美国材料化学课程 1-3

Dielectric constant as a function of frequency
• Determining kD over the entire frequency range is complicated • Typically can determine kD directly up to about 100 GHz • Electric dipoles → electric charge → internal electric field • Charge associated with field = capacitance
Case Study: Water, Methane and Hexane
• Total vdW interaction NRG
2 2 2 u u 2 3 h u o 1 2 w (r ) vdW 2 6 2 2 6 6 4 4 r 3 4 kTr 4 r o o o
vdW interactions are relatively weak compared to ionic and covalent forces and as such can be ignored
• Between atoms and molecules vdW interactions decrease by r-6 • HOWEVER, Hamaker showed that for condensed phases vdW interactions decrease by D-1 • THUS, vdW interactions are very important in determining properties of condensed materials
o 4 o n 1 3 M 2 n 2 4 N
2 o
was
calculated
using
the
Lorenz-Lorenz
equation:
where M is molecular weight (Mhexane = 86.18 g.mol-1 or 86.18x10-
vdW interactions cannot take place without light, because how would atoms generate EM waves
• First, wave-particle duality means electrons have a wave function associated with them • Second, the interaction of wave functions between two atoms means no external EM source needed (i.e. electronic polarization) • Third, in Keesom and Debye interactions an EM field generating dipole is already present • Experimental observations: surface tension of water does not change from a lit room to a dark room; deviations from ideal gas law for gases in closed dark containers still persists.







• Can be summarized as follows
w
vdW
(r)
C
vdW
r
6

C d
C r
o
C
i
6
Case Study: Water, Methane and Hexane
Table of selected properties for water, methane, and hexane at RT.
vdW Misconceptions
A vdW interaction is composed of only London (dispersion) forces.
1. London or Dispersion 2. Keesom or Rotational or Orientational 3. Debye or Induced
Solubility of a van der Waals Material in a Liquid
• vdW interactions tend to be generally attractive • HOWEVER, this does not imply that 2 vdW materials will mix • Must consider the NRG associated will all possible combinations

i 11
i
i


i
2
• However discontinuities are not convenient
N
C
k D ,imag inary ( ) 1

i 1 1


i

2
• Thus, we use imaginary kD when discussing dielectric constant
Water(l) (H2O) Methane(g) (CH4) n-Hexane(l) (C6H14)
a units for o are normalized to give o .
4 o
b 1D 3 . 336 x 10 30 C.m . c The electronic polarizability
Liquid Electronic Polarizability (10-30m3 a) 1.48 2.60 11.9c Dipole Moment (Debyesb) 1.85 0 ~0 Dielectric Constant 78 1.70 1.89 Refractive Index 1.3330 1.3038 1.3751
1791-1867
Let’s use the data
• What is the relationship between kD and refractive index? • What does having a kD larger than n2 imply about the vdW interactions present in the material? • Draw a graphical representation of kD as a function of frequency
Michael Faraday
• • • • • British Scientist – great experimentalist Inventor of the Bunsen burner Poor, self made with help from Davy Faraday’s law is one of the 4 Maxwell eqns Discovered benzene and invented oxidation numbering system; also first to liquefy chlorine • Faraday effect: light and magnetism are related • Diamagnetism • Faraday cage: external charge has no influence on anything enclosed inside a conductor
Dielectric constant as a function of frequency
• If we understand the source of kD, then upon inspection we can understand the nature of a material • Recall…
What happens when an external EM field is present
• When a external field is present:
– Dispersion – Keesom
• Take place in accordance to external field • Debye interactions are not relevant
J. Willard Gibbs
• A Yale man Passed away before the advent of the Nobel Prize (did win the Copley Medal from the Royal Society) • Father of Chemical Thermodynamics, one of the founders of vector analysis, optics, electromagnetic theory • Might be called one of the fathers of physical chemistry • First engineering Ph.D in the U.S. • Has his own stamp
C
kDA o t
Dielectric constant as a function of frequency
C kDA o t
• capacitance measured in Farads
C A 2 .s 4 1F V kg .m 2