 3.6 Static linear response 84 3.7 Application 1: dipole moment fluctuations and dielectric response 85 v vi Contents 3.8 Application 2: determination of the structure from diffraction experiments 3.9 Application 3: form factors of complex objects or molecules 3.10 Application 4: random phase approximation Further reading II Phase transitions 4 Mean field approaches 4.1 Lattice models and mean field treatment 4.2 Landau theory of phase transitions 4.3 Application 1: van der Waals theory of condensation 4.4 Application 2: Flory-Huggins theory of polymer blends 4.5 Application 3: isotropic-nematic transition 4.6 Application 4: freezing 5 Critical fluctuations and scaling 5.1 The correlation length 5.2 Fluctuations and dimensionality 5.3 Scaling ideas 5.4 Application 1: Ginzburg criterion for polymer blends 5.5 Application 2: scaling laws for polymer solutions 5.6 Application 3: finite size scaling III Interfaces and inhomogeneous fluids 6 Macroscopic description of interfaces 6.1 Interfacial tension and excess quantities 6.2 Geometry of curved surfaces 6.3 Wetting phenomena 6.4 Capillary pressure and capillary condensation 6.5 Disjoining pressure and film stability Further reading 7 The density functional approach 7.1 Variational principle 7.2 Some approximate functionals 7.3 Application 1: the fluid-fluid interface 7.4 Application 2: the adsorbed polymer layer 7.5 Application 3: self-assembly of copolymers 7.6 Application 4: electric double-layers 7.7 Application 5: colloid stability Further reading Contents vii 8 Curvature and fluctuations 213 8.1 Fluctuations of interfaces and capillary waves 213 8.2 Membranes and curvature moduli 215 8.3 Fluctuations of membranes 8.4 Steric interactions between membranes 218 Further reading 219 IV Dynamics 9 Phenomenological description of transport processes 9.1 Fluxes, affinities and transport coefficients 220 9.2 Application 1: the diffusion equation 221 9.3 Application 2: spinodal decomposition 224 Further reading 227

The Relaxation Dynamics of a Supercooled Liquid Confined by Rough Walls

“…to study the self part of the van Hove correlation function [68,69]. Also here we have to generalize this function in order to take into account its dependence on z:…”

Model colloidal fluid with competing interactions: Bulk and interfacial properties

“…[1][2][3][4][5][6] The longrange repulsion stems from the colloids being charged, and the short range attraction is generated by the depletion mechanism, 7 arising from the addition of nonadsorbing polymers to the solution. 8 Such competing interactions can give rise to phase behavior that can be very different from that found in "simple" liquids.…”

On the relaxation dynamics of glass-forming systems: Insights from computer simulations

“…Their structure is neither completely disordered as in a gas nor ordered as in a crystal. Therefore the investigation of structural and dynamical properties of liquids remains an active field of research, despite the knowledge that we have on these systems [1,2]. One of the most puzzling behavior of liquids is the temperature dependence of their viscosity η.…”