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 es/G0, strain rate de/dts/tG0,
  so that viscosity htG0
• In a microscopic picture tnexp(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 FG 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
T1
T2
T3
T4
T5
fG
T1ltT2ltT3.
4
The regular solution model describes the phase
diagram for two liquids
x1/T
In the liquid solid transition DGb can be
expressed in terms of the latent heat of fusion
Hm DGb - DTDHm/Tm