Forces, Energies, and Timescale in Condensed Matter

2004/10/04C. 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

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

Intermolecular Forces and Phase Transition

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

eG

yxe

F/Aσ

/ :modulusShear

e) small(for ~/ :StrainShear

:StressShear

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

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’

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

Relaxation Time

shear-thinning fluid:faster-moving, less viscous

shear-thickening fluid:faster-moving, more viscous