Viscoelastic response in soft matter

1. Viscoelastic response in soft matter • Soft matter materials are viscoelastic: solid behavior at short time – liquid behavior after a time t. • Shear strain; e=s/G0, strain rate; de/dt=s/tG0, so that viscosity; h~tG0 • In a microscopic picture: t~nexp(e/kT) where n is the frequency of molecular vibration and e is the bond energy. As a result we expect viscosity to be Arrhenius. • h often depends on (de/dt) resulting in a shear thinning or shear thickening

2. Phase transitions • Both F&G goes to a minimum at equilibrium. A first order phase transition occurs when two phases have identical F (Helmholtz free energy) or G (Gibbs free energy). • A change in free energy is determined by changes in internal energy (U) and entropy (S): DFmix = DU – TDS; or in enthalpy (H): DGmix = DH - TDS. • The c interaction parameter is a unit less parameter to compare the interaction energy between dissimilar molecules and their self-interaction energy. • The change of DFmix with c (and T) leads to stable, metastable and unstable regions of the phase diagram. • For simple liquids, with molecules of the same size, assuming non-compressibility, the critical point occurs when c = 2. • At the critical point, interfacial energy, g = 0.

3. Constructing a Phase Diagram Spinodal where: Co-existence where: c >2 c =2 T1 T2 T3 T4 T5 fG T1<T2<T3….

4. The regular solution model describes the phase diagram for two liquids x~1/T In the liquid solid transition DGb can be expressed in terms of the latent heat of fusion Hm; DGb= - DTDHm/Tm