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Polymers

Polymers A large molecule consisting of repeating smaller structural units (called monmrt units)
Polymerization The sequence of repetitive reactions between a monomer unit and the growing
macromolecule or polymer chain
ie. CH2=CH2 →→→→ [-CH2-CH2-]n

a monomer unit polymerization polymer


Categories of polymers, by Structural Linking of Monomer Units
Homopolymer Only one type of monomer molecule is used to make a polymer, with repeating units of
this one monomer
Copolymer Polymer formed by the combination of 2 or more different monomer molecules; The
sequence arrangement of these units can vary in four different ways.
1) Random copolymer random sequence of different monomer units (A and B)
-A-A-B-B-B-A-B-B-
2) Alternating copolymer alternating sequence of monomer units
-A-B-A-B-A-B-A-B-
3) Block copolymer a sequence where there are repeating blocks of identical monomer units.
-A-A-A-A-B-B-B-B-A-A-A-A-B-B-B-B-
4) Graft copolymer a chain which have side-chains from which to create extensions to
another polymer chain.
CH2 CH CH2 CH CH2 CH CH2 CH

side-chain extension
reaction
n
O OCH3 O OCH3
polystyrene chain
n

The ester could further be functionalized


by nucleophilic additon to the carbonyl
and expulsionof -OCH3 groups
-perhaps by a polyamide chain
Polymers are commonly named according to the chemical structure of the
monomer unit, and then the prefix poly is added.
Monomer Polymer Commercial Use
ethylene -[-CH2CH2-]n- plastic bags, film
CH2=CH2 polyethylene nearly everything
Cl
vinyl chloride CH2 CH plastic fittings and valves
n
CH2=CH-Cl poly(vinyl chloride) tubing
(PVC)
tetrafluoroethylene -[-CF2CF2-]n- inert, non-stickcaoting
CF2=CF2 poly(tetrafluoroethylene) used in carpets to make
(Teflon) them stain resistant
ethylene glycol poly(ethyleneglycol) emulsifying and thickening
HO-CH2CH2-OH (PEG) agent
(-CH2CH2-O)- (non edible) in shampoos,
lubricant oils, antifreeze
acrylonitrile CN
CH2 CH
used to make a co-polymer
CH2=CH-C≡N n with PMMA
poly(acrylonitrile) (polymethylmethacrylate) in
Orlon, Acrilan acrylic fibres for clothing
terephthalic acid O O plastic pop bottles
C C O CH2 CH2 O
O O n clothing
HO C C OH
poly(ethylene terephthalate) fibres
(PET
Physical properties

The structure of the monomer will confer unique structural and physical characteristics
in the polymer at different temperatures.
Some polymer chains can pack or arrange/order themselves in a highly organized
manner, resulting in highly crystalline material. For example linear polyethylene

Some polymer chains have branching on the chain and cannot order themselves in a
crystalline lattice and often said to be amorphous solids. For example rubber
(polyisoprene)
Most polymers are semi-crystalline, where some regions are highly ordered and
crystalline, while other regions are not and have amorphous properties.
Intermolecular forces that increase the melting point of a polymer are:
a) structural regularity in polymer chain
b) bond rigidity
c) close-packing ability
d) strong inter-chain attractive forces (eg. H-bonding)
Polymer R-Goup Physical Poperty
Examples O O solid
C C O R O
n
CH2 CH2 Melting point 265°C
a terephthalate-based
poyester
CH2 CH not crystalline
CH3
CH2 CH CH2 not crystalline
CH3
CH3 solid
CH2 C CH2
Melting point 140°C
CH3
H3C
O O
solid
C C O R O Melting point 170°C
n
CH2 CH2
CH3
O O solid
C C O R O
n
CH2 CH2 Melting point 70°C
CH3
soft and rubbery
CH 2 CH
n
C O
O
CH 3
poly(methacrylate)
CH3 hard plastic
CH2 C
n Melting point 200°C
C O
O
CH3
poly(methyl
methacrylate)
solid
CH2 CH
n absorbs water
C O used in diapers
OH
poly(acrylic acid)
soft plastic
CH2 CH
n used in making
C O soft contact lenses
NH2
polyacrylamide
Polymers

Free radical Polymerization


Initiation -usually by homolysis of an initiator molecule for example benzoyl peroxide.

Benzoyl peroxide
O O O
heat
Ph O O 2 O Ph + CO2
Ph Ph β-bond
homolysis
cleavage

Radical chain
polymerization
initiating
species

phenyl -- Ph
Radical Polymerization of vinyl Monomers: H2C CH

For example styrene.

Propagation steps: Styrene

Ph
In In
H2C Ph

styrene benzylic radical


Where "In" is formed
by homolysis of a suitable
initiator molecule
e.g. "In" = Ph from decomposition
of benozyl peroxide

Ph Ph Ph
In In
H2C Ph

etc. H2C Ph

Note: the polymer is not homogeneous Ph


with respect to molecular weight.
i.e. a mixture of polymers
with different number of units
in each chain is formed n

polystyrene
Chain termination:
Ph Ph Ph Ph
In In
Radical combination: n
n

Ph Ph Ph Ph
In In

n n

Ph
H-atom transfer Ph Ph
In Ph
H
n H
H
In
n

Ph Ph Ph
Ph In
In H +
n H H n
Chain transfer to polymer

R R
In
H H n
n

R
R R
In +
H
n H n

terminated poly mer chain new radical site along a poly mer molecule
chain

m R

Branched chain R
poly mer f ormation

R
m

R
Intramolecular H-Atom Transfer

new site f or poly mer


chain extension
H
H H
CH 2 C CH 2 CH 2 C CH 3

H2 C CH 2
H2 C CH 2
C
H2 C
H2
growing chain of poly ethy lene

CH2=CH2

CH 2 CH CH 2 CH 2

n
H2 C
4-carbon CH 2
branch

H2 C
CH 3
This process occurs frequently during free radical polymerization of polyethylene
Branching prevents close-packing of the polymer chains and lowers the density of
the polymer (called low-density polyethylene)

High density poly ethylene, formed by other methods, has little branching and has
substantial regions of crystallinity resulting from close-packing of the polymer chains

High Density Polyethylene Low Density P


What effect does branching have on the physical properties of a polymer (packing, density and melting point)

Branching causes a decrease in melting point, decreases density and makes the material more amorphous.
Branching causes a decrease in the intermolecular forces between the molecules. For example vegetable oils
are unsaturated and contain cis double bonds. The double bonds do not allow the molecules to pack well
together and thus the intermolecular forces between the molecules are weak. To make margarine vegetable
oil is hydrogenated (hydrogen is added to the double bonds) to make saturated fatty acids. Since the
molecules pack better together the oil becomes a solid. The oil is only partially hydrogenated because if the
oil becomes completely saturated it becomes hard and brittle. One problem with partial hydrogenation, is that
the catalyst isomerizes some of the unreacted cis double bonds to the unnatural trans arrangement, and there
is accumulating evidence that “trans” fats are associated with an increased risk of cardiovascular disease.
Frequent chain terminations by this mechanism decrease the average molecular weight of the polymer
obtained in this way
For some monomers (e.g. propylene) this process occurs so frequently that polymers of useful chain length
cannot be made by free radical polymerization
Some vinyl polymers

H2C CF2 used in piezoelectric material


audio speakers and microphones used in plastics, stryofoam
H2C CHCl vinylidine fluoride and isolation

vinyl chloride monomer styrene

ion exchange resins


N O plastics, plexiglas
CH2 CH
4-vinylpyridine
Cl n O
methyl methacrylate
PVC polymer
photoresists for
microelectronics thickeners adhesives
O sporting goods
O HO
acrylic acid
O
t-BOC styrene
O
O O soft contact
lenses
CH2
O (CH2)6 O CN
CH2
OH
cyano-biphenyl mesogenic monomer
side chain liquid crystal polymer hydroxy ethyl methacrylate
(HEMA)
Interpenetrating polymer

There are many compounds that have been developed containing more than
one polymerizable vinyl group. As you can expect with two reactive sites on one
monomer at some point crosslinking will occur. Interpenetrating polymer
networks or IPNs are combinations of two or more polymers in network form. At
least one of the polymers is synthesized and/or crosslinked in the presence of
another. As such, IPNs share some of the advantages of both polymer blends
and network polymers. One of the earliest commercial IPNs used in the
automotive industry consists of polypropylene and ethylene-propylene-diene
terpolymer (EPDM). Potential applications include toughened plastics, ion-
exchange resins, pressure sensitive adhesives, soft contact lenses, preparation
of novel membrane systems and sound- and vibration-damping material.
Given below is an example of the formation of an IPN. First formed is the
crosslinked poly(ethyl acrylate) (PEA) network by free radical polymerization.
Then the monomers styrene and divinylbenzene are added (this is called
swollen, i.e. the polymer is swollen with the monmers) and then polymerized to
form a crosslinked interpenetrating polystyrene (PS) network.
CH CH2 O(CH2CH2OCH2CH2O CH CH2 )2 AIBN
heat
C O + C O
OCH2CH3 OCH2CH3

ethyl acrylate tetraethylene glycol dimethacrylate PEA network

CH CH2 CH CH2

+ AIBN
+ heat

CH CH2

PEA network styrene divinylbenzene PEA-PS IPN


HC CH2 In HC CH2 In
HC CH2 CH CH2CH CH2
n
Ph Ph Ph

Cross linking: CH CH2


CH2 CH2 C CH2 CH CH2CH CH2
n
Ph Ph Ph

CH CH2
CH CH2

CH CH2CH CH2 CH CH2 C CH2 CH CH2CH CH2


n Ph Ph Ph Ph Ph n

CH CH2CH CH2 CH CH2 HC CH2 CH CH2CH CH2


n n
Ph Ph Ph Ph Ph
Catalysts for Cationic Polymerization
e.g. boron trifluoride

F F H
H
F B + O F B O
H H
F F

Lewis acid Lewis base this complex can now act as


(electron deficient) (electron rich) a protic acid
(i.e. proton donor)

Initiation
F H F
CH 3 H CH 3
F B O H2 C F B O + H3 C
H
F CH 3 F CH 3
CH 3
Propagation
H3 C H2 C
CH 3 CH 3
CH 3
CH 3
H3 C H2 C H3 C CH2
etc.
CH 3 CH 3 CH 3
H3 C

Chain Termination

Proton transfer to catalyst

CH 3 CH 3 CH 3 CH 2
H F

CH2 CH2 CH2 CH2


O B F
+
CH 3 CH 3
CH 3 F CH 3
terminated chain
+
H F

O B F
H F
Chain transfer to monomer
CH 3 CH 3 CH 3 CH 3 CH 2

CH2 CH2 + H2 C
CH2 CH2
CH 3
CH 3 CH 3
CH 3 CH 3

terminated chain

+
CH 3

H3 C

CH 3

Chain transfer to monomer results in short polymer chains (approx. molecular weight = 2,000 -3000) when the
polymerization is carried out at room temperature

Such polymers find some use as additives to lubricating oils but are not useful as plastics or rubber
Much longer chain polymers can be produced by using low temperature (-90o C).
-the activation energy for chain transfer to monomer reactions is higher than that for chain propagation;
therefore, lowering the temperature slows down the chain terminating step more so than the propagation step
These longer chain polymers are still too soft and pliable for use as rubber because the polymer chains move
fairly easily relative to one another

The polymers can be made tougher and more rigid by decreasing the ability of polymer chains to move
relative to one another by forming covalent bond between polymer chains

The polymer chain crosslinking of rubber is called vulcanization. In order to create polymer crosslinks,
potentially reactive sites for covalent bond formation have to be introduced along the polymer chain. This is
done by adding a small amount (approx. 1- 5%) of a second monomer (often isoprene) when polymerization
is carried out. The resultant co-polymer has vinyl (alkene) groups at some positions along the polymer chains
In older vulcanization processes, the co-polymer was simply heated
with elemental sulfur to form sulfide or poly sulfide crosslinks,
however this reaction is usually very slow.

Current vulcanization processes use so-called vulcanization


accelerators
N
SH
S

mercaptobenzothiazole
(MBT)

The mechanism of the acceleration process is not well understood


A reasonable speculation is that the accelerator may react with elemental
sulfur faster than does the copolymer to form a reactive sulfur containing
species which is soluble in the polymer and which then carries out the
crosslinking

Free radical addition of sulfur radicals the vinyl side chains of the co-
polymer is probably involved.
Vulcanization

CH 3 CH 3
CH 3 CH 3

CH 3 CH 3 CH 3 C H2 C H2
CH 3 C H2
CH 2
C H2 C H2 C H2 CH 3
CH 3 CH 3
H2 C
n
CH 3 CH 3 CH 3
H2 C n Sx

H2 C
S CH 3 CH 3
CH 3
CH 2
heat C H2 C H2 C H2

H2 C
CH 3 CH 3 CH 3 CH 3
CH 3 CH 3 CH 3
m
C H2 C H2 C H2

x = 1 (sulfide or thioether crosslink)


CH 3 CH 3
CH 3 CH 3
m
x > 1 (polysulfide crosslink)

N N
SH S Sx H
S S

mercaptobenzothiazole a hypothetical intermediate


(MBT) acelerated vulcanization
Condensation Polymerization

Involves the condensation of two different bifunctional monomers, resulting in the


elimination of a small stable molecule (H2O, HCl, ROH). It essentially involves a
nucleophilic acyl substitution by one nucleophilic monomer on the electrophilic monomer.

Examples:

1) Poly(amide) Synthesis, e.g. Nylon 6,6

O O O O
n HO C (CH2)4 C OH + nH2N (CH2)6 NH2 HN (CH2)6 NH C (CH2)4 C + 2n H2O
n vaporized
hexanedioic acid 1,6-hexanediamine
(adipic acid) which drives
Nylon 6,6 the reaction
6 carbons in diamine
6 carbons in the acid
Mechanism

O O O O

HO C (CH2)4 C OH HO C (CH2)4 C OH
H2N (CH2)6 NH2
H2N (CH2)6 NH2
+

amide linkage
O O
O O + H
HO C (CH2)4 C O H
HO C (CH2)4 C HN (CH2)6 NH2
+ H2O HN (CH2)6 NH2

O O
H2N (CH2)6 NH2 HO C (CH2)4 C OH

O O
HN (CH2)6 NH C (CH2)4 C
n
2) Polyester Synthesis e.g. PEN – polyethylene Naphthalate
O
C
OH High temp and pressure
n + n HO CH 2 CH 2 OH
HO
C acid buffer pH 4-5
O ethylene glycol

Naphthalene dicarboxylate
O
C
O CH 2 CH 2 + 2n H2O
O
C
n
Mechanism: O
poly(ethylenenaphthalate)

O O
O O
HO C R1 C OH
HO C R1 C OH HO R2 OH
HO R2 OH
+

ether linkage
O O O O
+ H
H2O + HO C R1 C O R2 OH HO C R1 C O H

HO R2 OH

O O
HO R2 OH HO C R1 C OH

O O
O R2 O C R1 C
n
3) Polycarbonate, or specifically polycarbonate of bisphenol A, is a clear plastic used to make
shatterproof windows and lightweight eyeglass lenses. General Electric sells it as Lexan.

CH3 O
n HO NaOH
C OH + n O C O
CH3
diphenyl carbonate
Bisphenol A
CH3 O
O C O C + 2n HO
CH3 n

or

CH3 O NaOH CH3 O


n HO C OH + n C O C O C + 2n HCl
CH3 Cl Cl CH3 n

Bisphenol A phosgene

O
HO OH C
Cl Cl

R
H O
O -HCl HO R OH
HO R O C HO R O C Cl
+ Cl
Cl O
C
O H O Cl Cl
-HCl
HO R O C O R OH HO R O C O R OH
+ etc
Cl
Glyptal polyester which can be used as
plasticizers create a network polymer, forming a
cross-linked polyester.

O O
C C O O
n
O
O O O
OH heat
n + n HO OH O
O
O
O O
C O O

n
Addition reactions

1) Poly(urethane) Synthesis

Polyurethanes are the most well known polymers used to make foams like foam cushions. Polyurethanes can also
be used as in paints, synthetic fibers, and they can also be used as adhesives.

Notice that in the mechanism not only monomers react, but also dimers, trimers, and so on. This makes it a step
growth polymerization. Also, because no small molecule by-products are produced, it is called an addition
polymerization

H 3O +
n O C N CH2 N C O + n HO CH2 CH2 OH
catlyst
ethylene glycol In this reaction there
a di-isocyanate
is not a loss of a small
molecule

O O
C N CH2 N C O CH2 CH2 O
H H
n
urethane
linkage
Mechanism

O C N CH2 N C O + HO OH

R2
R H
O
+
H
R N C O R N C O H + HO R2 R N C O R
+ +
catalyst
H

H H O
O O
+ -H+ etc
R N C O R2 R N C O R2 R N C O R2
+
H H H
urethane linkage

Sometimes, instead of using a small diol like ethylene glycol, a polyglycol, one with a molecular weight of
about 2000 can be used. This produces a polymer within a polymer and polyurethane that looks something like
this:

O O
Spandex C N CH2 N C O CH2 CH2 O
H H x
n
hard rigid block
soft rubbery block
Polyurea
If a diamine is used instead of a diol in this reaction a polyurea is made

n O C N CH2 N C O + n H2N CH2 CH2 NH2

a di-isocyanate ethylene diamine

O O
C N CH2 N C N CH2 CH2 O
H H H
n
urea
linkage

O C N CH2 N C O + H2N NH2

R2
R H
O
H+
R N C O R N C O H + H2N R2 R N C N R
+ +
catalyst H H

H H O
O O
+ -H+ etc
R N C N R2 R N C N R2 R N C N R2
+
H H H H
urea linkage
3) Urea-Formaldehyde (a polyurea plastic)

O O O O
pH 4-7
n H2N C + n C CH2
NH 2 H H N N N N
formaldehyde H H H H n
urea

Mechanism
H
+ H O O
O O O
+
H +
C C
C C + C
H2N NH2 H N NH2
H H H H H
H H

H H
O O H O etc
O O+ -H2O
+ C C C C
C C
H N NH2 H2N N N NH2
H2N NH2 H
H
H H H

H H
N n
H2N N NH2 N N N
O pH 4-7 n
n + n N N
N N C N N
Melamine - Formaldehyde resins
H H H
formaldehyde N H
NH2 N N N
H N
melamine N
N H
n
cross-linked polyurea
Phenol-Formaldehyde Resins – Bakelite used for heat and electrical
coatings
OH OH

OH
O pH 4-7
C OH
n + n H H
formaldehyde HO a crossed polyol
HO
phenol

HO

Mechanism
OH OH
OH
+ H H
O O O + -H+
H+ + H H
H H H H H H H
HO H HO H

OH OH

OH H
+ -H2O
H OH
H HO +
+ HO HO
H O H H + H
H

H+ OH OH
HO HO etc
Nucleophilic Substitution Reactions forming polyethers

5) Epoxy Resins Highly cross-linked polyethers made from epoxide


monomers

CH 3
O Cl
+ HO OH

CH 3
epichlorohydrin bisphenol-A

NaOH

o
50 - 100 C

Cl O CH 3 O Cl
O O
CH 3
O CH3 O

Cl H2C HC H2C O O CH2 CH CH2 Cl

CH3

CH3 O
O
H2C HC H2 C O O CH2 CH CH2

CH 3

CH3 O
O O H2C HC CH2 O R
CH3

CH3 O

O O CH2 CH CH2 O R

CH3

etc
Epoxy glues often consist of two components which the user mixes just
before the desired "gluing " process. One component is the polymer shown
above. The other component is often ethylene diamine. Ethylene diamine
reacts with the epoxide "end" groups of the epoxy resin shown above to
effect ring opening to form amino alcohols. Each amino group can react with
two epoxide groups so that the resultant system is a network of cross-linked
polymers which have very strong adhesion properties. The process of
forming this network of cross-links is called "curing ".
OH CH3 O
O CH3
O O
O O
CH3 CH3
n

NH2
H2N

OH CH3 OH
OH
CH3
O O
O O
CH3
CH3
N
N n

N
N HO
OH

O
O

H3C
CH3
CH3
H3C

O
O

OH
HO

O
O

H3C
CH3
CH3
H3C

O
HO
OH
Conducting Polymers
From the web site: Plastic polymers:
http://www.rsc.org/lap/educatio/eic/2003/higgins_may03.htm
Prior to the 1970’s all synthetic polymers were insulated

Conjugated polyacetylene was one of the first conducting polymers


But hard to work with – insoluble – unstable, sensitive to oxygen.

Polythiophene and polyohenylevinylene – less sensitive to oxygen


-- more stable – long chain backbones could be attached to the polymers
to make them more soluble in non-polar solvents.

Why are they conducting? Large number of delocalized π bonding


electrons allows movement along skeletal structure.

Conducting polymers (ICPs) have attracted much attention because of their potential applications in
organic light emitting diodes (OLEDs), printed circuits, chemical sensors, electronic switches,
rechargeable batteries, electrolytic capacitors, smart windows, EMI shielding and electrostatic charge
dissipation (ESD) coatings. In spite of the thousands of papers published and patents filed in this field,
the number of commercial applications of ICPs is still small. Poor long term stability and lack of
reasonable processing methods have been the major showstoppers to the commercialization of ICPs.
TDA's research on ICPs has focussed on improving the solvent processability of conducting polymers
with proven stability, including poly(3,4-ethylenedioxythiophene) (PEDOT) and polypyrrole.
Organic-Processable PEDOT:
Materials that combine electronic
conductivity with optical clarity are
sought for the fabrication of flat panel
displays and other electronic devices.
PEDOT has excellent transparency in the
visible region, good electrical
conductivity, and environmental
stability. Unfortunately PEDOT, like most
conducting polymers, is infusible and
insoluble and therefore difficult to
process in a thin-film form or in other
shapes. Lack of processability has been
a major impediment to the commercial
acceptance of this polymer. A water dispersion of PEDOT doped with
poly(styrenesulfonate) (PSS) is available from H.C. Starck under the trade name of
Baytron®
Potential use in medicine, computing and telecommunication –
molecular switches

http://quark.physics.uwo.ca/~smittler/Silvia%20Mittler%20Surface%20Fu
nctionalisation.htm
Langmuir Trough

Amphiphilic Molecules (Soap)


connection between hydrophilic and
hydrophobic liquids

Compression organizes monolayer

Monolayer can be transferred onto a solid


support

hydrophilic
bilayers can also be made
hydrophobic
hydrophilic
Molecular Switch
One of the focuses of our research is the development of novel molecular
electronic devices. That is, devices made from a hybridization of conventional
semiconductor fabrication methods and self-assembling synthetic molecules
which have unique and useful electronic characteristics. We presently utilize a
break junction method for making two terminal electrical contact to single
molecule. We also have a method for making electrical contact to both sides of a
molecular SAM (self-Assembled Monolayer): the nanopore. Using these
measurement tools we have identified molecules which work well as insulators,
conductors, diodes, two-terminal switches and random access memory cells.

http://www.eng.yale.edu/reedlab/research/device/mol_devices.html#overview
Molecular Switch

The conduction path in a


conventional microelectronics
transistor
is turned on using an applied
voltage at the gate electrode.
Similarly, the conduction path
through a molecular switch is
turned on by an applied voltage.

The applied voltage is believed to


cause a conformational shift
which, in concert with the
charging of the molecule, opens
the conduction pathway.

NH2
O
S C CH3

O2N

http://www.eng.yale.edu/reedlab/research/device/mol_devices.html#overview
Electroactive Polymers as Artificial Muscles - A Primer (J. Y. Cohen)
http://www.polysep.ucla.edu/Research%20Advances/EAP/electroactive_polymers_a

Electroactive polymers (EAPs) are touted as the basis for future artificial muscles. EAPs can be
deformed repetitively by applying external voltage across the EAP, and they can quickly recover their
original configuration upon reversing the polarity of the applied voltage. To explore the potential use
of EAP’s as artificial muscles, a brief evaluation is presented of an ionic-based EAP composite as a
candidate artificial muscle material. The electromechanical properties of the EAP under dry and moist
conditions are presented along with the EAP’s performance under load conditions. AS shown through
a series of simple tests, the EAP has a high load bearing capacity to mass ratio, short response time,
and nearly linear deformation response with respect to applied voltage
Illustration of an EAP-powered forceps. (a) forceps open; (b) forceps closes upon polarity reversal;
(c) and (d) lift action.
Upon the application of an electrical field across a moist EAP, which is held between metal electrodes
attached across a partial section of an EAP strip, bending of the EAP is induced. Positive counter
ions move towards the negative electrode (cathode), while negative ions that are fixed (or immobile)
to the polymer (e.g. SO3) experience an attractive force from the positive electrode (anode). At the
same time, water molecules in the EAP matrix diffuse towards the region of high positive ion
concentration (near the negative electrode) to equalize the charge distribution. As a result, the region
near the anode swells and the region near the cathode de-swells, leading to stresses which cause the
EAP strip to bend towards the positive anode.

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