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Forces, Energies, and Timescale in Condensed Matter

Forces, Energies, and Timescale in Condensed Matter. 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters. Intermolecular Forces. (Long range) Attraction → to condense (Hard core) Repulsion → to avoid collapse Isotropic as in the figure? → usually no for soft matters.

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Forces, Energies, and Timescale in Condensed Matter

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  1. Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters

  2. Intermolecular Forces • (Long range) Attraction → to condense • (Hard core) Repulsion → to avoid collapse • Isotropic as in the figure? → usually no for soft matters

  3. Type of Forces • Two types of bonds: permanent (chemical) bonds and temporary (physical) bonds • Van der Waals forces: U ~ a2/r6, a: polarizability, r: distance. Energy scale ~ 10-20 J ~ 724 K • Ionic interactions: Coulomb potential. Energy scale ~ 10-18 J • Covalent bonds: Energy scale ~ 30~100×10-20 J • Metallic bonds: Delocalization of electrons. Energy scale ~ covalent bonds • Hydrogen bonds: Energy scale~ 2~6×10-20 J • Hydrophobic interactions: Energy scale~ 10-20 J

  4. Intermolecular Forces and Phase Transition

  5. Elasticity: Hookean Solid • An ideal elastic solid • An applied shear stress （剪力） produces a shear strain in response • The shear strain is proportional to shear stress • The constant of proportionality is the shear modulus

  6. Viscosity: Newtonian Liquid • An ideal viscous liquid • An applied shear stress produces a flow with a constant shear strain rate in response • The strain rate is proportional to the shear stress, and the constant of proportionality is the viscosity

  7. Newtonian Liquid (conti.) • Imagine some liquid sandwiched between parallel plates of area A separated by a distance y • The plates are moved with a relative velocity v • The force resisting the relative motion of the plates F=Aηv/y • η is the viscosity • v/y is just the time derivative of shear strain, or e’, so it can be written as σ=ηe’

  8. Real Material: Viscoelastic • Hookean solid and Newtonian liquid are two limiting cases of elasticity and viscosity • The behavior of real materials is in between – viscoelastic • There is a particular timescale to determine which kind of response: elastic or viscous

  9. Relaxation Time

  10. shear-thinning fluid: faster-moving, less viscous shear-thickening fluid: faster-moving, more viscous

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