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

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

Forces, Energies, and Timescale in Condensed Matter

2004/10/04C. T. Shih

Special Topics on Soft Condensed Matters

Page 2: 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

Page 3: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.
Page 4: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

Type of Forces Two types of bonds: permanent (chemical) bonds an

d temporary (physical) bonds Van der Waals forces: U ~ 2/r6, : polarizability, r: dist

ance. 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 sc

ale ~ covalent bonds Hydrogen bonds: Energy scale~ 2~6×10-20 J Hydrophobic interactions: Energy scale~ 10-20 J

Page 5: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

Intermolecular Forces and Phase Transition

Page 6: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.
Page 7: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.
Page 8: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

Elasticity: Hookean Solid An ideal elastic solid An applied shear stress (剪力) pro

duces a shear strain in response The shear strain is proportional to she

ar stress The constant of proportionality is the

shear modulus

Page 9: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

eG

yxe

F/Aσ

/ :modulusShear

e) small(for ~/ :StrainShear

:StressShear

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

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

Page 11: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

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’

Page 12: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

Real Material: Viscoelastic Hookean solid and Newtonian liquid a

re 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

Page 13: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

Relaxation Time

Page 14: Forces, Energies, and Timescale in Condensed Matter 2004/10/04 C. T. Shih Special Topics on Soft Condensed Matters.

shear-thinning fluid:faster-moving, less viscous

shear-thickening fluid:faster-moving, more viscous


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