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Introduction To The PhysicalIntroduction To The Physical
Chemistry Of PolymerChemistry Of Polymer
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Lecture 1
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Introduction to polymersIntroduction to polymersPoly = many, mer = unit, many unitsPoly = many, mer = unit, many units
Polymer science is relatively a new branch of science . It deals with chemistryPolymer science is relatively a new branch of science . It deals with chemistry
physics and mechanical properties of macromolecule .physics and mechanical properties of macromolecule .
Macromolecule are involved in all human aspect ; the human body itself isMacromolecule are involved in all human aspect ; the human body itself is
made from proteins a polymer (made of poly amino acid ). Cellulose anmade from proteins a polymer (made of poly amino acid ). Cellulose an
Important natural material essential for the existence of man since the downImportant natural material essential for the existence of man since the down
of history, is the complicated polymer structure.of history, is the complicated polymer structure.
Beyond the many natural polymer , the man made polymers ore now forBeyond the many natural polymer , the man made polymers ore now for
human development . It is impossible to imagine modern life without all thehuman development . It is impossible to imagine modern life without all the
different types of synthetic textile materials (polyester , polyamide..)different types of synthetic textile materials (polyester , polyamide..)
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In this course we will discuss the followingIn this course we will discuss the following::
11-- Types of polymerTypes of polymer
22-- Step polymerizationStep polymerization33-- Addition free radical polymerizationAddition free radical polymerization
44-- Addition ionic polymerizationAddition ionic polymerization
55-- CopolymerizationCopolymerization
66-- Molecular weights of polymerMolecular weights of polymer
77-- Elucidation of the structure of polymerElucidation of the structure of polymer
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PolymerPolymeris a large molecule consisting of a number of repeatingis a large molecule consisting of a number of repeating
units with molecular weight typically several thousand orunits with molecular weight typically several thousand or
higherhigher
Repeating unitRepeating unit is the fundamental recurring unit of a polymeris the fundamental recurring unit of a polymer
MonomerMonomer -- is the smaller molecule(s) that are used to prepare ais the smaller molecule(s) that are used to prepare a
polymerpolymer
OligomerOligomeris a molecule consisting of reaction of several repeatis a molecule consisting of reaction of several repeat
units of a monomer but not large enough to be consider aunits of a monomer but not large enough to be consider a
polymer (dimer , trimer, tetramer, . . .)polymer (dimer , trimer, tetramer, . . .)
Degree of polymerizationDegree of polymerization -- number of repeating unitsnumber of repeating units
Definitions
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Nomenclature of polymerNomenclature of polymer11-- Based on monomer sourceBased on monomer sourceThe addition polymer is often named according to the monomer that wasThe addition polymer is often named according to the monomer that was
used to form itused to form itExample : poly( vinyl chloride ) PVC is made from vinyl chlorideExample : poly( vinyl chloride ) PVC is made from vinyl chloride
--CHCH22--CH(Cl)CH(Cl)--
If X is a single word the name of polymer is written outIf X is a single word the name of polymer is written out
directlydirectly
ex. polystyreneex. polystyrene --CHCH22--CH(Ph)CH(Ph)--
Poly XPoly X
If X consists of two or more words parentheses should beIf X consists of two or more words parentheses should be
usedused
ex , poly (vinyl acetateex , poly (vinyl acetate ) -CH2-CH(OCOCH
3)-
22-- Based on polymer structureBased on polymer structureThe most common method for condensation polymers since the polymerThe most common method for condensation polymers since the polymer
contains different functional groups than the monomercontains different functional groups than the monomer
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Classification schemes
Classification by Origin
Synthetic organic polymersSynthetic organic polymers
Biopolymers (proteins, polypeptides, polynucleotide,Biopolymers (proteins, polypeptides, polynucleotide,
polysaccharides, natural rubber)polysaccharides, natural rubber)
SemiSemi--synthetic polymers (chemically modified synthetic polymers)synthetic polymers (chemically modified synthetic polymers)
Inorganic polymers (siloxanes, silanes, phosphazenes)Inorganic polymers (siloxanes, silanes, phosphazenes)
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Classification by Monomer Composition
Homopolymer Copolymer
Block Graft Alternating Statistical
HomopolymerHomopolymerConsist of only one type of constitutional repeating unit (A)Consist of only one type of constitutional repeating unit (A)
AAAAAAAAAAAAAAA
copolymercopolymer
Consists of two or more constitutional repeating units (A.B )Consists of two or more constitutional repeating units (A.B )
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Several classes of copolymer arepossible
Statistical copolymer(Random)
ABAABABBBAABAABB
two or more different repeating unitare distributed randomly
Alternating copolymer
ABABABABABABABAB
are made of alternating sequences
of the different monomers Block copolymer
AAAAAAAAABBBBBBBBB
long sequences of a monomer arefollowed by long sequences of anothermonomer
Graft copolymerAAAAAAAAAAAAAAAAAA
B B B
B B B
Consist of a chain made from one type ofmonomers with branches of another
type (d)
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Classification by Chain structure (molecular architecture)
Linear chains :a polymer consisting of a single continuous chain of
repeat unitsBranched chains :a polymer that includes side chains of repeat unitsconnecting onto the main chain of repeat units
Hyper branched polymerconsist of a constitutional repeating unit
including a branching groups
Cross linked polymer:a polymer that includes interconnections
between chainsNet work polymer:a cross linked polymer that includes numerousinterconnections between chains
Linear Branched Cross-linked Network
Direction of increasing strength
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Classification by Chain Configuration and Conformation
Configuration or cisConfiguration or cis--trans isomerismtrans isomerismConfiguration :Configuration : Is defined by polymerization method. AIs defined by polymerization method. A
change in configuration require the rupture of covalentchange in configuration require the rupture of covalent
bonds .bonds .
Stereoisomerism or tacticityStereoisomerism or tacticity
IsotacticIsotactic
SyndiotacticSyndiotactic
AtacticAtactic
Conformation :Conformation : is defined by its sequence of bonds andis defined by its sequence of bonds and
torsion angles. The change in shape of a giventorsion angles. The change in shape of a givenmolecule due to torsion about single (molecule due to torsion about single ( ) bonds) bonds
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Geometric Isomerism
CH2 CH CH CH2
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isotactic
Microstructure - Tacticity
atactic syndiotactic
Side groups on alternating
sides of the backboneSide groups on the same
side of the backbone
Side groups on random
Sides of the backbone
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Polyolefins with side chains have stereocenters on every other carbon
C H3n
C H3 C H3 C H3 C H3 C H3 C H3C H3
With so many stereocenters, the stereochemistry can be complex. There
are three main stereochemical classifications for polymers.
Atactic: random orienta tion
Isotact ic: All stereocenters have same orientation
Syndiotact ic: Alternating stereochemistry
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1. Tacticity affects the physicalproperties
1. Atactic polymers will generally be amorphous, soft, flexiblematerials
2. Isotactic and syndiotactic polymers will be more crystalline, thusharder and less flexible
2. Polypropylene (PP) is a good example
1. Atactic PP is a low melting, gooeymaterial
2. Isoatactic PP is high melting (176), crystalline, tough materialthat is industrially useful
3. Syndiotactic PP has similarproperties, but is very clear. It is
harder to synthesize
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Classification by Thermal BehaviorThermoplastics - materials become fluid and processible uponheating, allowing them to be transformed into desired shapes that
are stabilized by cooling.
Thermosets - initial mixture of reactive, low molar mass compoundsreacts upon heating in the mold to form an insoluble, infusible
network
Classification by Application Plastics Fibers
Elastomers
Coatings
Adhesives
Classification Based on Kinetics or MechanismStep-growth
Chain-growth
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1. A number-average molecular weight Mn : divide chains into series of
size ranges and then determine the number fraction Ni of each sizerange
where Mi represents the mean molecular weight of the size range i, andN
iis the fraction of total numberof chains within the corresponding size
range
To create a solid with usefulmechanicalproperties the chain must be long !!One may describe chain length in terms ofpolymeraverage molecularweight, which can be defined in several ways:
Molecular weight averages
2. A weight average molecular weight Mw is based on the weightfraction wi within the size ranges:
Mn = MiNi/ Ni
Mw= MiWi / Wi
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Ameasure of the molecular-weight distribution is given by the ratios of molecular
-weight averages.
For this purpose, the most commonly used ratio is Mw/Mn, which is called the
polydispersity index orPDI.
PDI= Mw/Mn
Mw/Mn = 1 monodispersePolymer sample consisting of molecules all of which have the same
chain length
Mw/ Mn > 1 polydisperse
Polymer consisting of molecules with the variety of chain length
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Description of polymer physical propertiesDescription of polymer physical properties1-Primary bonds : the covalent bonds that connect the atoms of the mainchainchain
22-- Secondary bonds :Secondary bonds : nonnon covalent bonds that hold one polymer chain tocovalent bonds that hold one polymer chain toanother including hydrogen bond and other dipoleanother including hydrogen bond and other dipole dipole attractiondipole attraction33--Crystalline polymer :Crystalline polymer : solid polymers with a high degree of structural ordersolid polymers with a high degree of structural orderand rigidityand rigidity
44-- Amorphous polymers :Amorphous polymers :polymers with a low degree of structural orderpolymers with a low degree of structural order
55--SemiSemi crystalline polymer :crystalline polymer : most polymers actually consist of bothmost polymers actually consist of both
crystalline domains and amorphous domains with properties between thatcrystalline domains and amorphous domains with properties between thatexpected for a purely crystalline or purely amorphous polymerexpected for a purely crystalline or purely amorphous polymer
66--Glass :Glass : the solid form of an amorphous polymer characterized by rigiditythe solid form of an amorphous polymer characterized by rigidityand brittlenessand brittleness
Amorphous Crystalline
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77 Crystalline melting temperature (TCrystalline melting temperature (Tmm) :) : temperature at which crystallinetemperature at which crystallinePolymer converts to a liquid or crystalline domains of a semi crystallinePolymer converts to a liquid or crystalline domains of a semi crystalline
Polymer melt (increased molecular motion )Polymer melt (increased molecular motion )
88-- Glass transition temperature (TGlass transition temperature (Tgg) :) :temperature at which an amorphoustemperature at which an amorphous
polymer converts to a liquid or amorphous domains of a semi crystallinepolymer converts to a liquid or amorphous domains of a semi crystalline
polymer meltpolymer melt
99 Thermoplastics (plasticsThermoplastics (plastics )) ::polymers that undergo thermally reversiblepolymers that undergo thermally reversibleInterconversion between the solid state and the liquid stateInterconversion between the solid state and the liquid state
1010-- Thermosets :Thermosets :polymers that continue reacted at elevated temperaturespolymers that continue reacted at elevated temperatures
generating increasing number of crosslinks such polymers do not exhibitgenerating increasing number of crosslinks such polymers do not exhibitmelting or glass transitionmelting or glass transition
1111-- LiquidLiquid crystalline polymers :crystalline polymers :polymers with a fluid phase that retainspolymers with a fluid phase that retainssome ordersome order
1212-- Elastomers :Elastomers : rubbery , stretchy polymers the effect is caused by lightrubbery , stretchy polymers the effect is caused by lightcrosslinkingcrosslinking that pulls the chains back to their original statethat pulls the chains back to their original state
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Temperature
3
9
6
7
8
4
5
Glass phase (hard plastic)
Rubberphase (elastomer)
Liquid
Leatheryphase
Log (stiffness)Pa
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Polymerization mechanismsPolymerization mechanisms
Chain GrowthChain Growth
The only growth reaction isThe only growth reaction is
addition of monomer to aaddition of monomer to a
growing chain with agrowing chain with a
reactive monomerreactive monomer
The reaction mixture consistsThe reaction mixture consists
of high polymer andof high polymer and
unreacted monomers withunreacted monomers with
very few actively growingvery few actively growing
chainchainMonomer concentrationMonomer concentration
decreases steadily asdecreases steadily as
reaction time increasesreaction time increases
Step GrowthStep Growth
Reaction can occurReaction can occur
independently between anyindependently between any
pair of molecular speciespair of molecular species
The reaction mixture consists ofThe reaction mixture consists of
oligomers of many sizes in aoligomers of many sizes in a
statically calculablestatically calculable
distributiondistribution
Monomer disappear early in favorMonomer disappear early in favor
of low oligomerof low oligomer
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Chain growth
High polymer appearsHigh polymer appearsimmediately , averageimmediately , averagemolecular weight doesmolecular weight does
not change much asnot change much as
reaction proceedsreaction proceeds
Increased reaction timeIncreased reaction timeincreases overallincreases overall
product yield , but doesproduct yield , but does
not affect polymernot affect polymeraverage molecularaverage molecularweightweight
Step GrowthStep Growth
Oligomers steadilyOligomers steadilyincreases in size,increases in size,
polymer averagepolymer averagemolecular weightmolecular weight
increases as reactionincreases as reactionproceedsproceeds
Long reaction time areLong reaction time areessential to produceessential to produce
polymer with heightpolymer with heightaverage molecularaverage molecularweightweight
Polymerization mechanismsPolymerization mechanisms
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Lecture 2
Polymerization mechanisms
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Polymerization mechanisms
- Step-growth polymerization
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Stepwise (Condensation) polymerization Reaction
Requirements forStep-Growth PolymerizationHigh monomer conversionHigh monomer conversion
High monomer purityHigh monomer purity
High reaction yieldHigh reaction yield
Stoichiometric equivalence of functional groupsStoichiometric equivalence of functional groups
The characteristic features of this type of polymerizationThe characteristic features of this type of polymerization
process as followprocess as follow.11--Growth occurs throughout the matrixGrowth occurs throughout the matrix
22--There is the rapid loss of the monomer speciesThere is the rapid loss of the monomer species
33--The molecular weight slowly increases throughout the reactionThe molecular weight slowly increases throughout the reaction44-- The same mechanism operate throughout the reactionThe same mechanism operate throughout the reaction
55--The polymerization rate decreases as the number of functionalThe polymerization rate decreases as the number of functional
group decreasesgroup decreases
66--No initiator is required to start the reactionNo initiator is required to start the reaction
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Stage 1
C onsu ptionof ono er
n n
Stage 2
C o bina tionof s a ll fra g e nts
Stage 3
Re action ofo ligo ers to givehigh olecular
e ight poly e r
Step-Growth Polymerization
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ExampleExampleformation of polyesternHOnHO--RR--OH + nHOOCOH + nHOOC--RR--COOH HCOOH H--(O(O--RR--OOCOOC--RR--COCO--))nnOH+(OH+(22nn--11)H)H22OO
Kinetics of condensation (stepKinetics of condensation (step Growth ) polymerizationGrowth ) polymerizationConsider the synthesis of polyester from a diol and a diacid. The firstConsider the synthesis of polyester from a diol and a diacid. The first
step is the reaction of the diol and the diacid monomers to formstep is the reaction of the diol and the diacid monomers to form
dimerdimer,,
HO-R-OH + HOOC-R"-COOH--> HO-R-OCO-R'-COOH + H2OThe dimer then forms trimer by the reaction with diol
monomer,HOHO--RR--OCOOCO--R'R'--COOH + HOCOOH + HO--RR--OHOH----> HO> HO--RR--OCOOCO--R'R'--COOCOO--RR--OH +HOH +H22OO
and also with diacid monomer,HOHO--RR--OCOOCO--R'R'--COOH + HOOCCOOH + HOOC--R'R'--COOHCOOH---->>
HOOCHOOC--R'R'--COOCOO--RR--OCOOCO--R'R'--COOH + HCOOH + H22OO
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Kinetics of Condensation (Step-Growth) Polymerization StepStep--Growth polymerization occurs by consecutive reactions in whichGrowth polymerization occurs by consecutive reactions in which
the degree of polymerization and average molecular weight of thethe degree of polymerization and average molecular weight of thepolymer increase as the reaction proceeds. Usually (although notpolymer increase as the reaction proceeds. Usually (although not
always), the reactions involve the elimination of a small molecule (e.g.,always), the reactions involve the elimination of a small molecule (e.g.,water). Condensation polymerization may be represented by thewater). Condensation polymerization may be represented by thefollowing reactions:following reactions:
Monomer + Monomer Dimer + H2O
Monomer + Dimer Trimer + H2O
Monomer + Trimer Tetramer + H2O
Dimer + Dimer Tetramer + H2ODimer + Trimer Pentamer + H2O
Trimer + Trimer Hexamer + H2O
Generally, the reactions are reversible, thus the eliminated water must beGenerally, the reactions are reversible, thus the eliminated water must beremoved if a high molecular weight polymer is to be formed.removed if a high molecular weight polymer is to be formed.
Based on the assumption that the polymerization kinetics areBased on the assumption that the polymerization kinetics are
independent of molecular size, the condensation reactions may all beindependent of molecular size, the condensation reactions may all besimplified to:simplified to:
~~~~COOH + HO~~~~~~~~COOH + HO~~~~ pp ~~~~COO~~~~ + H~~~~COO~~~~ + H22OO
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Kinetic analysisKinetic analysis~~~~COOH + HO~~~~ p ~~~~COO~~~~ + H2OMost step polymerization involve bimolecular reaction that are often catalyzed
~~~~A + B~~~~ + catalyst p ~~~~AB~~~~ + catalystThe rate is accelerated according to
-d [A]
By
integration
dtdt= k= k [A[A][B]][B][catalyst][catalyst]
--d [A]d [A]
dtdt
= k= k''[A[A][B]][B]
--d [A]d [A]
dtdt= k= k''[A[A]]22
11
[M][M]--
11= k 't= k 't
[M]o[M]o
OrOr
Where k =Where k = kk[catalyst][catalyst]
I f [AI f [A] = [B]] = [B]
****
By use the extent of the reaction P (fraction of A or B functional groupsBy use the extent of the reaction P (fraction of A or B functional groups
that has reacted at time t )that has reacted at time t )
P = extent of the reaction = the fraction of conversionP = extent of the reaction = the fraction of conversion
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The concentration at any time given by[M]
[M] =[M] = [M]o[M]o -- [M]o P = [M]o ([M]o P = [M]o (11-- P )P )
By substitution in (** )By substitution in (** )
11
((11--p)p)
= k= k''[A[A]o t +]o t + 11
Note that experimental data are usuallylinearonly beyond ca. 80% conversion.
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Polyesterification Without Acidic Catalyst
dt= k[A]2[B]
-d [A]
dt
= k[A]3
Or
I f [A] = [B]
1
[M]2-
1= 2k t
[M]o2**
The rate equation is given by
- d[A]
By
integration
[M
]=
[M
]o -[M]o P = [M]o (1- P )
By substitution in (** )
1
(1-p)2=2 k [A]2ot + 1
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Uncatalyzed Polyesterification
Note that experimental data for esterification reactions show that plots ofNote that experimental data for esterification reactions show that plots of
11/(/(11--p)p)22vs. time are linear only after ca.vs. time are linear only after ca. 8080% conversion% conversion..
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This behavior has been attributed to the reaction medium changingThis behavior has been attributed to the reaction medium changingfrom one of pure reactants to one in which the ester product is thefrom one of pure reactants to one in which the ester product is the
solvent.solvent.
Thus, the true rate constants for condensation polymerizationsThus, the true rate constants for condensation polymerizations
should only be obtained from the linear portions of the plots (i.e., theshould only be obtained from the linear portions of the plots (i.e., the
latter stages of polymerization).latter stages of polymerization).
For example, the kinetic plots for the polymerization of adipic acid andFor example, the kinetic plots for the polymerization of adipic acid and
11,,1010--decamethylene glycol show that atdecamethylene glycol show that at 202202ooC, the thirdC, the third--order rateorder rate
constant for the uncatalyzed polyesterification is k =constant for the uncatalyzed polyesterification is k = 11..7575 xx 1010--22
(kg/equiv)(kg/equiv)22minmin--11..
Polyesterification Without Acidic Catalyst (continued)
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The NumberAverage Molecular Weight in
Polycondensation
. The number. The number--average degree of polymerization Xaverage degree of polymerization Xnn is given as the totalis given as the totalnumber of monomer molecules initially present divided by the total numbernumber of monomer molecules initially present divided by the total number
of molecules present at time t,of molecules present at time t,
XXnn = N= Noo/N= [M ]/N= [M ]oo/[M ] [M ] = [M ]/[M ] [M ] = [M ]oo (( 11 P )P )
XXnn == 11 // 11 -- PP
This relationship is theThis relationship is the Carother's EquationCarother's Equation..
ExampleExampleIf monomer conversion is 99% what is X
n
?
Xn = 1 / 1 P = 1 / 1 - 0.99 = 100If P =99.5 % Xn = 1 / 1 - 0.995 = 200If P =99.6 % Xn = 1 / 1 - 0.996 = 250
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The numberThe number--average molecular weight Maverage molecular weight Mnn
, defined as, defined as
MMnn = M= MooXXnn + M+ Megeg = M= Moo// 11 P + MP + Megegwhere Mwhere Moo is the mean of the molecular weights of the structuralis the mean of the molecular weights of the structural
units, and Munits, and Megegis the molecular weight of the end groups. The latteris the molecular weight of the end groups. The latter
becomes negligible at even moderate molecular weightbecomes negligible at even moderate molecular weight
MMnn = M= MooXXnn + M+ Megeg = M= Moo// 11 PP1
(1-p)= k'[A]ot + 1
Xn= k'[A]ot + 1
X2n=2 k [A]2ot + 1
HH--(O(O--RR--OOCOOC--RR--COCO--))nnOHOH
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Mn as a Function of Conversion
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3- Another method of controlling the molecular weight is by addingAnother method of controlling the molecular weight is by adding
small amounts of monofunctional monomer. (Acetic acid )small amounts of monofunctional monomer. (Acetic acid )
Type (Type (22))
For the polymerization of bifunctional monomers AFor the polymerization of bifunctional monomers A--A and BA and B--B where BB where B--BB
is present in excess, the numbers of A and B F.gs. are given byNis present in excess, the numbers of A and B F.gs. are given byNAA andNandNBB. Notice thatN. Notice thatNAA andNandNBB are equal to twice the number of Aare equal to twice the number of A--A and BA and B--BB
molecules, respectively.molecules, respectively.
The stoichiometric imbalance r of the two f.gs. is given byThe stoichiometric imbalance r of the two f.gs. is given by
r = Nr = NAA/N/NBB. . 11The total number of monomer molecules is given byThe total number of monomer molecules is given by
(N(NAA+N+NBB)/)/22 orNorNAA((11++11/r)//r)/22..
, the total number of polymer molecules is one half the total number, the total number of polymer molecules is one half the total number
of chain ends orof chain ends or
[N[NAA((11--p)+Np)+NBB((11--rp]/rp]/22..
The numberThe number--average DP( Xaverage DP( Xnn)is the total number of A)is the total number of A--A and BA and B--B moleculesB molecules
initially present divided by the total number of polymer molecules:initially present divided by the total number of polymer molecules:
XXnn = N= NAA((11++11/r)//r)/22..
[N[NAA((11--p)+Np)+NBB((11--rp]/rp]/22..
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Xn
= 1 + r
1 + r 2rP
If r = 1
Xn = 1 / 1-p
If p = 1Xn = 1 + r / 1 - r
ExampleExampleWhat is XWhat is Xnn when P =when P = 11 but usebut use 00.. 98009800 moles of Amoles of A--A andA and 11.. 01000100
moles of Bmoles of B BB
r = Nr = NAA/N/NBB == 00..9898 xx 22 // 11..0101 xx 22 == 00..9797
XXnn == 11 + r /+ r / 11 r =r = 11..9797 // 00..0303 == 6666
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Type (Type (33))the molecular weight can also be controlled by adding smallthe molecular weight can also be controlled by adding small
amounts of monofunctional monomer.amounts of monofunctional monomer.
Moles of AMoles of A--A = NA = NAA// 22Moles of BMoles of B--B = NB = NBB// 22
Moles of mono functional B = NMoles of mono functional B = NBB
r = Nr = NAA/ N/ NBB + N+ NBB = N = NAA/N/NBB ++ 22NNBB
ExampleExampleFind Xn for 1 mole of A-A ,1mole of B-B and 0.01 mole of RB when P = 1r = 1/ 1 + 2x 0.01 = 0.99
Xn 1 + r / 1 r = 1 + 0.99 / 1 0.99 = 199
The poly dispersity indexThe poly dispersity indexXXww/ X/ Xnn == 11 + P+ P
XXnn == 11 //11--P XP Xww== 11 + p /+ p / 11 -- PP
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SummarySummary11((11--p)p)
= k= k''[A[A]o t +]o t + 11
1(1-p)2
=2 k [A]2ot + 1
XXnn = N= Noo/N= [M ]/N= [M ]oo/[M]/[M] XXnn == 11 // 11 -- PP
MMnn = M= MooXXnn + M+ Megeg = M= Moo// 11 PP
Xn= k'[A]ot + 1
X2n=2 k [A]2ot + 1
r = Nr = NAA/N/NBB. . 11
Xn = 1 + r1 + r 2rP
If r = 1Xn = 1 / 1-p
If p = 1Xn = 1 + r / 1 - r
r = Nr = NAA/ N/ NBB + N+ NBB = N = NAA/N/NBB ++ 22NNBB
The poly dispersity indexThe poly dispersity index
XXww/ X/ Xnn == 11 + P+ P
XXnn == 11 //11--P XP Xww== 11 + p /+ p / 11 -- PP
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Lecture 3
Polymerization mechanisms
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Polymerization mechanisms
- Chain-growth polymerization
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ChainpolymerizationChainpolymerization
The characteristic of chain polymerization are as followThe characteristic of chain polymerization are as follow::11-- Growth is by the addition of the monomer at the end of the chainGrowth is by the addition of the monomer at the end of the chain22--Even at long reaction time some monomer are remain in the reactionEven at long reaction time some monomer are remain in the reaction
mixturemixture
33--The molecular weight of the polymer are increase rapidlyThe molecular weight of the polymer are increase rapidly
44--Different mechanisms operates at different stages of the reactionDifferent mechanisms operates at different stages of the reaction
55--The polymerization rate initially increases and then become constantThe polymerization rate initially increases and then become constant66--An initiator is required to start the reactionAn initiator is required to start the reaction
Chain polymerization reaction consists of three stagesChain polymerization reaction consists of three stages1- Initiation
2- Propagation
3-Termination
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Polymerization depend on thermodynamicPolymerization depend on thermodynamicPolymerization is possible only if the free energy difference betweenPolymerization is possible only if the free energy difference between
monomer and polymer is negativemonomer and polymer is negative
((G =G = ((HH -- TT((SS00Must beMust be --ve forve for
Polymerization toPolymerization to
workwork In chainIn chain
polymerizationpolymerization
are exothermicare exothermic
AlwaysAlways
+ve+ve
AlwaysAlways ve in chainve in chain
polymerizationpolymerization
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ChainpolymerizationChainpolymerization
Radical polym.Radical polym.The C=C is preferThe C=C is prefer
the Polym. by R.P.the Polym. by R.P.
and also can beand also can be
used in the stericused in the steric
hindrance of thehindrance of the
substituentsubstituent
Ionic polymIonic polym..
Anionic polym.Anionic polym. Cationic polym.Cationic polym.
X X X
radical cationic anionic
Electron with drawingElectron with drawing
substituent decreasingsubstituent decreasing
the electron density onthe electron density onthe double bond andthe double bond and
facilitate the attack offacilitate the attack of
anionic speciesanionic species
such as cyano andsuch as cyano and
carbonylcarbonyl++ --
CHCH22=CH Y=CH Y
Electron donatingElectron donating
substituent increasingsubstituent increasing
the electron density onthe electron density onthe double bond andthe double bond and
facilitate the attack offacilitate the attack of
cationic speciescationic species
such as alkoxy, alkyl,such as alkoxy, alkyl,
alkenyl, and phenylalkenyl, and phenyl-- ++
CHCH22=CH Y=CH Y
Vi l f dditi
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Unsubstituted (ethylene)
Works fine.
Monosubstituted
Works fine.
1,1-Disubstituted
Usually works.
1,2-DisubstitutedSeldom works.
TrisubstitutedAlmost never works.
Tetrasubstituted
Almost never works.
The only exceptions to the
unreactivity of tri- and tetra-
substituted vinyl monomers are
those with fluorine, liketetrafluoroethylene (CF2=CF2). The
main cause of this reactivity
pattern is the steric size of the
substituents.
Vinylmonomers for additionpolymerizations
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Free Radical Vinyl Chain PolymerizationFree Radical Vinyl Chain Polymerization
Rate of Radical Chain PolymerizationRate of Radical Chain Polymerization
Radical polymerization consists of three stepsRadical polymerization consists of three steps--initiation, propagation,initiation, propagation,and termination.and termination.
TheThe initiationinitiation step consists of two reactions.step consists of two reactions.
11--The production of the free radicalThe production of the free radical
kd
I ------> 2R22-- Addition of this radical to a monomer molecule to produce theAddition of this radical to a monomer molecule to produce thechain initiating species Mchain initiating species M11
kkiiR + MR + M11 ----------> M> M11
TheThepropagationpropagation consists of the growth of Mconsists of the growth of M11kkppMMnn ++ MM11
------------> M> Mn+n+11
(Rapid reaction )(Rapid reaction )
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. TerminationTermination with the annihilation of the radical centers occurs bywith the annihilation of the radical centers occurs by
bimolecular reaction between radicals either by combination or,,bimolecular reaction between radicals either by combination or,,
by disproportionationby disproportionation
kktctcMMnn + M + Mmm ----------> M> Mn+mn+m
kktdtdMMnn + M + Mmm ----------> M> Mnn+ M+ Mmm
The termination step can be represented byThe termination step can be represented by
kkttMMnn+ M+ Mmm
--------> dead polymer> dead polymer
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Kinetic Rate ExpressionKinetic Rate Expression
The rate of monomer disappearance, = the rate of polymerization,The rate of monomer disappearance, = the rate of polymerization,
is given byis given by
pi RRdt
]M[d!
Since forthe productionofhighmolarmassmaterialRSince forthe productionofhighmolarmassmaterialRpp RRii thisequationcanbe rethisequationcanbe re--writtenas:writtenas:
]M][M[kRdt
]M[dpp !!
Fromthe beginningofthe polymerization:Fromthe beginningofthe polymerization: increasingnumberofradicalsdue todecompositionoftheincreasingnumberofradicalsdue todecompositionofthe
initiatorinitiator increasingterminationdue toincreasingradicalincreasingterminationdue toincreasingradical
concentration(Rconcentration(Rtt ww [M][M]22)) eventuallyasteadystate inradicalconcentration:eventuallyasteadystate inradicalconcentration:
****
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This is equivalent to stating that the rate of initiation RThis is equivalent to stating that the rate of initiation Riiequals theequals the
rate of termination Rrate of termination Rtt
RRpp =k=kpp [M] ( R[M] ( Rii//22kktt) )
Ri = 2kt[M.
]2
[M ] = ( R[M ] = ( Rii//22kktt) )
and substitution in Eq.* * yields for the rate of polymerization.and substitution in Eq.* * yields for the rate of polymerization.
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Initiation free radical polymerizationInitiation free radical polymerization
ThermalThermal initiatorsinitiators
PhotochemicalPhotochemical
Redox initiatorsRedox initiators Ionizing radiationIonizing radiation
Thermal initiators:Thermal initiators:
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Thermal initiators:Thermal initiators:
Most common kind of FR initiator.Most common kind of FR initiator.
Unimolecular decomposition.Unimolecular decomposition.
First order kinetics.First order kinetics.
Most common examples: peroxides (benzoyl peroxide)orMost common examples: peroxides (benzoyl peroxide)or
azo compounds(azo isobuteronitrile).azo compounds(azo isobuteronitrile).
Peroxides Azo compaunds
(I p 2R)
(Temperatures are for 10 hour half-lives.)
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The thermal, homolytic dissociation of initiators is the most widelyThe thermal, homolytic dissociation of initiators is the most widely
used method for generating radicals to initiate polymerization.used method for generating radicals to initiate polymerization.
The compounds used as initiators are those with bond dissociationThe compounds used as initiators are those with bond dissociation
energies in the rangeenergies in the range 100100--170170 kJ/mole.kJ/mole.
The rate of producing primary radicals by thermal homolysis of anThe rate of producing primary radicals by thermal homolysis of an
initiator Rinitiator Rddis given byis given by
RRdd== 22fkfkdd[I][I]
where [I] is the concentration of the initiator and f is the initiatorwhere [I] is the concentration of the initiator and f is the initiatorefficiency.efficiency.
and the rate of initiation is given byand the rate of initiation is given by
RRii==22fkfkdd[I][I]
By substitute inBy substitute in RRpp =k=kpp [M] ( R[M] ( Rii//22kktt) )
RRpp =k=kpp [M] (fk[M] (fkdd[I] /k[I] /ktt) )
PhotochemicalPhotochemical initiatorsinitiators:
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PhotochemicalPhotochemical initiatorsinitiators:One or two component.One or two component.
Used for thin films.Used for thin films.
PeroxidesPeroxides
Azo compaundsAzo compaunds DisulfidesDisulfides
KetonesKetones
S S S
h
R
RedoxRedox initiatorsinitiators::
UsuallyUsually 22 component.component.Rarely used.Rarely used.
Ionizing radiation:
XX--ray, gammaray, gamma--ray.ray.Random destruction leads toRandom destruction leads to
radical formation.radical formation.
Used only in very specialUsed only in very special
casescases.
Fentons reagent
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Experimental Determination of RExperimental Determination of Rpp
RRpp can be experimentally determined by measuring the change in anycan be experimentally determined by measuring the change in any
property that differs for the monomer(s) and polymer, for example,property that differs for the monomer(s) and polymer, for example,solubility, density, refractive index, and spectral absorptionsolubility, density, refractive index, and spectral absorption
The polymerization can also be followed by separation and isolation ofThe polymerization can also be followed by separation and isolation of
the reaction products. Chemical analysis of the unreacted monomersthe reaction products. Chemical analysis of the unreacted monomers
as a function time is also used.as a function time is also used.
The disappearance of monomers or the appearance of polymer can beThe disappearance of monomers or the appearance of polymer can be
followed spectroscopically, i.r. or uv spectroscopyfollowed spectroscopically, i.r. or uv spectroscopy
DilatometryDilatometry
Dilatometry is the volume changes that occurs upon polymerization toDilatometry is the volume changes that occurs upon polymerization tofollow the conversion. It is the most accurate method for chainfollow the conversion. It is the most accurate method for chain
polymerization because of the large difference in density betweenpolymerization because of the large difference in density between
monomer and polymermonomer and polymer
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Kinetic chain lengthKinetic chain length RR
i
p
R
R
speciesinitiating
unitsmonomerofnumber!!R
By substituteBy substitute
RRii==22f kf kdd[I] R[I] Rpp =k=kpp [M] (f k[M] (f kdd[I] /k[I] /kii) )
=R=Rpp/R/Rii=R=Rpp/R/Rtt= k= kpp [M] /[M] / 22 (f k(f kddkktt[I] )[I] )11//22
Kinetic chain length v is defined as the average number of monomerKinetic chain length v is defined as the average number of monomer
molecules polymerized per each radical, which initiate amolecules polymerized per each radical, which initiate a
polymer chain. In other words, v is the ratio between the propagationpolymer chain. In other words, v is the ratio between the propagation
rate to that of initiation, or termination.rate to that of initiation, or termination.
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The number average degree of polymerization XThe number average degree of polymerization Xnn of chainsof chains
formed at a certain moment is dependent on the terminationformed at a certain moment is dependent on the termination
mechanism:mechanism:** combination: Xcombination: Xnn == 22YY
** disproportionation: Xdisproportionation: Xnn == YY
chemistry:chemistry:
CH2 C
H
+ C
H
CH2 CH2 C
H
C
H
CH2
CH2 C
CH3
C O
OMe
+ C
CH3
C
CH2
O
OMe
CH2 C
CH3
C
H
O
OMe
+ C
CH2
C
CH2
O
OMe
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Lecture 4
Polymerization mechanisms
Polymerization
Monomer Polymer
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Chain TransferChain TransferChain transfer is a chain breaking reaction; it is a premature terminationChain transfer is a chain breaking reaction; it is a premature termination
of polymer growing radical by the transfer of hydrogen or other atomof polymer growing radical by the transfer of hydrogen or other atom
or species to it from some compound present in the system .or species to it from some compound present in the system .
This leads to a decrease in the molecular weight than expected.This leads to a decrease in the molecular weight than expected.
MMnn + XY M+ XY Mnn--X +YX +Y
..
where XY may be monomer, solvent, initiator, or other moleculewhere XY may be monomer, solvent, initiator, or other molecule
and X is the atom or species transferred.and X is the atom or species transferred.
The rate of chain transfer reaction is given byThe rate of chain transfer reaction is given by
RRtrtr= K= Ktrtr[M[M..][XY]][XY]
where Kwhere Ktrtr is the chain transfer rate constant.is the chain transfer rate constant.
Chain transfer results in the production of a new radical Y which couldChain transfer results in the production of a new radical Y which could
induce polymerization. The effect of chain transfer on the polymerizationinduce polymerization. The effect of chain transfer on the polymerization
rate depends on whether the rate of reinitiation is comparable to therate depends on whether the rate of reinitiation is comparable to the
original rate of initiationoriginal rate of initiation
kktrtr
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Effect on XEffect on XnnEffect onEffect on
RRpp
Type ofeffectType ofeffectRelative rateconstantsRelative rateconstants
for Transfer,for Transfer,Propagation, andPropagation, and
ReinitiationReinitiation
CaseCase
DecreaseDecreaseNoneNoneNormalchainNormalchain
transfertransfer
KKpp>>k>>ktrtr kkaa~K~Kpp11
LargeLargedecreasedecrease
NoneNoneTelomerizationTelomerizationKKppktrtr kkaa
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The degree of polymerization now should be redefined as theThe degree of polymerization now should be redefined as the
polymerization rate divided by the sum of all the chain breakingpolymerization rate divided by the sum of all the chain breaking
reactions:reactions:
XXnn = R= Rpp(R(Rtt//22) + K) + KtrMtrM [M][M] + K[M][M] + Ktrstrs [M][S] + K[M][S] + KtrItrI[M][I][M][I]
C=chain transfer constant = KC=chain transfer constant = Ktrtr/ K/ Kpp
CCMM=K=KtrMtrM/K/Kpp CCSS=K=KtrStrS/K/Kpp CCII=K=KtrItrI/K/Kpp RRpp=K=Kpp [M][M][M][M]
11/X/Xnn=R=Rtt//22RRpp+ K+ KtrMtrM[M][M]/R[M][M]/Rpp+ K+ Ktrstrs [M][S]/R[M][S]/Rpp+K+KtrItrI[M][I]/R[M][I]/RppSubstitute by the value of RSubstitute by the value of Rpp11/X/Xnn=R=Rtt// 22RRpp+K+KtrMtrM/ K/ Kpp+ K+ Ktrstrs [S] / K[S] / Kpp[M] +K[M] +KtrItrI[I] / K[I] / Kpp [M][M]
Substitute by the value of CSubstitute by the value of C
11/X/Xnn=R=Rtt// 22RRpp+C+CMM+C+CSS[S] /[M] +C[S] /[M] +CII[I] /[M][I] /[M] MayoMayo walling equationwalling equation
11/X/Xnn== 11/(X/(Xnn))oo +C+CMM+C+CSS[S] /[M]+C[S] /[M]+CII[I] /[M][I] /[M]
F i t f i iti t [I] d [M] dF i t f i iti t [I] d [M] d
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1/D
s
1
/D
[ ]/[ ]
Generic Mayo plotGeneric Mayo plot
For a given amount of initiator[I] and monomer[M] andFor a given amount of initiator[I] and monomer[M] and
In the presence of chain transfer agentIn the presence of chain transfer agent
11/X/Xnn == 11/(X/(Xnn))oo +C+CSS[S] /[M ][S] /[M ]
Energetic CharacteristicsEnergetic Characteristics
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Energetic CharacteristicsEnergetic Characteristics
Activation Energy and Frequency FactorActivation Energy and Frequency Factor
. Increasing the temperaure usually increase the rate and decrease theIncreasing the temperaure usually increase the rate and decrease the
molecular weight.molecular weight.The rate constants of initiation, propagation, and termination can beThe rate constants of initiation, propagation, and termination can be
expressed by an Arrheniusexpressed by an Arrhenius--type relationshiptype relationship
k = A ek = A e E / RTE / RT
orlnk = lnAlnk = lnA E / RTE / RT
where A is the collision frequency factor, and E the Arrheniuswhere A is the collision frequency factor, and E the Arrhenius
activation energy. A plot of ln k vsactivation energy. A plot of ln k vs 11/T allows the determination/T allows the determination
of both values.of both values.
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Rate of PolymerizationRate of Polymerization
For a polymerization initiated by the thermal decomposition of anFor a polymerization initiated by the thermal decomposition of an
initiator the polymerization rate depends on three rate constantsinitiator the polymerization rate depends on three rate constants
KKpp ( k( kdd/ k/ ktt))1/21/2
? A40)-(3
)2/()2/(lnln
2/12/1
RT
EEE
A
AA
k
kk tdP
t
dP
t
dP
-
!
-
The composite or overall activation energy for the rate of polymerizationThe composite or overall activation energy for the rate of polymerization
EERRis [Eis [Epp + (E+ (Edd//22))--(E(Et/t/22)]. can be written as)]. can be written as
? A 41)-(3RTE-][])[(lnlnln R2/1
2/1
MIfAAAR
t
d
-
!
RRpp =k=kpp [M] (fk[M] (fkdd[I] /k[I] /ktt) ) WhereWhere
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Must beMust be --ve forve forPolymerization toPolymerization to
workwork In chainIn chain
polymerizationpolymerization
are exothermicare exothermic
AlwaysAlways
+ve+ve
AlwaysAlways ve in chainve in chain
polymerizationpolymerization
((G =G = ((HH -- TT((SS00
Thermodynamics of PolymerizationThermodynamics of Polymerization
Polymerization ofPolymerization of 11,,22--Disubstituted EthylenesDisubstituted Ethylenes
11,,22--Disubstituted ethylenes exhibit very little or no tendency toDisubstituted ethylenes exhibit very little or no tendency to
undergo polymerization. Steric inhibition is the cause of thisundergo polymerization. Steric inhibition is the cause of this
behaviorbehavior
RR RR substitutedsubstituted
PolymerizationPolymerization Depolymerization EquilibriaDepolymerization Equilibria
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PolymerizationPolymerization--Depolymerization EquilibriaDepolymerization Equilibria
Ceiling TemperatureCeiling Temperature
For most chain polymerization there is some temperature at which theFor most chain polymerization there is some temperature at which the
reaction becomes a reversible one, that is, the propagation step shouldreaction becomes a reversible one, that is, the propagation step shouldbe written as an equilibrium reactionbe written as an equilibrium reaction
Mn + Mkp
kdpMn+1 (3- 3)
where kwhere kdpdp is rate constant for the reverse reactionis rate constant for the reverse reaction--termedtermed
depolymerization or depropagationdepolymerization or depropagation
The reaction isothermThe reaction isotherm
G = Go + RT lnK
. For an equilibrium situationFor an equilibrium situation ((G=G=00 byby
(Go = (Ho - T(So = - RT ln K
equilibrium constant is defined by Kp/kdp or by
46)-(3][
1
]][[
][.
.
1
MMM
MK
n
n!!
48)-(3ln[M]
or
47)-(3][
1]ln[
cR
S
RT
H
MMRSHT
o
c
o
c
o
o
c
(
(!
!((!
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Ionic chain polymerizationIonic chain polymerization
The characteristic of ionic chain polymerization are as followThe characteristic of ionic chain polymerization are as follow
11--Ionic polymerization is limited because the ions are usually unstableIonic polymerization is limited because the ions are usually unstable
and require stabilization by solvation and lower temperature forand require stabilization by solvation and lower temperature for
polymerization to proceedpolymerization to proceed
22-- The ionic polymerization proceeds with very high rates and is veryThe ionic polymerization proceeds with very high rates and is very
sensitive to the presence of small amounts of impuritiessensitive to the presence of small amounts of impurities
33--Cationic and anionic polymerizations have very similar characteristics.Cationic and anionic polymerizations have very similar characteristics.both depend on the formation and propagation of ionic speciesboth depend on the formation and propagation of ionic species
44--solvents of high polarity cannot be used. The highly polar hydroxylicsolvents of high polarity cannot be used. The highly polar hydroxylic
solvents (water, alcohol) react and destroy most ionic initiators. Other polarsolvents (water, alcohol) react and destroy most ionic initiators. Other polar
solvents such as ketones form highly stable complexes with the initiatorssolvents such as ketones form highly stable complexes with the initiators
preventing thus the polymerization. Ionic polymerization,thus require solventpreventing thus the polymerization. Ionic polymerization,thus require solventof low or moderate polarity such as CHof low or moderate polarity such as CH33Cl,CHCl,CH22ClCl22, and pentane, and pentane..
55--Ionic polymerizations are characterized by a wide variety of modesIonic polymerizations are characterized by a wide variety of modes
of initiation and termination.of initiation and termination.
CATIONIC POLYMERIZATIONCATIONIC POLYMERIZATION
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CATIONIC POLYMERIZATIONCATIONIC POLYMERIZATION
InitiationInitiation
aa--Protonic AcidsProtonic Acids
Protonic acids can be used to some extent but the anion of the acidProtonic acids can be used to some extent but the anion of the acidshould not be highly nucleophilicshould not be highly nucleophilic
HA+ RR"C=CH2 RR"C+(A)
-
CH3
(4_1)
Halogen acids areHalogen acids are not usednot usedbecause of the highly nucleophilicbecause of the highly nucleophilic
character of the halide ioncharacter of the halide ionOther strong acids such as perchloric, sulfuric, phosphoric,Other strong acids such as perchloric, sulfuric, phosphoric,
chlorosulfonic, methansulfonic,etc,chlorosulfonic, methansulfonic,etc,usedusedfor cationicfor cationic
polymerization.polymerization.
mineral acids (initiators): H2SO4, H3PO4 (p provide H+)
The molecular weight obtained is low (few thousand).The molecular weight obtained is low (few thousand).
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bb--Lewis AcidsLewis Acids
Lewis acids used to initiate cationic polymerization at lowLewis acids used to initiate cationic polymerization at low
temperatures, may yield high molecular weight polymerstemperatures, may yield high molecular weight polymers
Lewis acids (co-initiators): AlCl3, BF3, TiCl4, SnCl4(often require otherproton or cation source)
Forming (co-initiator / initiator) system
BF3 + H H BF3-H+ (7.2)
lCl3 + Cl AlCl4-R
+ (7.3)
Very active Lewis acids p can undergo auto-ionization
2AlBr3 AlBr4-
AlBr2(7.4)
The initiation process can be generalized asThe initiation process can be generalized as
I + ZYk Y
+(IZ)
-
Y
+
(IZ)
-+M
k YM+(IZ)
- (4-5 )
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Propagation:Propagation:depending on the association degree between ions
The initiator ion pair (the carbonium ion and its counter ion)The initiator ion pair (the carbonium ion and its counter ion)produced in the initiation step proceeds to grow by theproduced in the initiation step proceeds to grow by the
successive addition of monomer moleculessuccessive addition of monomer molecules
This addition can be occuring by insertion of ( M ) between theThis addition can be occuring by insertion of ( M ) between the
carbonium ion and its counter ioncarbonium ion and its counter ion
HMHMnn++(IZ)(IZ) --+ M HM+ M HMnnMM
++(IZ)(IZ)--
TerminationTermination
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11--Chain Transfer to MonomerChain Transfer to Monomer. This involves transfer of a proton to a monomer molecule withThis involves transfer of a proton to a monomer molecule with
the formation of terminal unsaturation in the polymer moleculethe formation of terminal unsaturation in the polymer molecule
HMnM+(IZ)- + M Mn+1 + HM
+(IZ)-
22--Spontaneous TerminationSpontaneous TerminationSpontaneous termination involves regeneration of the initiatorSpontaneous termination involves regeneration of the initiator--
coinitiator complex by expulsion from the propagating ion paircoinitiator complex by expulsion from the propagating ion pairwith the polymer molecule left with terminal unsaturation.with the polymer molecule left with terminal unsaturation.
HMnM+(IZ)- Mn+1 + H
+(IZ)-
33--Combination with counter ionCombination with counter ionTermination by combination of the propagating carbonium ionTermination by combination of the propagating carbonium ion
with its counter ion occurswith its counter ion occurs
HMnM+(IZ)- HMnMIZ
TerminationTermination
Ki tiKi ti
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KineticsKineticsUnder steady state conditions (RUnder steady state conditions (Rii=R=Rtt) follows in a manner similar) follows in a manner similar
to that for radical polymerization. The rates of initiation, propagation,to that for radical polymerization. The rates of initiation, propagation,
and termination are given byand termination are given by
RRii= Kk= Kkii[I][ZY][M] R[I][ZY][M] Rpp = K= Kpp [YM[YM++(IZ)(IZ)--][M]][M] RRtt= k= ktt[YM[YM
++(IZ)(IZ)--]]
Where [YMWhere [YM++(IZ)(IZ)--] is the total concentration of all sized] is the total concentration of all sized
propagation centerspropagation centers
13)-(4]][][[
])([t
i
k
MZYIkIZYM !
14)-(4]][][[][ 2
t
Pi
t
PiP
k
MZYIkKk
k
MkRR !!
The numberThe number--average degree of polymerization is obtained as theaverage degree of polymerization is obtained as the
propagation rate over the termination ratepropagation rate over the termination rate
1 )-(4][
tt
nk
Mk
R
RX !!
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When chain breaking involves chain transfer to monomer and/orWhen chain breaking involves chain transfer to monomer and/or
termination in addition to combination with gegenion, the degree oftermination in addition to combination with gegenion, the degree of
polymerization ispolymerization is
1 )-(4,Mtrt
nRR
RX
!
The rate of chain transfer to monomer is given byThe rate of chain transfer to monomer is given by
Rtr,M = ktr,M[YM+(IZ-)][M]
17a)-(4][
][
, Mkk
MkX
Mtrt
Pn !
ThenThen
OrOr
17b)-(4C
][
1M
!
Mk
k
X P
t
n
where Cwhere CMMis the chain transfer constant for monomer.is the chain transfer constant for monomer.
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Effect of Reaction MediumEffect of Reaction Medium
Solvent EffectsSolvent Effects
Large increase in the rate and degree of polymerization are observedLarge increase in the rate and degree of polymerization are observed
if one increases the solvating power of the solvent.if one increases the solvating power of the solvent.
. The free ion concentration increases with increased solvating power,. The free ion concentration increases with increased solvating power,
this leads to an increase in Rthis leads to an increase in Rpp as the free ions propagate faster thanas the free ions propagate faster than
the ion pair.the ion pair.
Effect of GegenionEffect of Gegenion
The larger and less tightly bound the gegenion, the greater shouldThe larger and less tightly bound the gegenion, the greater should
be the reactivity of the ion pair toward propagationbe the reactivity of the ion pair toward propagation
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EnergeticsEnergetics
Cationic polymerization is also exothermic, since the reaction involvesCationic polymerization is also exothermic, since the reaction involvesthe conversion of the conversion of --bond into bond into --bond.bond.
the activation energies for the rate and degree of polymerization arethe activation energies for the rate and degree of polymerization are
obtained asobtained as
EERR= E= Eii+E+Epp--EEtt
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Trommsdorff effect
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Trommsdorff effect
In radical polymerization we speak about:1) lowconversion, i.e. polymerchainsare in dilute solution (no
contactamong chains)2) intermediate conversion, i.e. the area in between low andhigh conversion3) high conversion, i.e. chainsare getting highly entangled; kpdecreases.
Somewhere in the intermediate conversion regime:* polymerchains loose mobility.* Termination rate decreases* Radical concentration increases* Rate ofpolymerization increases* Molarmass increases
Thiseffect iscalled: gel effect, Trommsdorff effect,orauto-acceleration
In the polymerization of MMA thisoccursatrelatively low
conversion.
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Molar mass
R!
R!
n
n
P
2P If termination takes place by combination)
If termination by takes place disproportionation)
However, a growing chain may transfer its activity to a new chain:
This reaction is then followed by re-initiation, the start of a new chain:
Mi + T Mi + Tktr
T + M M1ki'
in the ideal case:
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Kinetics of free-radical chain polymerizationconsidering chain transfer reactions
RMn + S-Hp RMn-H+ S
Rtr=ktr[M][Transfer agent]
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Chaintransfer
chaintransferto: monomer initiator solventorchaintransferagent polymer allylic transfer
monomer, initiatorand chaintransferagentare mathematically treated identically:
][X]M[k]M[k2]M[kdt
]polymer[dX,tr
2
td
2
tc !
As derived beforethis leads to:
]M[k
]I[k
]M[k
]S[k
k
k
]M[k
]M[k2
]M[k
]M[k
]M[k]X[k
]M[k]M[k2
]M[k]M[k1
p
I,tr
p
S,tr
p
M,tr
p
td
p
tc
p
X,tr
p
td
p
tc
n
!
!!
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The rate ofpolymer formation is now defined as:
]T][M[k]M[k2]M[kdt
]polymer[dtr
2
td
2
tc !
The rate of polymerization as derived before:
]M][M[kdt
]M[d p!
From the definition of number average degree of polymerization it follows:
dt
]polymer[d
dt
]M[dPn !
]M[k
]T[k
]M[k
]M[k2
]M[k
]M[k
]M][M[k
]T][M[k]M[k2]M[k
P
1
p
tr
p
td
p
tc
p
tr2
td2
tc
n
!
!! thus:
]M[
]T[C
P1
1P
T0,n
n
!
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Chain transfer to polymer
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p y
Intermolecular chain transfer
Intramolecular chain transfer
Traditional approach: intermolecular, strong increase in
branching density towards high conversion.
Recent results:
Hardly conversion dependent
Dilution results in higher
degree of grafting
0 10 20 30 40 50
1
2
3
4
5
6
7
8
co rsio c . 25%
co rsio > 80%
m
ol
%
r
c
s
[BA]0
/ %( / )
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Summary
tMkL p ][!
]][[ y! MMkR pp
Chain-length
Rate ofpolymerization
Initiator decomposition is the reaction stepmost stronglyinfluenced by temperature.
][
1
~ yMtTime of chain-growth
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Thermodynamics of radical
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Ea = 1/2Ed+(Ep-1/2Et)Overall activation energy of polymerization:
Ed } 125 170 kJ mol-1 (Ep-1/2Et) } 20 30 kJ mol-1 Thus, initiation is the rate determining step
Polymeriszation rate } exp(-Ea/RT) Thus, it will increase as the temperature is raised
y
polymerisation
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Copolymerization
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Copolymerizationffii:: fraction ofmonomerfraction ofmonomeriiin reaction mixturein reaction mixture
ff11 = [M= [M11] / ([M] / ([M11] [M] [M22])])
FFii:: fraction ofmonomerfraction ofmonomeriibuilt intopolymerbuilt intopolymer
FF11 = d[M= d[M11] / (d[M] / (d[M11] d[M] d[M22])])
22221
211
212
111
2 ffff
fffF
Long chain assumption (Long chain assumption (kkii,, kkdd ignored;ignored; kkpp,, kkttnot ~ chainnot ~ chainlength)length)
Reactivity ratios independent of environmental factorsReactivity ratios independent of environmental factors
22221111
22221
211
p
2
kfrkfr
frfffrk
!Average copolymerisation rate:Average copolymerisation rate:
Id l l i i
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0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1f1
F1
MMA / BA
Ethene / VAc
VDC / VC
Ideal copolymerisation
Composition driftComposition drift
IfIfff11 F F11
ff11 changeschanges FF11 changeschanges
What does compositionWhat does compositiondrift mean for the polymerdrift mean for the polymerthat is formed?that is formed?
Polymerization techniques
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Polymerization techniques
Kinetic / mechanistic factors related to chain
length, chain composition Technological factors e.g. heat removal,reaction rate, viscosityof the reaction mixture,morphologyof the product
Economic factors; production costs,enviromental aspects, purification steps etc.
Sometimes for one monomer several techniques of
polymerizing are available. Choice of a specifictechnique depends on a number of factors:
Polymerization techniques
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Homogeneous systems Bulk polymerization Solution polymerization
Heterogeneous systems Suspension polymerization Emulsion polymerization Precipitation polymerization Polymerization in solid state Polymerization in the gas phase
Polymerization techniques
Bulk polymerization
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Advantages: Disadvantages:
Simple, only the monomer and initiatorare present in the reaction mixture
High molecular weight
Exothermof the reaction might be hard tocontrol- molecular weights verydisperse
The polymer is solublein the monomer:
Thepolymeris not soluble
inthe monomer:
Viscosityof the reactionincreases markedly (geleffect)
Polymerprecipitates outwithout increase in solutionviscosity
Rp
Solution polymerization
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Solution polymerizationMonomer dissolved in solvent, formed polymer stays
dissolved. epending on concentration ofmonomer thesolution does not increase in viscosity.
Advantagesisadvantages* Product sometimes * Contamination with
directly usable solvent* Controlled heat * Chain transfer to
release solvent* Recycling solvent
ApplicationsAcrylic coating, fibrespinning, film casting
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Suspension polymerization
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p p y
Water insoluble monomers are dispersed in water.
Initiator dissolved in monomer. Stabilization of droplets/polymerparticles with non-micelle formingemulsifiers like polyvinylalcohol or Na-carboxymethylcellulose.
Equivalent to bulk polymerization,small droplets dispersed in water.
Product can easily be separated,particles 0.01-1mm.
Pore sizes can be controlled by adding a combination of solvent(swelling agent) and non-solvent.
Viscosity does not change much.
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Emulsion Polymerization
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y
A micelle forming emulsifier is used.
Initiator is water soluble. The formed latex particles are much smaller
than suspension particles (0.05-2 m). Kinetics differ considerable fromother techniques. Polymer is formed within the micelles
and not in the monomer droplets.
Emulsion Polymerization
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y
Advantages Disadvantages
* Low viscosity even * Contamination ofat high solid contents products with additives
* Independent control * More complicatedof rate and in case of watermolecular-weight soluble monomers
* Direct application ofcomplete reactor contents
Overview of Ionic Polymerization:
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Ionic polymerizations are more selective than radicalprocesses due to strict
requirements for stabilization of ionic propagating species.Cationic: limited tomonomers with electrondonating groups
y
Selectivity
limited tomonomers with electron withdrawing groupsAnionic:
Overview of Ionic Chain Polymerization:
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A counterion is present in both anionic and cationic polymerizations,yielding ion pairs, not free ions.
Cationic: ~~~C+(X-) Anionic: ~~~C-(M+)
There will be similar effects of counterion and solvent on the rate,
stereochemistry, and copolymerization for both cationic and anionicpolymerization.
Formation of relatively stable ions is necessary in order to have
reasonable lifetimes for propagation. This is accomplished by using low
temperatures (-100 to 50 C) to suppress termination and transfer and
mildly polar solvents (pentane, methyl chloride, ethylene dichloride).
y
Counterions
Overview of Ionic Polymerization
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There are four states of ion-pair binding:(I) ~~~BA ~~~B+A- (II)covalent bond tight or contact ion pair,
intimate ion pair
(III) ~~~B+||A- ~~~B+ + A- (IV)
solvent-separated, Free ion, very reactiveloose ion pair but low concentration
Most ionic polymerizations have equilibrium between ion pairs (II or III,
depending upon solvent) and free ion (IV).
Ion-pairBinding
Overview of Ionic Chain Polymerization:
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Reactions are fast but are extremely sensitive to small amounts ofimpurities. Highly polar solvents (water, alcohols, ketones) will reactwith and destroy or inactivate the initiator. Moreover, heterogeneous
initiators are used making the nature of the reaction medium unclear
and determination of the mechanism difficult.
Termination by neutralization of the carbo-cation (carbonium ion,carbenium ion) occurs by several processes for cationicpolymerization, but termination is absent for anionic polymerization.
y
Mechanistic Analysis
Initiation of Cationic Chain Polymerization:
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Initiation of Cationic Chain Polymerization:
ProtonicAcids HBr, HI
HA + (CH3)2C=CH2 (CH3)3C+(A-)
LewisAcids AlCl3
, BF3
, SnCl4
A co-initiator (water, protonic acids, alkyl halides) is needed to activatethe Lewis acid.
BF3 + H2O BF3-OH2
BF3-OH2 + (CH3)2=CH2 (CH3)2C+(BF3OH)
-
m
o
nCationic Chain Propagation:
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no
m
ers:
CH
2=CH
RM
ono
m
er
Substituents must be able to stabilize a formalpositive charge. Forolefins, tertiary secondary primary due to inductive effect.For styrenic monomers:
Monomer kp, liter/mole sec
R = Cl 0.0012R = H 0.0037R = CH3 0.095R = OCH3 6
Steric effects dominate forortho substitution in styrene,and all substituents reduce kp irrespective of inductive effects.
Cationic Chain Propagation:
MonomerStructure
Cationic initiators:
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Proton acids with unreactive counterions
Lewis acid + other reactive compound
R
S
O
OH
O O
H
R
S
O
OH
O O
H
R
S
O
OH
O O
HNOT
With Lewis acid initiator one must need a co-initiator,
a protogen:
a cationogen:
or
Common steps of cationic polymerization:
(i ii) initiation propagation
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(i, ii) initiation, propagation
The mechanism of cationic polymerization is a kind of repetitive alkylation reaction.
Electron donating groups are needed as the R groups because these can stabilize the
propagating species by resonance. Examples:Propagation is usually very
fast. Therefore, cationic
vinyl polymerizations must
often be run at low
temperatures. Unfortunately,cooling large reactors is
difficult and expensive. Also,
the reaction can be inhibited
by water if present in more
than trace amounts, so
careful drying of ingredients
is necessary (another
expense).
Lewis acids form active catalyst-co-catalyst
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complexes with proton donors
Regiochemistry of propagation
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Markownikov addition form the most stable carbocation:
Electron-donating groups R stabilize a cation and affect regiochemistry by
directing the incoming groupE to an opposite side to the donating group.
RH
H H
E
RH
H H
E
RH
H H
ENOT
R = Alkyl,Aryl,
Halide,OR
Common steps of cationic polymerization: (iii)
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termination by unimolecular rearrangment of the ion pair
A
B
Common steps of cationic polymerization:
(i ) h i t f t
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(iv) chain transfer to monomer
Cationic vinyl polymerization canbe stopped also by numerousside reactions, most of whichlead to chain transfer. It isdifficult to achieve high MWbecause each initiator can give
rise to many separate chainsbecause of chain transfer. Theseside reactions can be minimizedbut not eliminated by running thereaction at low temperature.
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Initiation
General kinetic scheme for cationic polymerisation
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Initiation
Propagation
Termination
Ri =kic[M]
I+ A +Mp IM+ A
IM1+ A +Mp IM2
+A
IMn+ Ap IMn +H
+ A
Rt =kt[M+]
+
M
IM1+A
XX
I
X
I
X
IM2+A
XX
I
IMn+A
n-1
+
XX
R
IMn
n
A H+A
I+
+
M
IM+
X
I
X
A
A
A
IMn+A+Mp IMn+1
+A
Rp =kp[M+][M]
XX
R
n-
+
M
X XX
R
n
IMn+A IMn+1
+A
General kinetic scheme for cationic polymerisation
(continuation)
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(continuation)
Steady-state approximation:Ri =Rt
kic[M]=kt[M+]
[M+] =kic[M]/kt
Rp =kp[M+][M]= (kpki/kt)c[M]
2
Xn =vp/vt = (kp/kt) [M]
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Anionic initiators:
For initiation to be successful, the free energy of the initiation step must be favorable.
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, gy pTherefore, it is necessary to match the monomer with the appropriate strength ofinitiator so that the first addition is "downhill." If the propagating anion is not ver y
strongly stabilized, a powerful nucleophile is required as initiator. On the other hand,if the propagating anion is str ongly stabilized, a rather weak nucleophile will besuccessful as initiator. (Of course, more powerful ones would work, too, in the lattercase.)
But two EWGs are so effective in stabilizing anions that even water can initiatecyanoacrylate ("Super Glue"). Weak bases (such as those on the proteins in skin)
work even better.
Anionic initiators (continuation):
There is one other category of initiator known as electron transfer that works best
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There is one other category of initiator, known as electron transfer, that works bestwith styrene and related monomers. The actual initiating species is derived from analkalai metal like sodium. An ar omatic compound is required to catalyze the
process by accepting an electron from sodium to form a radical anion salt with Nacounterion. A polar solvent is required to stabilize this complex salt. The electron issubsequently transferred to the monomer to create a new radical anion whichquickly dimerizes by free radical combination (similar to the termination reaction infree radical polymerization). The eventual result i s a dianion, with reactive groups ateither end. Propagation then occurs from the middle outwards. This system is
especially useful for producing ABA block copolymers, which have importanttechnological uses as thermoplastic elastomers.
Common steps of anionic polymerization:
(iii) chain transfer
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(iii) chain transfer
Acrylates have problems in anionic propagation because of chain transfer topolymer. The hydrogen atoms adjacent to the ester groups are slightly acidic, andcan be pulled off by the propagating anion. The new anion thus created canreinitiate, leading to branched polymers. This side reaction is difficult to suppress.
Common steps of anionic polymerization:
(iv) termination (continuation)
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(iv) termination (continuation)
When carried out under the appropriate conditions, termination reactions do notoccur in anionicpolymerization. One usually adds purposefully a compound suchas wateror alcohol to terminate the process. The new anionic species is too weakto reinitiate.
The "Dark Side:" Compounds such as water, alcohols, molecular oxygen, carbon dioxide,
etc. react very quickly with the carbanions at the chain ends, terminating the propagation.Therefore, one must scrupulously dry and deaerate the polymerization ingredients to be able
to get a truly living system. This is not easy to do, and adds to the potential costs of the
process.
Functionalization of the chain ends in anionic polymerization
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The beauty of anionic polymerization lies in the lack of ter mination reactions when
carried out under the appropriate conditions (livingpolymerization). This means thatthe propagating species remains unchanged at the chain end when the monomer isconsumed, so subsequent chemical reactions can be carried out. (The chain end is acarbanion, and the organic chemistry of carbanions is diverse.) Here are a fewexamples among many possible:
Carboxylation of end groups:
Alcohol end groups viaethylene oxide:
Coupling agents:
Living anionic polymerization
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Chains are initiated all at once (fastinitiation) Little or no termination (exceptpurposeful). Little or no depolymerization.All chains grow under identical conditions.
The usual circumstances:
The resultis thatthe monomers getdivided evenly among chains.
Narrow MW distribution (P approaches 1.0, typically 1.05 - 1.2). The MW is predictable (unlike otherpolymerizations).
For monofunctional initiators, the chain length is simply x = [monomer] /[initiator]. For difunctional initiators (electron transfer), the chain lengthis twice as large.
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T f B I iti t
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Types ofBase Initiators:
Base Initiators are often organometallic compounds or salt of astrong base, such as an alkali metal alkoxide.Examples: Potassium with liquid ammonia. Stable alkali metal complexes may be formed with aromaticcompounds (e.g. Na/naphthalene) in ether.
Sodiummetal in tetrahydrofuran.
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Anionic Initiation:
T f f El t t I t di t
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M +A: A: -M+
A:-M+ + CH2=CHR [CH2=/CHR]-M+ + A:
Monomer radical anion
Stable alkali metal complexes may be formed with aromatic compounds(e.g. Na/naphthalene) in ether.
Rapid dimerization often occurs due to high free radical concentration:
2[CH2=/CHR]-Na+ Na+-RHCCH2CH2CHR-+Na
Propagation from both ends! dianion
Transfer of an Electron to an Intermediate
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Mechanism ofBase Initiation:
Relative Initiator Activity
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Initiation could be instantaneous, of comparable rate, ormuch slower
than propagation. If termination is absent,
Termination
By impurities and transfer agents: Oxygen and carbon dioxide can react with propagating anions, andwater will terminate the chain byproton transfer. Thus, the reactionsmust be carried out under high vacuumor in an inert atmosphere.
By nucleophilic attack of initiator on polar monomer Polarmonomers such as methylmethacrylate, methyl vinyl ketone,and acrylonitrile have substituents that will react with nucleophiles.These side reactions broaden the molecular weight distribution. Tominimize the effect, use a less nucleophilic initiator, lower reactiontemperatures, and more polar solvents.
Relative InitiatorActivity
Effect of Reaction Medium: Solvent
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Solvent ielectric Constant kp (liter/mole sec)
Benzene 2.2 2ioxane 2.2 5
Tetrahydrofuran 7.6 5501,2-Dimethoxyethane 5.5 3,800
As the dielectric constant increases, the solvating powerof the reactionmedium increases and there is an increased fraction of free ions (whichare highly reactive).
Effect of Reaction Medium: Counterion
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The separation between the counterion and the carbanion end grouponthe polymer is the major factor determining the rate, equilibrium, andstereochemistry.
Counterion kp, liter/mole secin tetrahydrofuran in dioxane
Cation
sizeLi+ 160 0.94Na+ 80 3.4K+ 60-80 19.8Rb+ 50-80 21.5
Cs+ 22 24.5Free anion 65,000!
Tetrahydrofuran is a good solvating solvent ( = 7.4)Dioxane is a poor solvating solvent ( = 2.2)
Kinetics ofAnionic Polymerization:
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Reaction Set
Initiation:GA G+ + A-
G+ + A- + M G+ + AM-
Note that the nature of the solvent will determine whether the propagatinganion behaves as a free ion, AM-, as a loose or tight ion pair, AM-G+, or
both. We will assume free ions for this treatment.
Propagation:AM- + M AMM-
AMM-+ M AM2M-
AMn-1M
-
+ M AMnM
-
Termination:There is no termination step in the absence of impurities.
Rate of Polymerization
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[A-] = total concentration of anions of alllengths=[GA]o = concentration of initiator before dissociation
Integrate toobtain:
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Solid-State Properties
POLYMERS IN THE SOLIDSTATE
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Semi-crystallineAmorphous
Glassy Rubbery
Questions: Relationship to microstructureRelationship of structure to properties
Glass Transition Temperature
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The glass transition, Tg, is temp. below which a
polymer OR glass is brittle or glass-like; above that
temperature the material is more plastic.
The Tg to a first approximation is a measure of thestrength of the secondary bonds between chains in a
polymer; the stronger the secondary bonds; the
higher the glass transition temperature.
Polyethylene Tg = 0C; Polystyrene = 97 C
PMMA (plexiglass) = 105 C.Since room temp. is < Tg for PMMA, it is brittle at
room temp.
For rubber bands; Tg = - 73C. So to make rubber
brittleyou need to cool it. Had the Challenger taken off on a
warm day the disaster may never have happened!
Determination of the glass transition temperature:
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Dynamic Mechanical tests: E', E", TanH
Torsionpendulum Tensile