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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

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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.

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

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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

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