Complex Fluids, Soft Matter and the Jamming Transition Problem

fr. Matière Molle.

When experiments are performed on thermodynamic systems, the quantities which are easiest to measure are the response functions. Generally, we change one parameter in the system and see how other parameters respond to that change under highly controlled conditions. They also provide a measure of the size fluctuations in a thermodynamic system (Reichl 1998). Response functions are the usual method for characterizing the macroscopic behaviour of a system. They are experimentally measured from changes in thermodynamic coordinates with external probes.

Supramolecular structures are large molecules formed by bonding smaller molecules together.

Viscoelasticity is referred to as the phenomenon in which the stress and strain of some materials depends on time. Viscoelasticity is the combination of viscous and elastic response of a material subjected to constant strain, constant stress, or oscillatory stress and strain. Let recall that elasticity deals with the mechanical properties of elastic solids, which obey Hooke’s law: stress (\(\sigma \)) is proportional to strain (\(\gamma \)), i.e., \(\sigma = G \gamma \), where \(G\) is the shear modulus which is independent of the applied strain at low values. On the other hand, viscosity deals with the properties of liquids in the classical theory of hydrodynamics according to Newton’s law: \(\sigma = \eta \dot{\gamma }\), where \(\eta \) is the viscosity which is independent of the applied shear rate at low values. Whether a material behaves as an elastic solid or a viscous liquid depends on the length time over which an experiment will be done. Shear modulus is defined as the ratio of shear stress to the shear strain, and it is useful for measuring the stiffness of materials.

We have introduced features for granular matter trying to make a broad classification of all of them.

Amphiphilic molecules possess both hydrophilic (polar) and lipophilic (fat loving) parts. They are related to molecules having a polar, water-soluble group attached to a nonpolar, water-insoluble hydrocarbon chain.

What does a self-assembly mean? It is a type of process in which a disordered system of pre-existing components forms an organized structure of patterns as a consequence of specific, local interactions among the components themselves, without external direction.

A micelle is an aggregate of surfactant molecules dispersed in a liquid colloid. A surfactant is a substance which exhibits some superficial o interfacial activity.

In the smectic-A mesophase, the director is perpendicular to the smectic plane and there is no particular positional order in the layer. Similarly, the smectic-B mesophase is faced with the director perpendicular to the smectic plane, but the molecules are arranged into a network of hexagons within the layer. In the smectic-C mesophase, molecules are arranged as in the smectic-A mesophase, but the director is at a constant tilt angle measured normally to the smectic plane.

They should have considered the work done by Ciamarra et al. (2010), where they made certain modifications to the Liu-Nagel’s phase diagram taking into account the role of infinite relaxation times and the convex shape of the jamming region.

An important feature of granular materials is that the internal forces are not carried uniformly by the material, but instead through long chain-like structures whose density and orientation depend on the state and history of the sample. This feature allows us to study some problems of information propagation in GM using percolation theory.

Following H. A. Barnes (1999), yield stress is defined for liquids and solids. In the first case, yield stress is a point at which, when decreasing the applied stress, solid-like behaviour is first seen, i.e., no continual deformation. In the latter case, it is essentially the point at which, when increasing the applied stress, the solid first shows liquid-like behaviour, i.e. continual deformation.

For some super-cooled liquids, the temperature dependence on relaxation times or on transport properties, such as the diffusion constant, is stronger than predicted by Arrhenius law. Arrhenius law refers to the fact that in some viscous liquids \(\log \eta \) (\(\eta \) is the viscosity) is linear in \(T^{-1}\) (\(T\) is the temperature).

Critical phenomena are phenomena observed near a critical point and this is precisely a point in the phase diagram where a continuous phase transition takes place.

\(\xi =\xi _0 e^{\frac{A}{T-T_0}}\).

Owing to the co-existence of quantities that vary continuously at the transition, such as the pressure and the shear modulus, and of quantities that change discontinuously, such as the mean contact number per particle (van Hecke 2010).

\(V(r_{i,\,j})=\dfrac{A}{r_{i,\,j}^{36}}+B\dfrac{e^{-k r_{i,\,j} }}{r_{i,\,j}}-\dfrac{C}{r_{i,\,j}^{6}}\).