Transcript Polymer Physics Ph.D. Course - Polymer Engineering Faculty

Behzad Pourabbas
Sahand University of Technology
Faculty of Polymer Engineering




Conductivity Concept in Polymers
Electrically Conductive Polymers
Liquid Crystal Polymers
Electro Active Polymers and their
Applications in Advanced Technologies

2 CDs are available,
 full of Ebooks and references,



Electrical conductivity of A MATTER is its
ability to conduct electrons.
We can measure it by measuring Resistivity
very easily by several methods, Using one
OHM meter forexample.
There are more complicated and standard
method to do this.

Range of Conductivity in Materials
Electrical Conductivity () may occur by Electrons or
IONS.
 What is the Charge of Carriers? How many Carriers?
And with what speed (mobility)?

  qn
The ease with which the charged species will move
under the influence of the applied electric field E and
is usually expressed as a velocity per unit field (m2V-1s1)
 What happens in the absence of an electric field for
the charge carriers?


There is a drift velocity: and an average for it:
: time between
scattering events
qE
 
.
m

+
+
+
+
q
whence  

E
m
-

Mobile Species:
 Electrons and Holes: (Electronic Conductors)
▪ Electron is an Electron but (Negative Charge)
▪ Hole is the empty place of a moved electron (Positively
Charged).
 Cations and Anions, (Ionic Conductors).



Theories of Conductions are aimed to explain
how n and  depend on molecular structure,
T and applied field.
In Polymers, the mobility depends on
morphology as well.
There is a large range of mobity values for
different materials. (The next Slide).
 Mobility values for different materials

Conductivity in POLYMERS:
 They are usually insulators if:
▪ There is no charged species : (polymers are composed of covalent
bonds)
▪ Careful separation of any ionic species from for example: catalysts
residues; Initiators, Ionic End groups, Oxidation Products.

Conversely,
 One insulating polymer can made conductive by adding
conductive fillers such as carbon black or metallic particles
(Gold, Silver, Nickel,..) (Conductive Composites).

There are substantially conductive polymers as
well!!!!!

in order of conductivity: superconductors,
conductors, semiconductors, insulators
 conductors: material capable of carrying electric current, i.e. material
which has “mobile charge carriers” (e.g. electrons, ions,..)
e.g. metals, liquids with ions (water, molten ionic compounds), plasma
 insulators: materials with no or very few free charge carriers; e.g. quartz,
most covalent and ionic solids, plastics
 semiconductors: materials with conductivity between that of conductors
and insulators; e.g. germanium Ge, silicon Si, GaAs, GaP, InP
 superconductors: certain materials have zero resistivity at very low
temperature.
.

some representative resistivities ():

R = L/A, R = resistance, L = length, A = cross section area; resistivity at 20o C
resistivity in  m
▪
▪
▪
▪
▪
▪
▪
▪
▪
▪
▪
▪
resistance(in )(L=1m, diam =1mm)
aluminum 2.8x10-8
brass
8x10-8
copper
1.7x10-8
platinum 10x10-8
silver
1.6x10-8
carbon
3.5x10-5
germanium
0.45
silicon
 640
porcelain 1010 - 1012
teflon
1014
blood
1.5
fat
24
3.6x10-2
10.1x10-2
2.2x10-2
12.7x10-2
2.1x10-2
44.5
5.7x105
 6x108
1016 - 1018
1020
1.9x106
3x107
 In solid materials, electron energy levels form bands of allowed energies,





separated by forbidden bands
valence band = outermost (highest) band filled with electrons (“filled” = all
states occupied)
conduction band = next highest band to valence band (empty or partly filled)
“gap” = energy difference between valence and conduction bands, = width of
the forbidden band
Note:
▪ electrons in a completely filled band cannot move, since all states
occupied (Pauli principle); only way to move would be to “jump” into next
higher band - needs energy;
▪ electrons in partly filled band can move, since there are free states to
move to.
Classification of solids into three types, according to their band structure:
▪ insulators: gap = forbidden region between highest filled band (valence
band) and lowest empty or partly filled band (conduction band) is very
wide, about 3 to 6 eV;
▪ semiconductors: gap is small - about 0.1 to 1 eV;
▪ conductors: valence band only partially filled, or (if it is filled), the next
allowed empty band overlaps with it
Atoms form a solid  valence electrons interact  two quantum mechanical
effects.
Heisenberg's uncertainty principle: constrain electrons to a small volume  raises
their energy called promotion.
Pauli exclusion principle limits the number of electrons with the same energy.
Result: valence electrons form wide electron energy bands in a solid.
Bands separated by gaps, where electrons cannot exist.
16
 Fermi Energy (EF) - highest filled state at 0 K
 Conduction band -partially filled or empty band
 Valence band – highest partially or completely
filled band
Semiconductors and insulators, valence band is filled, and no more electrons can
be added (Pauli's principle).
Insulators
> 2 eV

Intrinsic silicon:

DOPED SEMICONDUCTORS

:
“doped semiconductor”: (also “impure”, “extrinsic”) = semiconductor with small
admixture of trivalent or pentavalent atoms;

donor (n-type) impurities:
▪ dopant with 5 valence electrons (e.g. P, As, Sb)
▪ 4 electrons used for covalent bonds with surrounding Si atoms, one
electron “left over”;
▪ left over electron is only loosely bound only small amount of energy
needed to lift it into conduction band (0.05 eV in Si)
▪  “n-type semiconductor”, has conduction electrons, no holes (apart from
the few intrinsic holes)
▪ example: doping fraction of 10-8 Sb in Si yields about 5x1016 conduction
electrons per cubic centimeter at room temperature.
 acceptor (p-type) impurities:
▪ dopant with 3 valence electrons (e.g. B, Al, Ga, In)  only 3 of
the 4 covalent bonds filled  vacancy in the fourth covalent
bond  hole
▪ “p-type semiconductor”, has mobile holes, very few mobile
electrons (only the intrinsic ones).
▪ Can “tune” conductivity by choice of doping fraction
▪ can choose “majority carrier” (electron or hole)
▪ can vary doping fraction and/or majority carrier within
piece of semiconductor
▪ can make “p-n junctions” (diodes) and “transistors”

p-n JUNCTION:
▪ p-n junction = semiconductor in which impurity changes abruptly from p-type to n-type ;
▪ “diffusion” = movement due to difference in concentration, from higher to lower
concentration;
▪ in absence of electric field across the junction, holes “diffuse” towards and across
boundary into n-type and capture electrons;
▪ electrons diffuse across boundary, fall into holes (“recombination of majority carriers”); 
formation of a “depletion region” (= region without free charge carriers) around the
boundary;
▪ charged ions are left behind (cannot move):
▪ negative ions left on p-side  net negative charge on p-side of the junction;
▪ positive ions left on n-side  net positive charge on n-side of the junction
▪  electric field across junction which prevents further diffusion.
 diode = “biased p-n junction”, i.e. p-n junction with voltage applied
across it
 “forward biased”: p-side more positive than n-side;
 “reverse biased”: n-side more positive than p-side;
 forward biased diode:
▪ the direction of the electric field is from p-side towards n-side
▪  p-type charge carriers (positive holes) in p-side are pushed
towards and across the p-n boundary,
▪ n-type carriers (negative electrons) in n-side are pushed towards
and across n-p boundary
 current flows across p-n boundary

Depletion region and potential barrier
reduced
 reverse biased diode: applied voltage makes n-side more positive than
p-side  electric field direction is from n-side towards
p-side
 pushes charge carriers away from the p-n boundary
 depletion region widens, and no current flows

diode only conducts when positive voltage applied to p-side and
negative voltage to n-side
 diodes used in “rectifiers”, to convert ac voltage to dc.

Depletion region becomes wider,
barrier potential higher


Shockley, Brattain and Bardeen start
working with p- and n- type germanium
and silicon semiconductors in 1946
Bardeen and Brattain put together the first
transistor in December 1947:
 a point-contact transistor consisting of a single
germanium crystal with a p- and an n- zone.
Two wires made contact with the crystal near
the junction between the two zones like the
“whiskers” of a crystal-radio set.
 (bipolar) transistor = combination of two diodes that share middle portion,




called “base” of transistor; other two sections: “emitter'' and “collector”;
usually, base is very thin and lightly doped.
two kinds of bipolar transistors: pnp and npn transistors
“pnp” means emitter is p-type, base is n-type, and collector is p-type
material;
in “normal operation of pnp transistor, apply positive voltage to emitter,
negative voltage to collector;
 if emitter-base junction is forward biased, “holes flow” from battery into
emitter, move into base;
 some holes annihilate with electrons in n-type base, but base thin and lightly
doped  most holes make it through base into collector,
 holes move through collector into negative terminal of battery; i.e. “collector
current” flows whose size depends on how many holes have been captured by
electrons in the base;
 this depends on the number of n-type carriers in the base which can be
controlled by the size of the current (the “base current”) that is allowed to
flow from the base to the emitter; the base current is usually very small; small
changes in the base current can cause a big difference in the collector
current;
 transistor acts as amplifier of base current, since small changes in base
current cause big changes in collector current.
 transistor as switch: if voltage applied to base is such that emitter-base
junction is reverse-biased, no current flows through transistor -- transistor is
“off”
 therefore, a transistor can be used as a voltage-controlled switch; computers
use transistors in this way.

“field-effect transistor” (FET)
 in a pnp FET, current flowing through a thin channel of n-type material is
controlled by the voltage (electric field) applied to two pieces of p-type
material on either side of the channel (current depends on electric field).
 This is the kind of transistor most commonly used in computers.

Due to improvements in manufacturing, integrated circuits became
smaller and smaller

Gordon Moore observed that “the number of transistors on a chip
seems to double every year….”
 Moore’s Law: the number of transistors on a chip seems to double every 18
months, while the price remains the same.
 Grosch’s law for mainframes: every year, the power of computers doubles
while the price is cut in half
Electronic conduction in organic molecular substance
differs in several important ways from familiar metallic
and inorganic semiconductors like silicone and
germanium.
 Even in idealized model, there are significant
differences between inorganic and polymer conductors.

 In polymers, the interaction between charge carriers is
generally less well screened than in inorganic materials
(Electron-electron and electron-hole interaction tend to
localize electronic states to a much larger extend ) .
 Resent studies of theses effects show that band structure
may not be the best model even for ideal chains.
Usual band structure
formation in
Crystalline
inorganic and
metallic
substances:


Exposure of a semiconductor to light or other
electromagnetic radiation may produce a
temporary increase in the population of free
charge carriers, and the resulting extra flow
of current under influence of an applied
electric fields is called photoconduction,

Interaction of light photons with semiconductors:
 Adsorption of single photons to promote an electron to
conduction band

Electron-hole pair
formation
 Absorption edge
h  E g




Recombination (Electron-hole):
If electron-hole pair have enough Energy
grater than Coulomb interaction No
recombination occurs.
If the electron –hole separation is such that
Coulomb Interaction < kT, They are easily
movable.
Coulomb Capture Radius: When Coulumb
Interaction is equal to Thermal Energy (kT).

Excitons:
 If electron-hole pair can not escape their
electrostatic attraction, this can lead to EXCITONS.
 Excitons are mobile electronic States.
 They can not transport charge by themselves but
they can produce unbound charges

Excitons:
 Can collid to each other or other impurities:
▪ Fusion; Collide to produce electron-hole pairs
▪ Fission; Collide to defects, surface (NanoTechnology) and impurities to
separate into charge carriers.
▪ The surface effect ; Photoinjection of Carrieres is especially important in
organic materials where direct charge carries is less probable.
 Hopping condition makes charge transport
possible where band conduction no longer
occurs.
 Just as carriers can be generates thermally by
excitation of electrons across the band gap from
the valance band to acceptor states or from donor
to the conduction band – so it is also possible to
move charges between localized states by
thermal excitation.
 Energy Barrier across the jump path.
 An Electron may either hop over or tunnel
through the barrier.
 The relative importance of these two mechanisms
depends on the shape of the barrier, the
separation of the sites and the accessability of
thermal energy.
 both is also possible.
 Temperature dependence of conduction is a good
criteria for the mechanisms Identification.
Electron
needs
enough
energy
Sepa ration must be
short enough
 As the disorder in the lattice increases both the
energetic and spatial distribution of atoms (in
amorphous material), the electronic energy states
spread as a continuous tail into what is normally
the forbidden energy zone, and the electrons in
these states are localized.


There are intra- and inter-molecular types of
electronic motion.
Intermolecular conduction is less important,
Why?
If the polymer chain is considered as
1-dimensional lattice: the assumptions for
conductions are:
1. A definitely spaced series of atoms with fixed
distance between nearest neighbors.
2. Small separation of atoms giving good overlap
of atomic orbital.
3. A full valance shell. Analogous to a full valance
band.
4. A relatively large excitation energy to the
lowest excited electronic state, corresponding
to strong chemical binding.



In the case of a saturated
polymers such as polyethylene,
the strength of -bonding is so
that the band gap will be
comparable to that in diamond
For a polymer such as
polyacetylene the chemical
binding of the π-electrons is
much weaker, a gap of a few eV
comparable to those in
inorganic semiconductors , as is
anticipated.

Polyethylene:
 Perfect single Crystal is needed. (Practically almost impossible).
 Chain defects makes the calculation and experiments difficult
to be carried out.
 Using models: Waxes or Small chains (n-alkanes as models)
 Predicted band gap: greater than 5 ev
 Holes Mobility: 5x10-3 m2V-1s-1 .

Polyethylene:
 Experimental methods for band structure studies:
▪ UV-visble absorption spectroscopy
▪ Electron Energy Loss spectroscopy (EELS)
▪ Photo electron spectroscopy (XPS and UPS)

Polyethylene:
 Calculated band structure for polyethylene:
Different theoretical models: Solid lines: valence bands,
Dashed lines: empty bands: Conduction bands.

Polyethylene:
 Density of states obtained by XPS and theoretical
approximations:
a) Calculated density of states for PE;
b and c: Calculated photoelectron
spectroscopy with instrumental half-width
of 0.2 and 0.75 eV.
d) Comparison of calculated and observed
XPS spectrum.

Polyethylene:
 There are ambiguity in Band gap energies
obtained by different experimental methods.
 7.6, 8.8 and 9.1 eV have been reported.
 Molten state (amorphous) changes the band
structure specially the conduction band (lowers).
 This is still an open problem.

Polyacetylene:
 Trans-Polyacetylen (t-PAc); the first polymer with
metallic levels of conduction (1977, Shirakava).
 The simplest conductive polymer:
 Two main structures: equal bond lengths and
alternation band lengths:

Polyacetylene:
 A framework by σ-bonds that support π–




electrons.
One electron per lattice site.
One dimensional lattice.
In this model, electrons are considered to be able
to move along the chain.
This model is unstable: leading to shorter and
longer (structure b)

Polyacetylene:
 In this model, electrons are localized.
 An energy gap is introduced into the electron
states which lowers the energy of the π-electrons.
 This is the most stable structure for polyacetylene
(with energy gap).

Polyacetylene:
 Another proposed structure: Bond alternation defect (1962).
 One unpaired π–electron at the place of defect.
 ESR experiments support this structure.
 This would be thermodynamically unstable unless the length of the
defect increase to several repeating unit (solitons).
 Solitons are predicted to move along the chain.
 Further discussions on unsaturated conductive polymer will be given
in future sections.







Conduction with zero electrical resistivity.
This occurs in metals usually below 20K (1911).
The phenomenon has been utilized in high magnetic
field production and lossless power transmission.
The superconduction occurs in polymers at high
temperatures (1964).
Organic salts (selenium organics and fulleren salts
have shown superconductivity at 2 and 40 K.
For complex cooper oxides higher transition
temperatures Tc, has been recorded.
Poly sulfur nitride, was the first polymer (inorganic)
with superconduction properties (0.26 K).