Polymer PhysicsPh.D. CourseBehzad PourabbasSahand University of TechnologyFaculty of Polymer Engineering

Outlook

Conductivity Concept in Polymers Electrically Conductive Polymers Liquid Crystal Polymers Electro Active Polymers and their

Applications in Advanced Technologies

References

2 CDs are available, full of Ebooks and references,

Electrical Conductivity

Electrical Conductivity

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.

Electrical Conductivity

Range of Conductivity in Materials

Electrical Conductivity Electrical Conductivity () may occur by Electrons or

IONS. What is the Charge of Carriers? How many Carriers?

And with what speed (mobility)?

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-1s-1)

What happens in the absence of an electric field for the charge carriers?

qn

Electrical Conductivity

There is a drift velocity: and an average for it:

mq

E

mqE

whence

.

+ -+++

---

: time between scattering events

Electrical Conductivity

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).

Electrical Conductivity

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).

Electrical Conductivity

Mobility values for different materials

Electrical Conductivity 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!!!!!

ELECTRICAL CONDUCTIVITY

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.

ELECTRICAL CONDUCTIVITY

. 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)▪ aluminum2.8x10-8 3.6x10-2

▪ brass 8x10-8 10.1x10-2

▪ copper 1.7x10-8 2.2x10-2

▪ platinum 10x10-8 12.7x10-2

▪ silver 1.6x10-8 2.1x10-2

▪ carbon 3.5x10-5 44.5▪ germanium 0.45 5.7x105

▪ silicon 640 6x108

▪ porcelain 1010 - 1012 1016 - 1018

▪ teflon 1014 1020

▪ blood 1.5 1.9x106

▪ fat 24 3x107

ENERGY BANDS IN SOLIDS:

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

Energy Band Structures

16

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.

Band structure and conductivity

Fermi Energy (EF) - highest filled state at 0 K Conduction band -partially filled or empty band Valence band – highest partially or completely

filled bandSemiconductors and insulators, valence band is filled, and no more electrons can be added (Pauli's principle).

Insulators

> 2 eV

Band structure and conductivity

Intrinsic silicon:

DOPED SEMICONDUCTORS: “doped semiconductor”: (also “impure”, “extrinsic”) = semiconductor

with small admixture of trivalent or pentavalent atoms;

n-type material

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.

p-type material

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).

advantages of doped semiconductors:

▪ 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”

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 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

Forward biased pn-junction

Depletion region and potential barrier reduced

Reverse biased diode 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.

Reverse biased diode

Depletion region becomes wider, barrier potential higher

Nobel Prize in 1956 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.

Point-contact-transistor

TRANSISTORS

(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;

operation of pnp transistor:

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 operation 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 Transistors “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.

FET Structure

Polymer Field Effect Transistor

Polymer FETs

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

Conduction Theories

Theories of Electronic ConductionBand structure:

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.

Theories of Electronic Conduction Usual band structure formation in Crystallineinorganic and metallic substances:

Theories of Electronic ConductionPhotoconduction

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,

Theories of Electronic ConductionPhotoconuction

Interaction of light photons with semiconductors: Adsorption of single photons to promote an

electron to conduction band Electron-hole pair formation Absorption edge

gEh

Photoconduction

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).

Photoconduction

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

Photoconduction 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.

Theories of Electronic ConductionHopping Conduction

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.

Theories of Electronic ConductionHopping Conduction

Energy Barrier across the jump path.

Theories of Electronic ConductionHopping Conduction

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.

Theories of Electronic ConductionHopping Conduction

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

Theories of Electronic ConductionHopping Conduction

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.

Band Theory Applied to Polymers There are intra- and inter-molecular

types of electronic motion. Intermolecular conduction is less

important, Why?

Band Theory Applied to Polymers 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.

Band Theory Applied to Polymers 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.

Band Structure: Saturated polymers 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 .

Band Structure: Saturated polymers Polyethylene:

Experimental methods for band structure studies:▪ UV-visble absorption spectroscopy▪ Electron Energy Loss spectroscopy (EELS)▪ Photo electron spectroscopy (XPS and UPS)

Band Structure: Saturated polymers Polyethylene:

Calculated band structure for polyethylene:

Different theoretical models: Solid lines: valence bands, Dashed lines: empty bands: Conduction bands.

Band Structure: Saturated polymers 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.

Band Structure: Saturated polymers 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.

Band Structure: UnSaturated polymers 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:

Band Structure: UnSaturated polymers 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)

Band Structure: UnSaturated polymers 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).

Band Structure: UnSaturated polymers 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.

SuperConduction 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).

The End