Viscoelastic response in soft matter Soft matter materials are viscoelastic: solid behavior at short time – liquid behavior after a time  Shear strain; e=  /G 0, strain rate; de/dt=  /  G 0, so that viscosity;  ~  G 0 In a microscopic picture:  ~ exp(  /kT) where is the frequency of molecular vibration and  is the bond energy. As a result we expect viscosity to be Arrhenius.  often depends on (de/dt) resulting in a shear thinning or shear thickening

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):  F mix =  U – T  S; or in enthalpy (H):  G mix =  H - T  S. The  interaction parameter is a unit less parameter to compare the interaction energy between dissimilar molecules and their self-interaction energy. The change of  F mix with  (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  = 2. At the critical point, interfacial energy,  = 0.

Constructing a Phase Diagram T1T1 T2T2 T3T3 T4T4 T5T5 T 1 <T 2 <T 3 …. Co-existence where: Spinodal where: GG  =2  >2

The regular solution model describes the phase diagram for two liquids x~1/T In the liquid solid transition  G b can be expressed in terms of the latent heat of fusion H m ;  G b = -  T  H m /T m