Introduction To The PhysicalIntroduction To The Physical Chemistry Of PolymerChemistry Of Polymer

Lecture 1

Introduction to polymersIntroduction to polymersPoly = many, mer = unit, many unitsPoly = many, mer = unit, many unitsPolymer science is relatively a new branch of science . It deals with chemistryPolymer science is relatively a new branch of science . It deals with chemistryphysics and mechanical properties of macromolecule .physics and mechanical properties of macromolecule .Macromolecule are involved in all human aspect ; the human body itself is Macromolecule are involved in all human aspect ; the human body itself is made from proteins a polymer (made of poly amino acid ). Cellulose an made from proteins a polymer (made of poly amino acid ). Cellulose an Important natural material essential for the existence of man since the down Important 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………..)

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 polymer77 - -Elucidation of the structure of polymerElucidation of the structure of polymer

Polymer Polymer –is a large molecule consisting of a number of repeating –is a large molecule consisting of a number of repeating units with molecular weight typically several thousand or units with molecular weight typically several thousand or higherhigher

Repeating unitRepeating unit – is the fundamental recurring unit of a polymer – is the fundamental recurring unit of a polymer

Monomer Monomer - is the smaller molecule(s) that are used to prepare a - is the smaller molecule(s) that are used to prepare a polymerpolymer

Oligomer Oligomer –is a molecule consisting of reaction of several repeat –is a molecule consisting of reaction of several repeat units of a monomer but not large enough to be consider a units 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 units - number of repeating units

Definitions

Nomenclature of polymerNomenclature of polymer11 - -Based on monomer sourceBased on monomer source

The 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 it Example : 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. polystyrene -CHex. polystyrene -CH22-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(OCOCH3) -

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

Classification schemesClassification by Origin Synthetic organic polymersSynthetic organic polymers

Biopolymers (proteins, polypeptides, polynucleotide, Biopolymers (proteins, polypeptides, polynucleotide, polysaccharides, natural rubber)polysaccharides, natural rubber)

Semi-synthetic polymers (chemically modified synthetic polymers)Semi-synthetic polymers (chemically modified synthetic polymers)

Inorganic polymers (siloxanes, silanes, phosphazenes)Inorganic polymers (siloxanes, silanes, phosphazenes)

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 )

Several classes of copolymer are possible

Statistical copolymer (Random) ABAABABBBAABAABBtwo or more different repeating unitare distributed randomly Alternating copolymer ABABABABABABABABare made of alternating sequencesof the different monomers Block copolymer AAAAAAAAABBBBBBBBBlong sequences of a monomer are followed

by long sequences of another monomer Graft copolymer AAAAAAAAAAAAAAAAAA B B B B B BConsist of a chain made from one type of

monomers with branches of another type

)d(

Classification by Chain structure (molecular architecture)

Linear chains :a polymer consisting of a single continuous chain of repeat units Branched chains :a polymer that includes side chains of repeat units connecting onto the main chain of repeat unitsHyper branched polymer consist of a constitutional repeating unit including a branching groupsCross linked polymer :a polymer that includes interconnections between chainsNet work polymer :a cross linked polymer that includes numerous interconnections between chains

Linear Branched Cross-linked Network

Direction of increasing strength

Classification by Chain Configuration and Conformation

Configuration or cis-trans isomerismConfiguration or cis-trans isomerismConfiguration :Configuration : Is defined by polymerization method. A Is defined by polymerization method. A

change in configuration require the rupture of covalent change 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 and is defined by its sequence of bonds and torsion angles. The change in shape of a given torsion angles. The change in shape of a given molecule due to torsion about single (molecule due to torsion about single (σσ ) bonds ) bonds

Geometric Isomerism

CH2 CH CH CH2

isotactic

Microstructure - Tacticity

atactic syndiotacticSide groups on alternating sides of the backbone

Side groups on the same side of the backbone

Side groups on randomSides of the backbone

Polyolefins with side chains have stereocenters on every other carbon

CH3n

CH3 CH3 CH3 CH3 CH3 CH3CH3

With so many stereocenters, the stereochemistry can be complex. There are three main stereochemical classifications for polymers.

Atactic: random orientation

Isotactic: All stereocenters have same orientation

Syndiotactic: Alternating stereochemistry

1. Tacticity affects the physical properties1. Atactic polymers will generally be amorphous, soft, flexible

materials2. Isotactic and syndiotactic polymers will be more crystalline, thus

harder and less flexible2. Polypropylene (PP) is a good example

1. Atactic PP is a low melting, gooey material2. Isoatactic PP is high melting (176º), crystalline, tough material

that is industrially useful3. Syndiotactic PP has similar properties, but is very clear. It is

harder to synthesize

Classification by Thermal BehaviorThermoplastics - materials become fluid and processible upon heating, allowing them to be transformed into desired shapes that are stabilized by cooling.

Thermosets - initial mixture of reactive, low molar mass compounds reacts 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

1. A number-average molecular weight Mn : divide chains into series of size ranges and then determine the number fraction Ni of each size range

where Mi represents the mean molecular weight of the size range i, and Ni is the fraction of total number of chains within the corresponding size range

To create a solid with useful mechanical properties the chain must be long!!

One may describe chain length in terms of polymer average molecular weight, 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 = ∑ Mi Ni / ∑ Ni

Mw = ∑ Mi Wi / ∑ Wi

(1)The number-average molecular weight for a discrete distribution of molecular weights is given as

   

where N is the total number of molecular-weight species in the distribution.

(2) The weight-average molecular weight is given as

A measure 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 or PDI.

PDI= Mw/Mn

Mw/Mn = 1 monodispersePolymer sample consisting of molecules all of which have the same

chain length

Mw/ Mn > 1 polydispersePolymer consisting of molecules with the variety of chain length

Description of polymer physical propertiesDescription of polymer physical properties 1-Primary bonds : the covalent bonds that connect the atoms of the main

chainchain22 - -Secondary bonds :Secondary bonds : non – covalent bonds that hold one polymer chain to non – covalent bonds that hold one polymer chain to

another including hydrogen bond and other dipole –dipole attractionanother including hydrogen bond and other dipole –dipole attraction33--Crystalline polymer :Crystalline polymer : solid polymers with a high degree of structural order solid polymers with a high degree of structural order

and rigidityand rigidity44 - -Amorphous polymers :Amorphous polymers : polymers with a low degree of structural order polymers with a low degree of structural order

55--Semi – crystalline polymer :Semi – crystalline polymer : most polymers actually consist of both most polymers actually consist of both crystalline domains and amorphous domains with properties between thatcrystalline domains and amorphous domains with properties between that

expected for a purely crystalline or purely amorphous polymerexpected for a purely crystalline or purely amorphous polymer66--Glass :Glass : the solid form of an amorphous polymer characterized by rigidity the solid form of an amorphous polymer characterized by rigidity

and brittlenessand brittleness

Amorphous Crystalline

7 – Crystalline melting temperature (T7 – Crystalline melting temperature (Tmm ) : ) : temperature at which crystalline temperature at which crystalline Polymer converts to a liquid or crystalline domains of a semi crystalline Polymer converts to a liquid or crystalline domains of a semi crystalline Polymer melt (increased molecular motion )Polymer melt (increased molecular motion )8- Glass transition temperature (T8- Glass transition temperature (Tg g ) :) : temperature at which an amorphous temperature at which an amorphous polymer converts to a liquid or amorphous domains of a semi crystalline polymer converts to a liquid or amorphous domains of a semi crystalline polymer meltpolymer melt9 – Thermoplastics (plastics9 – Thermoplastics (plastics( ( : :polymers that undergo thermally reversible polymers that undergo thermally reversible Interconversion between the solid state and the liquid state Interconversion between the solid state and the liquid state 10- Thermosets :10- Thermosets : polymers that continue reacted at elevated temperatures polymers that continue reacted at elevated temperaturesgenerating increasing number of crosslinks such polymers do not exhibitgenerating increasing number of crosslinks such polymers do not exhibitmelting or glass transitionmelting or glass transition11- Liquid – crystalline polymers :11- Liquid – crystalline polymers : polymers with a fluid phase that retains polymers with a fluid phase that retainssome ordersome order12- Elastomers :12- Elastomers : rubbery , stretchy polymers the effect is caused by light rubbery , stretchy polymers the effect is caused by light crosslinkingcrosslinking that pulls the chains back to their original state that pulls the chains back to their original state اا

Temperature3

9

6

7

8

4

5

Glass phase (hard plastic)

Rubber phase (elastomer)

Liquid

Leathery phase

Log (stiffness)Pa

Polymerization mechanismsPolymerization mechanisms

Chain GrowthChain GrowthThe only growth reaction is The only growth reaction is

addition of monomer to a addition of monomer to a growing chain with a growing chain with a reactive monomerreactive monomer

The reaction mixture consists The reaction mixture consists of high polymer and of high polymer and unreacted monomers with unreacted monomers with very few actively growing very few actively growing chainchain

Monomer concentration Monomer concentration decreases steadily as decreases steadily as reaction time increasesreaction time increases

Step GrowthStep GrowthReaction can occur Reaction can occur

independently between any independently between any pair of molecular speciespair of molecular species

The reaction mixture consists of The reaction mixture consists of oligomers of many sizes in a oligomers of many sizes in a statically calculable statically calculable distributiondistribution

Monomer disappear early in favor Monomer disappear early in favor of low oligomerof low oligomer

Chain growth High polymer appears High polymer appears

immediately , average immediately , average molecular weight does molecular weight does

not change much as not change much as reaction proceedsreaction proceeds

Increased reaction time Increased reaction time increases overall increases overall product yield , but does product yield , but does not affect polymer not affect polymer average molecular average molecular weightweight

Step GrowthStep GrowthOligomers steadily Oligomers steadily

increases in size, increases in size, polymer average polymer average molecular weight molecular weight increases as reaction increases as reaction proceedsproceeds

Long reaction time are Long reaction time are essential to produce essential to produce polymer with height polymer with height average molecular average molecular weightweight

Polymerization mechanismsPolymerization mechanisms

Lecture 2

Polymerization mechanisms

Polymerization mechanisms

- Step-growth polymerization

Stepwise (Condensation) polymerization Reaction

Requirements for Step-Growth Polymerization • •High 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 polymerization The characteristic features of this type of polymerization process as followprocess as follow.

1-Growth occurs throughout the matrix 1-Growth occurs throughout the matrix 2-There is the rapid loss of the monomer species2-There is the rapid loss of the monomer species3-The molecular weight slowly increases throughout the reaction 3-The molecular weight slowly increases throughout the reaction 4- The same mechanism operate throughout the reaction 4- The same mechanism operate throughout the reaction 5-The polymerization rate decreases as the number of functional 5-The polymerization rate decreases as the number of functional group decreases group decreases 6-No initiator is required to start the reaction6-No initiator is required to start the reaction

Stage 1

Consumptionof monomer

n n

Stage 2

Combinationof small fragments

Stage 3

Reaction of oligomers to give high molecular weight polymer

Step-Growth Polymerization

ExampleExample formation of polyesternHO-R-OH + nHOOC-Rˉ-COOH H-(O-R-OOC-Rˉ-CO-)nHO-R-OH + nHOOC-Rˉ-COOH H-(O-R-OOC-Rˉ-CO-)nnOH+(2n-1)HOH+(2n-1)H22OO

Kinetics of condensation (step – Growth ) polymerizationKinetics of condensation (step – Growth ) polymerizationConsider the synthesis of polyester from a diol and a diacid. The first Consider the synthesis of polyester from a diol and a diacid. The first step is the reaction of the diol and the diacid monomers to form step is the reaction of the diol and the diacid monomers to form dimerdimer,,HO-R-OH + HOOC-R"-COOH--> HO-R-OCO-R'-COOH + H2O

The dimer then forms trimer by the reaction with diol monomer,HO-R-OCO-R'-COOH + HO-R-OH--> HO-R-OCO-R'-COO-R-OH +HHO-R-OCO-R'-COOH + HO-R-OH--> HO-R-OCO-R'-COO-R-OH +H22OO

and also with diacid monomer,HO-R-OCO-R'-COOH + HOOC-R'-COOH-->HO-R-OCO-R'-COOH + HOOC-R'-COOH-->HOOC-R'-COO-R-OCO-R'-COOH + HHOOC-R'-COO-R-OCO-R'-COOH + H22OO

Kinetics of Condensation (Step-Growth) Polymerization• Step-Growth polymerization occurs by consecutive reactions in which Step-Growth polymerization occurs by consecutive reactions in which

the degree of polymerization and average molecular weight of the the degree of polymerization and average molecular weight of the polymer increase as the reaction proceeds. Usually (although not polymer 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 the water). Condensation polymerization may be represented by the following reactions: following reactions:

Monomer + Monomer Dimer + H2O Monomer + Dimer Trimer + H2O Monomer + Trimer Tetramer + H2O Dimer + Dimer Tetramer + H2O Dimer + Trimer Pentamer + H2O Trimer + Trimer Hexamer + H2O• Generally, the reactions are reversible, thus the eliminated water must be Generally, the reactions are reversible, thus the eliminated water must be

removed 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 are Based on the assumption that the polymerization kinetics are

independent of molecular size, the condensation reactions may all be independent of molecular size, the condensation reactions may all be simplified to:simplified to:~~~~COOH + HO~~~~ ~~~~COOH + HO~~~~ ~~~~COO~~~~ + H ~~~~COO~~~~ + H22OO

Kinetic analysisKinetic analysis~~~~COOH + HO~~~~ ~~~~COO~~~~ + H2OMost step polymerization involve bimolecular reaction that are often catalyzed~~~~A + B~~~~ + catalyst ~~~~AB~~~~ + catalyst The rate is accelerated according to

-d [A]

By integration

dtdt= k= k [A][B] [A][B] [catalyst][catalyst]

-d [A]-d [A]

dtdt= k= k ' '[A][B][A][B]

-d [A]-d [A]

dtdt= k= k ' '[A]2[A]2

11[M][M]

--11

= k 't= k 't[M]o[M]o

OrOr

Where kWhere k= ‘ = ‘ k [catalyst]k [catalyst]

I f [A] = [B]I f [A] = [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

The concentration at any time given by

[M]

[M] =[M] = [M]o - [M]o - [M]o P = [M]o (1- P )[M]o P = [M]o (1- P )

By substitution inBy substitution in( **) ( **) 11

(1-p)(1-p)= k= k ' '[A]o t + 1[A]o t + 1

•Note that experimental data are usually linear only beyond ca. 80% conversion.

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

Uncatalyzed Polyesterification

Note that experimental data for esterification reactions show that plots of Note that experimental data for esterification reactions show that plots of 1/(1-p)1/(1-p)22 vs. time are linear only after ca. vs. time are linear only after ca. 80% conversion80% conversion. .

• This behavior has been attributed to the reaction medium changing This behavior has been attributed to the reaction medium changing from one of pure reactants to one in which the ester product is the from one of pure reactants to one in which the ester product is the solvent. solvent.

• Thus, the true rate constants for condensation polymerizations Thus, the true rate constants for condensation polymerizations should only be obtained from the linear portions of the plots (i.e., the should 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 and For example, the kinetic plots for the polymerization of adipic acid and 1,10-decamethylene glycol show that at 2021,10-decamethylene glycol show that at 202ooC, the third-order rate C, the third-order rate constant for the uncatalyzed polyesterification is k = 1.75 x 10-2 constant for the uncatalyzed polyesterification is k = 1.75 x 10-2 (kg/equiv)(kg/equiv)22 min min-1-1..

Polyesterification Without Acidic Catalyst (continued)

The Number Average Molecular Weight in Polycondensation

. The number-average degree of polymerization X. The number-average degree of polymerization Xn n is given as the total is given as the total number of monomer molecules initially present divided by the total number number 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 ( 1 – P ) ( 1 – P )

XXnn = 1 / 1 - P = 1 / 1 - P•This relationship is the This relationship is the Carother's EquationCarother's Equation. .

ExampleExampleIf monomer conversion is 99% what is Xn ?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

The number-average molecular weight MThe number-average molecular weight Mnn, defined as, defined as

MMnn = M = Moo X Xnn + M + Megeg = M = Moo / 1 – P + M / 1 – P + Megeg

where Mwhere Mo o is the mean of the molecular weights of the structural is the mean of the molecular weights of the structural units, and Munits, and Megeg is the molecular weight of the end groups. The latter is the molecular weight of the end groups. The latter becomes negligible at even moderate molecular weightbecomes negligible at even moderate molecular weightMMnn = M = Moo X Xnn + M + Meg eg = M = Moo / 1 – P / 1 – P

1(1-p)

= k '[A]ot + 1

Xn= k '[A]ot + 1

X2n=2 k [A]2

ot + 1

H-(O-R-OOC-Rˉ-CO-)H-(O-R-OOC-Rˉ-CO-)nnOHOH

Mn as a Function of Conversion

Molecular Weight Control in Linear PolymerizationMolecular Weight Control in Linear PolymerizationIn the synthesis of polymers one is usually interested in obtaining a product of very specific molecular weight since its properties are highly dependent on its molecular weight.

The desired molecular weight can be obtained byThe desired molecular weight can be obtained by1-Quenching the reaction (e.g., by cooling) at the appropriate time. 1-Quenching the reaction (e.g., by cooling) at the appropriate time. However, the polymer obtained in this case is unstable, since it can However, the polymer obtained in this case is unstable, since it can undergo further polymerization if it is heated. This is because the end undergo further polymerization if it is heated. This is because the end groups on the polymer chains are still active and they can react with groups on the polymer chains are still active and they can react with each other. each other.

2-By increasing one reactant over the other. In this way the monomer in2-By increasing one reactant over the other. In this way the monomer inexcess will block any further increase in the polymer chains.excess will block any further increase in the polymer chains.

Excess HExcess H22N-R-NHN-R-NH22 + HOOC-R'-COOH ---> H-(-NH-R-NHCO-R'-CO-) + HOOC-R'-COOH ---> H-(-NH-R-NHCO-R'-CO-)nn-NH-R-NH-NH-R-NH22

The use of excess diacid accomplishes the same result; the polyamideThe use of excess diacid accomplishes the same result; the polyamide in this case has carboxyl end groupsin this case has carboxyl end groups

ExcessHOOC-R'-COOH+HExcessHOOC-R'-COOH+H22N-R-NHN-R-NH22 --->HO-(-CO-R'-CONH-R-NH-) --->HO-(-CO-R'-CONH-R-NH-)nn-CO-R'-COOH-CO-R'-COOH

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 (2)Type (2)For the polymerization of bifunctional monomers A-A and B-B where B-BFor the polymerization of bifunctional monomers A-A and B-B where B-B

is present in excess, the numbers of A and B F.gs. are given by Nis present in excess, the numbers of A and B F.gs. are given by NAA and N and NBB

. .Notice that NNotice that NA A and Nand NB B are equal to twice the number of A-A and B-Bare equal to twice the number of A-A and B-B 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 = NA A /N/NBB. ≤ 1. ≤ 1The total number of monomer molecules is given byThe total number of monomer molecules is given by

(N(NAA+N+NBB)/2 or N)/2 or NAA(1+1/r)/2. (1+1/r)/2. , 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 or of chain ends or [N[NAA(1-p)+N(1-p)+NBB(1-rp]/2.(1-rp]/2.

The number-average DP( XThe number-average DP( Xnn )is the total number of A-A and B-B molecules )is the total number of A-A and B-B molecules initially present divided by the total number of polymer molecules:initially present divided by the total number of polymer molecules:

XXnn = N = NAA(1+1/r)/2. (1+1/r)/2. [N[NAA(1-p)+N(1-p)+NBB(1-rp]/2.(1-rp]/2.

Xn = 1 + r 1 + r – 2rP

If r = 1Xn = 1 / 1-p

If p = 1Xn = 1 + r / 1 - r

ExampleExampleWhat is XWhat is Xnn when P = 1 but use 0. 9800 moles of A-A and 1. 0100 when P = 1 but use 0. 9800 moles of A-A and 1. 0100

moles of B – Bmoles of B – Br = Nr = NAA / N / NB B = 0.98 x 2 / 1.01 x 2 = 0.97= 0.98 x 2 / 1.01 x 2 = 0.97XXn n = 1 + r / 1 – r = 1.97 / 0.03 = 66= 1 + r / 1 – r = 1.97 / 0.03 = 66

Type (3)Type (3)the molecular weight can also be controlled by adding small the molecular weight can also be controlled by adding small amounts of monofunctional monomeramounts of monofunctional monomer..Moles of A-A = NMoles of A-A = NAA / 2 / 2Moles of B-B = NMoles of B-B = NBB / 2 / 2Moles of mono functional B = NMoles of mono functional B = NBBˉ̄r = ½ Nr = ½ NAA / ½ N / ½ NBB + N + NBBˉ = Nˉ = NAA / N / NBB + 2 N + 2 NBBˉ̄

ExampleExample Find Xn for 1 mole of A-A ,1mole of B-B and 0.01 mole of RBˉ when P = 1r = 1/ 1 + 2x 0.01 = 0.99Xn 1 + r / 1 – r = 1 + 0.99 / 1 – 0.99 = 199

The poly dispersity indexThe poly dispersity indexXXww / X / Xn n = 1 + P= 1 + P

XXnn = 1 /1-P X = 1 /1-P Xw w = 1 + p / 1 - P= 1 + p / 1 - P

SummarySummary11(1-p)(1-p)

= k= k ' '[A]o t + 1[A]o t + 1

1(1-p)2 =2 k [A]2ot + 1

XXnn = N = No o / N = [ M ]/ N = [ M ]oo / [ M] / [ M] XXnn = 1 / 1 - P = 1 / 1 - P

MMnn = M = Moo X Xnn + M + Megeg = M = Moo / 1 – P / 1 – P

Xn= k '[A]ot + 1

X2n=2 k [A]2

ot + 1

r = Nr = NAA /N /NBB. ≤ 1. ≤ 1Xn = 1 + r 1 + r – 2rP

If r = 1Xn = 1 / 1-p

If p = 1Xn = 1 + r / 1 - r

r = ½ Nr = ½ NAA / ½ N / ½ NBB + N + NBBˉ = Nˉ = NAA / N / NB B + 2 N+ 2 NBBˉ̄

The poly dispersity indexThe poly dispersity indexXXww / X / Xnn = 1 + P = 1 + P

XXnn = 1 /1-P X = 1 /1-P Xww = 1 + p / 1 - P = 1 + p / 1 - P

Lecture 3

Polymerization mechanisms

Polymerization mechanisms

- Chain-growth polymerization

Chain polymerizationChain polymerizationThe characteristic of chain polymerization are as followThe characteristic of chain polymerization are as follow: :

1- Growth is by the addition of the monomer at the end of the chain1- Growth is by the addition of the monomer at the end of the chain2-Even at long reaction time some monomer are remain in the reaction2-Even at long reaction time some monomer are remain in the reactionmixturemixture3-The molecular weight of the polymer are increase rapidly3-The molecular weight of the polymer are increase rapidly4-Different mechanisms operates at different stages of the reaction4-Different mechanisms operates at different stages of the reaction5-The polymerization rate initially increases and then become constant5-The polymerization rate initially increases and then become constant6-An initiator is required to start the reaction6-An initiator is required to start the reaction

Chain polymerization reaction consists of three stagesChain polymerization reaction consists of three stages 1- Initiation 2- Propagation 3-Termination

Polymerization depend on thermodynamicPolymerization depend on thermodynamicPolymerization is possible only if the free energy difference betweenPolymerization is possible only if the free energy difference betweenmonomer and polymer is negativemonomer and polymer is negative

G = G = H - TH - TS S 0 0Must be -ve forMust be -ve forPolymerization to Polymerization to workwork In chainIn chain

polymerizationpolymerization are exothermicare exothermic

AlwaysAlways++veve

Always –ve in chainAlways –ve in chain polymerizationpolymerization

Chain polymerizationChain polymerization

Radical polym.Radical polym.The C=C is prefer The C=C is prefer the Polym. by R.P.the Polym. by R.P.and also can be and also can be used in the steric used in the steric hindrance of the hindrance of the substituentsubstituent

Ionic polymIonic polym..

Anionic polym.Anionic polym. Cationic polym.Cationic polym.

X X X

radical cationic anionic

Electron with drawingElectron with drawingsubstituent decreasingsubstituent decreasingthe electron density on the electron density on the double bond andthe double bond and facilitate the attack offacilitate the attack ofanionic speciesanionic speciessuch as cyano andsuch as cyano and carbonyl carbonyl δ+ δ+ δ- δ- CHCH22=CH Y=CH Y

Electron donatingElectron donatingsubstituent increasingsubstituent increasingthe electron density onthe electron density on the double bond andthe double bond and

facilitate the attack offacilitate the attack ofcationic speciescationic speciessuch as alkoxy, alkyl, such as alkoxy, alkyl, alkenyl, and phenylalkenyl, and phenyl δ-δ- δ+ δ+ CHCH22 =CH Y =CH Y

Unsubstituted (ethylene)Works fine.

MonosubstitutedWorks fine .

1,1-DisubstitutedUsually works.

1,2-DisubstitutedSeldom works .

TrisubstitutedAlmost never works .

TetrasubstitutedAlmost never works .

The only exceptions to the unreactivity of tri- and tetra-substituted vinyl monomers are those with fluorine, like tetrafluoroethylene (CF2=CF2). The main cause of this reactivity pattern is the steric size of the substituents.

Vinyl monomers for addition polymerizations

Free Radical Vinyl Chain PolymerizationFree Radical Vinyl Chain PolymerizationRate of Radical Chain PolymerizationRate of Radical Chain PolymerizationRadical polymerization consists of three steps-initiation, propagation, Radical polymerization consists of three steps-initiation, propagation, and termination.and termination. The The initiationinitiation step consists of two reactions. step consists of two reactions.1-The production of the free radical 1-The production of the free radical kd

I ------> 2R˙2- Addition of this radical to a monomer molecule to produce the2- Addition of this radical to a monomer molecule to produce thechain initiating species Mchain initiating species M11

kkii

R˙ + MR˙ + M11 -----> M -----> M11˙̇

The The propagationpropagation consists of the growth of M consists of the growth of M1 1

kkpp MMnn + + M M11

˙ ˙ ------> M------> Mn+1n+1˙ ˙

(Rapid reaction ) (Rapid reaction )

.Termination Termination with the annihilation of the radical centers occurs bywith the annihilation of the radical centers occurs by bimolecular reaction between radicals either by combination orbimolecular reaction between radicals either by combination or ,, ,,

by disproportionationby disproportionation kktctc

MMnn˙ + M˙ + Mm m ˙ -----> M˙ -----> Mn+m n+m

kktdtd

MMnn˙ + M˙ + Mmm ˙ -----> M ˙ -----> M nn+ M+ MmmThe termination step can be represented byThe termination step can be represented by k k tt

MMn n ˙̇+ M+ Mm m

˙ ˙ ----> dead polymer ----> dead polymer

Kinetic Rate ExpressionKinetic Rate ExpressionThe 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 for the production of high molar mass Since for the production of high molar mass material Rmaterial Rpp » R » Rii this equation can be re-written as: this equation can be re-written as:

•]M][M[kRdt

]M[dpp

From the beginning of the polymerization:From the beginning of the polymerization:• increasing number of radicals due to decomposition of increasing number of radicals due to decomposition of

the initiatorthe initiator• increasing termination due to increasing radical increasing termination due to increasing radical

concentration (Rconcentration (Rtt [M·] [M·]22))• eventually a steady state in radical concentration:eventually a steady state in radical concentration:

****

This is equivalent to stating that the rate of initiation RThis is equivalent to stating that the rate of initiation Rii equals the equals the rate of termination Rrate of termination Rtt

RRpp =k =kpp [M] ( R [M] ( Rii /2k /2ktt) ½) ½

Ri = 2kt[M.]2

[ M˙ ] = ( R[ M˙ ] = ( Rii /2k /2kt t ) ½) ½

and substitution in Eq.* * yields for the rate of polymerization.and substitution in Eq.* * yields for the rate of polymerization.

Initiation free radical polymerizationInitiation free radical polymerization

• ThermalThermal initiators initiators• PhotochemicalPhotochemical• Redox initiatorsRedox initiators• Ionizing radiationIonizing radiation

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)or Most common examples: peroxides (benzoyl peroxide)or azo compounds(azo isobuteronitrile).azo compounds(azo isobuteronitrile).

Peroxides Azo compaunds

(I 2R•)

(Temperatures are for 10 hour half-lives.)

The thermal, homolytic dissociation of initiators is the most widely The 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 range 100-170 kJ/mole. energies in the range 100-170 kJ/mole.

The rate of producing primary radicals by thermal homolysis of an The rate of producing primary radicals by thermal homolysis of an initiator Rinitiator Rdd is given by is given by RRdd= 2fk= 2fkdd[I][I] where [I] is the concentration of the initiator and f is the initiator where [I] is the concentration of the initiator and f is the initiator efficiency.efficiency.

and the rate of initiation is given byand the rate of initiation is given by RRii=2fk=2fkdd[I][I]By substitute in By substitute in RRpp =k =kpp [M] ( R [M] ( Rii /2k /2ktt) ½) ½

RRpp =k =kpp [M] (fk [M] (fkd d [I] /k[I] /kt t ) ½) ½

PhotochemicalPhotochemical initiators initiators:•One or two component. One or two component. •Used for thin films.Used for thin films.

PeroxidesPeroxides

Azo compaundsAzo compaunds DisulfidesDisulfides

KetonesKetones

S S S2h

RedoxRedox initiators initiators::•Usually 2 component.Usually 2 component.•Rarely used.Rarely used.

Ionizing radiation:•X-ray, gamma-ray.X-ray, gamma-ray.•Random destruction leads to Random destruction leads to radical formation.radical formation.•Used only in very specialUsed only in very special casescases.Fentons reagent

Experimental Determination of RExperimental Determination of Rpp

RRpp can be experimentally determined by measuring the change in any can 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 absorption solubility, density, refractive index, and spectral absorption

The polymerization can also be followed by separation and isolation of The polymerization can also be followed by separation and isolation of the reaction products. Chemical analysis of the unreacted monomers the 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 be The disappearance of monomers or the appearance of polymer can be followed spectroscopically, i.r. or uv spectroscopyfollowed spectroscopically, i.r. or uv spectroscopy

Dilatometry Dilatometry Dilatometry is the volume changes that occurs upon polymerization to Dilatometry is the volume changes that occurs upon polymerization to follow the conversion. It is the most accurate method for chain follow the conversion. It is the most accurate method for chain polymerization because of the large difference in density between polymerization because of the large difference in density between monomer and polymer monomer and polymer

Kinetic chain lengthKinetic chain length

i

p

RR

species initiatingunitsmonomer ofnumber

By substituteBy substitute

RRii=2f k=2f kd d [I] R[I] Rpp =k =kpp [M] (f k [M] (f kd d [I] /k[I] /ki i ) ½) ½

νν =R =Rpp/R/Rii =R =Rpp/R/Rtt = k = kp p [M] / 2 (f k[M] / 2 (f kd d kkt t [I] )[I] )1/21/2

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 polymer chain. In other words, v is the ratio between the propagationpropagation

rate to that of initiation, or terminationrate to that of initiation, or termination..

The number average degree of polymerization XThe number average degree of polymerization Xnn of chains of chains formed at a certain moment is dependent on the termination formed at a certain moment is dependent on the termination mechanism:mechanism:** combination: Xcombination: Xnn = 2 = 2** disproportionation: Xdisproportionation: Xnn = =

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

Lecture 4

Polymerization mechanisms

Polymerization

Monomer Polymer

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 systemor species to it from some compound present in the system. . This leads to a decrease in the molecular weight than expectedThis leads to a decrease in the molecular weight than expected . .

MMnn˙ ˙ + XY M+ XY Mnn-X +Y -X +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 transferredand 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 initiation original rate of initiation

kktrtr

CaseCaseRelative rate constants Relative rate constants for Transfer, for Transfer, Propagation, and Propagation, and Reinitiation Reinitiation

Type of effectType of effectEffect on Effect on RRpp

Effect on XEffect on Xnn

11KKpp>>k>>ktrtr k kaa~K~KppNormal chain Normal chain transfertransfer

NoneNoneDecreaseDecrease

22KKpp<<k<<ktrtr k kaa~K~KppTelomerizationTelomerizationNoneNoneLarge Large decreasedecrease

33KKp p >>k>>ktrtr k kaa<K<KppRetardationRetardationDecreaseDecreaseDecreaseDecrease

44KKpp<<k<<ktrtr k kaa<K<KppDegradative Degradative chain transferchain transfer

Large Large decreasedecrease

Large Large decreasedecrease

Effect of Chain Transfer on REffect of Chain Transfer on Rpp and X and Xnn

In case (1) In case (1) νν ( chain length ) is not changed ( chain length ) is not changedXXnn (number average degree of polymerization ) is altered (number average degree of polymerization ) is altered

The degree of polymerization now should be redefined as the The degree of polymerization now should be redefined as the polymerization rate divided by the sum of all the chain breaking polymerization rate divided by the sum of all the chain breaking reactions:reactions:XXnn = R = Rpp

(R(Rtt/2) + K/2) + KtrM trM [M˙][M] + K[M˙][M] + Ktrs trs [M˙][S] + K[M˙][S] + KtrI trI [M˙][I][M˙][I]

C=chain transfer constant = KC=chain transfer constant = Ktr tr / K/ Kpp

CCMM=K=KtrM trM /K/Kpp C CSS=K=KtrS trS /K/Kp p C CII=K=KtrI trI /K/Kp p R Rpp=K=Kp p [M][M˙][M][M˙]

1/X1/Xnn=R=Rt t /2R/2Rpp+ K+ KtrMtrM [M˙][M]/R [M˙][M]/Rpp+ K+ Ktrs trs [M˙][S]/R[M˙][S]/Rpp+K+KtrI trI [M˙][I]/R[M˙][I]/Rpp

Substitute by the value of RSubstitute by the value of Rpp

1/X1/Xnn=R=Rt t / 2R/ 2Rpp+K+KtrM trM / K/ Kpp+ K+ Ktrs trs [S] / K[S] / Kpp[M] +K[M] +KtrI trI [I] / K[I] / Kp p [M][M]Substitute by the value of CSubstitute by the value of C

11//XXnn=R=Rtt/ 2R/ 2Rpp+C+CMM+C+CS S [S] / [M] +C[S] / [M] +CI I [I] / [M] [I] / [M] Mayo – walling equationMayo – walling equation

11//XXnn= 1/(X= 1/(Xnn))o o +C+CMM+C+CS S [S] / [M]+C[S] / [M]+CI I [I] / [M][I] / [M]

1/DP0

Cs

1/D

P

[S]/[M]

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] andIn the presence of chain transfer agent In the presence of chain transfer agent

1/X1/Xn n = 1/(X= 1/(Xnn))o o +C+CSS [S] / [M ] [S] / [M ]

Energetic CharacteristicsEnergetic CharacteristicsActivation 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 beexpressed by an Arrhenius-type relationshipexpressed by an Arrhenius-type relationship

k = A e k = A e – E / RT– E / RT

or lnk = lnA – E / RTlnk = lnA – E / RTwhere A is the collision frequency factor, and E the Arrhenius where A is the collision frequency factor, and E the Arrhenius activation energy. A plot of ln k vs 1/T allows the determinationactivation energy. A plot of ln k vs 1/T allows the determinationof both values.of both values.

Rate of PolymerizationRate of Polymerization For a polymerization initiated by the thermal decomposition of an For a polymerization initiated by the thermal decomposition of an initiator the polymerization rate depends on three rate constants initiator the polymerization rate depends on three rate constants KKp p ( k( kd d / k/ kt t ))1/21/2

40)-(3 )2/()2/(lnln

2/12/1

RTEEE

AAA

kkk 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 EERR is [E is [Epp + (E + (Edd/2)-(E/2)-(Et/t/2)]. can be written as2)]. can be written as

41)-(3 RTE- ][])[(lnlnln R2/1

2/1

MIfAAAR

t

dPP

RRpp =k =kpp [M] (fk [M] (fkdd [I] /k [I] /ktt ) ½ ) ½�ً�ًWhereWhere

Must be -ve forMust be -ve forPolymerization to Polymerization to workwork In chainIn chain

polymerizationpolymerization are exothermicare exothermic

AlwaysAlways++veve

Always –ve in chainAlways –ve in chain polymerizationpolymerization

G = G = H - TH - TS S 0 0Thermodynamics of Polymerization Thermodynamics of Polymerization

Polymerization of 1,2-Disubstituted EthylenesPolymerization of 1,2-Disubstituted Ethylenes

1,21,2--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 this undergo polymerization. Steric inhibition is the cause of this behavior behavior

RR RR substitutedsubstituted

Polymerization-Depolymerization EquilibriaPolymerization-Depolymerization EquilibriaCeiling Temperature Ceiling 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 should reaction becomes a reversible one, that is, the propagation step should be written as an equilibrium reactionbe written as an equilibrium reaction

Mn + Mkpkdp

Mn+1 (3-43)

where kwhere kdpdp is rate constant for the reverse reaction-termed is rate constant for the reverse reaction-termed depolymerization or depropagationdepolymerization or depropagation

The reaction isothermThe reaction isotherm∆G = ∆Go + RT lnK. For an equilibrium situation For an equilibrium situation G=0 by G=0 by Go = Ho - TSo = - RT ln K

equilibrium constant is defined by Kp/kdp or by

46)-(3

][1

]][[][

.

.1

MMMMK

n

n

48)-(3 ln[M]

or

47)-(3 ][

1]ln[

c RS

RTH

MMRSHT

o

c

o

co

o

c

Ionic chain polymerizationIonic chain polymerizationThe characteristic of ionic chain polymerization are as followThe characteristic of ionic chain polymerization are as follow1-Ionic polymerization is limited because the ions are usually unstable 1-Ionic polymerization is limited because the ions are usually unstable and require stabilization by solvation and lower temperature for and require stabilization by solvation and lower temperature for polymerization to proceedpolymerization to proceed

2- The ionic polymerization proceeds with very high rates and is very2- The 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

3-Cationic and anionic polymerizations have very similar characteristics.3-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

4-solvents of high polarity cannot be used. The highly polar hydroxylic 4-solvents of high polarity cannot be used. The highly polar hydroxylic solvents (water, alcohol) react and destroy most ionic initiators. Other polar solvents (water, alcohol) react and destroy most ionic initiators. Other polar solvents such as ketones form highly stable complexes with the initiators solvents such as ketones form highly stable complexes with the initiators preventing thus the polymerization. Ionic polymerization,thus require solvent preventing thus the polymerization. Ionic polymerization,thus require solvent of low or moderate polarity such as CHof low or moderate polarity such as CH33Cl,CHCl,CH22ClCl22, and pentane, and pentane..

5-Ionic polymerizations are characterized by a wide variety of modes 5-Ionic polymerizations are characterized by a wide variety of modes of initiation and termination. of initiation and termination.

CATIONIC POLYMERIZATIONCATIONIC POLYMERIZATIONInitiationInitiation

a-Protonic Acidsa-Protonic AcidsProtonic acids can be used to some extent but the anion of the acid Protonic acids can be used to some extent but the anion of the acid should not be highly nucleophilicshould not be highly nucleophilic HA + RR"C=CH2 RR"C+(A)-

CH3

(4 _1)

Halogen acids are Halogen acids are not usednot used because of the highly nucleophilic because 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, used used for cationic for cationic

polymerization.polymerization.mineral acids (initiators): H2SO4, H3PO4 ( provide H+)

The molecular weight obtained is low (few thousand). The molecular weight obtained is low (few thousand).

b-Lewis Acidsb-Lewis Acids

Lewis acids used to initiate cationic polymerization at low Lewis 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 other proton or cation source) Forming (co-initiator / initiator) system

BF3 + H2O HOBF3-H+ (7.2)

AlCl3 + RCl AlCl4-R+ (7.3)

Very active Lewis acids 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)- + Mki YM+(IZ)- (4-5b)

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 the produced 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 ion carbonium ion and its counter ion

HMHMnn++(IZ) (IZ) -- + M HM + M HMnnMM++(IZ)(IZ)--

1-Chain Transfer to Monomer1-Chain Transfer to Monomer. This involves transfer of a proton to a monomer molecule This involves transfer of a proton to a monomer molecule with the formation of terminal unsaturation in the polymer with the formation of terminal unsaturation in the polymer moleculemolecule

HMnM+(IZ)- + M Mn+1 + HM+(IZ)-

2-Spontaneous Termination2-Spontaneous TerminationSpontaneous termination involves regeneration of the initiator-Spontaneous termination involves regeneration of the initiator-coinitiator complex by expulsion from the propagating ion pair coinitiator complex by expulsion from the propagating ion pair with the polymer molecule left with terminal unsaturation.with the polymer molecule left with terminal unsaturation.

HMnM+(IZ)- Mn+1 + H+(IZ)-

3-Combination with counter ion3-Combination with counter ionTermination by combination of the propagating carbonium ion Termination by combination of the propagating carbonium ion with its counter ion occurswith its counter ion occurs

HMnM+(IZ)- HMnMIZ

TerminationTermination

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, propagationto that for radical polymerization. The rates of initiation, propagation,, and termination are given byand termination are given by

RRii = Kk = Kki i [I][ZY][M] R[I][ZY][M] Rpp = K = Kpp [YM [YM++(IZ)(IZ)--][M]][M] R Rtt = 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 centers propagation centers

13)-(4 ]][][[])([t

i

kMZYIKkIZYM

14)-(4 ]][][[][ 2

t

Pi

t

PiP k

MZYIkKkk

MkRR

The number-average degree of polymerization is obtained as theThe number-average degree of polymerization is obtained as thepropagation rate over the termination ratepropagation rate over the termination rate

15)-(4 ][

t

P

t

Pn k

MkRRX

When chain breaking involves chain transfer to monomer and/or When chain breaking involves chain transfer to monomer and/or termination in addition to combination with gegenion, the degree of termination in addition to combination with gegenion, the degree of polymerization is polymerization is

15)-(4 ,Mtrt

Pn RR

RX

The rate of chain transfer to monomer is given by The rate of chain transfer to monomer is given by Rtr,M = ktr,M[YM+)IZ-(][M]

17a)-(4 ][

][

, MkkMkXMtrt

Pn ThenThen

OrOr17b)-(4 C

][1

MMk

kX P

t

n

where Cwhere CMM is the chain transfer constant for monomer is the chain transfer constant for monomer..

Effect of Reaction MediumEffect of Reaction MediumSolvent 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 solventif 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 than as 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

EnergeticsEnergeticsCationic polymerization is also exothermic, since the reaction involvesCationic polymerization is also exothermic, since the reaction involves the conversion of π-bond into σ-bond.the conversion of π-bond into σ-bond. the activation energies for the rate and degree of polymerization are the activation energies for the rate and degree of polymerization are obtained asobtained as

EERR = E = Eii+E+Epp-E-Ett

Trommsdorff effect

In radical polymerization we speak about:1( low conversion, i.e. polymer chains are in dilute solution )no contact among chains(2( “intermediate” conversion, i.e. the area in between low and high conversion3( high conversion, i.e. chains are getting highly entangled; kp decreases.

Somewhere in the “intermediate” conversion regime:* polymer chains loose mobility.* Termination rate decreases* Radical concentration increases* Rate of polymerization increases* Molar mass increases

This effect is called: gel effect, Trommsdorff effect,or auto-acceleration

In the polymerization of MMA this occurs at relatively low conversion.

Molar mass

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:

Kinetics of free-radical chain polymerization considering chain transfer reactions

RMn• + S-H RMn-H + S•

Rtr = ktr[M•][Transfer agent]

Chain transfer

chain transfer to:• monomer• initiator• solvent or chain transfer agent• polymer• allylic transfer

monomer, initiator and chain transfer agent are mathematically treated identically:

•][X]M[k•]M[k2•]M[kdt

]polymer[dX,tr

2td

2tc

As derived beforethis leads to:

]M[k]I[k

]M[k]S[k

kk

]M[k•]M[k2

]M[k•]M[k

]M[k]X[k

]M[k•]M[k2

]M[k•]M[k

P1

p

I,tr

p

S,tr

p

M,tr

p

td

p

tc

p

X,tr

p

td

p

tc

n

The rate of “polymer formation” is now defined as:

]T][•M[k]•M[k2]•M[kdt

]polymer[dtr

2td

2tc

The rate of polymerization as derived before:

•]M][M[kdt

]M[dp

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

P1

p

tr

p

td

p

tc

p

tr2

td2

tc

n

thus:

]M[]T[CP

1

1PT

0,n

n

Chain transfer to polymer

• 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 40 501

2

3

4

5

6

7

8

conversion ca. 25% conversion > 80%

mol

% b

ranc

hes

[BA]0 / %(w/w)

Summary

tMkL p ][

]][[ MMkR pp

Chain-length

Rate of polymerization

Initiator decomposition is the reaction step most strongly influenced by temperature.

][1~M

tTime of chain-growth

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

Thermodynamics of radical polymerisation

G = H - TS 0 G will increase if T is raised

Increasing the temperature G eventually becomes 0 and the polymerization stops. This occurs because the loss in entropy arising from joining many molecules into one starts to outweigh the energetic benefit of converting double bonds to single bonds. The temperature above which a monomer cannot be converted to long chain polymer is known as the ceiling temperatute Tc.

RMn• + M RMn+1• kp

kdp

Rp = kp[M•][M] - kdp[M•] = 0[M•](kp[M] – kdp) = 0 or kp[M] = kdp if [M•] constK = (kp / kdp) = 1/ [Me] G = -RTclnK = RTcln [Me] = H - TcS RTcln[Me] + TcS = H

Tc = H/(S + Rln[Me])

Thermodynamics of radical polymerisation

12

111 k

kr

21

222 k

kr

kk1111

kk1212

kk2121

kk2222

Copolymerization

——MM11• + M• + M11 —M—M11••

——MM11• + M• + M22 —M—M22••

——MM22• + M• + M11 —M—M11••

——MM22• + M• + M22 —M—M22••

}}

}}

Copolymerizationffii:: fraction of monomer fraction of monomer ii in reaction mixture in reaction mixture

ff11 = [M = [M11] / ([M] / ([M11] + [M] + [M22])])

FFii:: fraction of monomer fraction of monomer ii built into polymer built into polymer

FF11 = d[M = d[M11] / (d[M] / (d[M11] + d[M] + d[M22])])

22221

211

212

111 2 frfffr

fffrF

Long chain assumption (Long chain assumption (kkii, , kkdd ignored; ignored; kkpp, , kktt not ~ chain not ~ chain length)length)Reactivity ratios independent of environmental factorsReactivity ratios independent of environmental factors

22221111

22221

211

p2

kfrkfrfrfffrk

Average copolymerisation rate: Average copolymerisation rate:

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1f 1

F 1

MMA / BAEthene / VAcVDC / VC

Ideal copolymerisation

Composition driftComposition drift

If If ff11 ≠ F ≠ F11

→ → ff11 changes changes→ → FF11 changes changes

What does composition What does composition drift mean for the polymer drift mean for the polymer that is formed?that is formed?

Polymerization techniques

• Kinetic / mechanistic factors related to chain length, chain composition

• Technological factors e.g. heat removal, reaction rate, viscosity of the reaction mixture, morphology of the product

• Economic factors; production costs, enviromental aspects, purification steps etc.

Sometimes for one monomer several techniques of polymerizing are available. Choice of a specific technique depends on a number of factors:

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

Advantages: Disadvantages:• Simple, only the monomer and initiator

are present in the reaction mixture• High molecular weight

Exotherm of the reaction might be hard to control- molecular weights very disperse

The polymer is solublein the monomer:

The polymer is not soluble in the monomer:

Viscosity of the reaction increases markedly (gel effect)

Polymer precipitates out without increase in solution viscosity

Rp

Solution polymerizationMonomer dissolved in solvent, formed polymer stays dissolved. Depending on concentration of monomer the solution does not increase in viscosity.

AdvantagesDisadvantages * Product sometimes * Contamination with directly

usable solvent* Controlled heat * Chain transfer to

release solvent* Recycling solvent

Applications Acrylic coating, fibrespinning, film casting

Suspension polymerization• Water insoluble monomers are dispersed in water.• Initiator dissolved in monomer.• Stabilization of droplets/polymer particles with non-micelle forming

emulsifiers 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.

Advantages Disadvantages * Heat control simple * Contamination with * Product directly stabilizing agent

usable * Coagulation possible * Easy handling

ApplicationsIon-exchange resins, polystyrene foam, PVC

Suspension Polymerization

Emulsion Polymerization• A micelle forming emulsifier is used.• Initiator is water soluble.• The formed latex particles are much smaller than suspension particles (0.05-2 µm).• Kinetics differ considerable from other techniques.• Polymer is formed within the micelles and not in the monomer droplets.

Emulsion Polymerization

Advantages Disadvantages* Low viscosity even * Contamination of at high solid contents products with additives

* Independent control * More complicated of rate and in case of water

molecular-weight soluble monomers

* Direct application of complete reactor contents

• Ionic polymerizations are more selective than radical processes due to strict requirements for stabilization of ionic propagating species.Cationic: limited to monomers with electrondonating groups

Overview of Ionic Polymerization:Selectivity

Anionic: limited to monomers with electron withdrawing groups

• 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 anionic polymerization.

• 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).

Overview of Ionic Chain Polymerization:Counterions

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).

Overview of Ionic PolymerizationIon-pair Binding

•Reactions are fast but are extremely sensitive to small amounts of impurities. Highly polar solvents (water, alcohols, ketones) will react with 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 cationic polymerization, but termination is absent for anionic polymerization.

Overview of Ionic Chain Polymerization:Mechanistic Analysis

Initiation of Cationic Chain Polymerization:

Protonic Acids HBr, HI

HA + (CH3)2C=CH2 → (CH3)3C+(A-)

Lewis Acids AlCl3, BF3, SnCl4

A co-initiator (water, protonic acids, alkyl halides) is needed to activate the Lewis acid.

BF3 + H2O → BF3-OH2

BF3-OH2 + (CH3)2=CH2 → (CH3)2C+(BF3OH)-

Cati

oni

c

Chai

n

Propagati

on:

Mono

mer

Struct

ureSubstit

uents

must

be

abl

e

to

st

abili

ze

a

f

or

mal

positi

vecharge.

For

ol

efi

ns,

terti

ary

>

secondary

>

pri

mary

due

t

oi

nducti

ve

eff

ect.

For

styreni

c

mono

mers:

CH2=CHRMono

mer

kp, lit

er/

mol

e

secR

=

Cl

0.

0012R

=

H

0.

0037R

=

CH3

0.

095R

=

OCH3

6St

eri

c

eff

ects

do

mi

nat

e

for

ort

ho

substit

uti

on

i

n

styrene,

and

all

substit

uents

reduce

kp

irrespecti

ve

of i

nducti

ve

eff

ects.

Substituents must be able to stabilize a formal positive charge. For olefins, tertiary > secondary > primary due to inductive effect. For styrenic monomers:

Monomer kp, liter/mole sec R = Cl 0.0012 R = H 0.0037 R = CH3 0.095 R = OCH3 6Steric effects dominate for ortho substitution in styrene,and all substituents reduce kp irrespective of inductive effects.

Cationic Chain Propagation:Monomer Structure

Cationic initiators:

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

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 complexes with proton donors

Regiochemistry of propagation

Markownikov addition – form the most stable carbocation:

Electron-donating groups R stabilize a cation and affect regiochemistry by directing the incoming group E 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) termination by unimolecular rearrangment of the ion pair

A

B

Common steps of cationic polymerization: (iv) chain transfer to monomer

Cationic vinyl polymerization can be stopped also by numerous side reactions, most of which lead to chain transfer. It is difficult to achieve high MW because each initiator can give rise to many separate chains because of chain transfer. These side reactions can be minimized but not eliminated by running the reaction at low temperature.

Common steps of cationic polymerization: (iv) chain transfer to polymer

backbiting:

hydraide transfer:

H

+H

+

•Initiation

•Propagation

•Termination

i = kic[M] I+ A─ + M IM+ A─

IM1+ A─ + M IM2

+ A─

…

IMn+ A─ IMn + H + A─

t = kt[M+]

General kinetic scheme for cationic polymerisation

+M

IM1+A

XXI

XI

X

IM2+A

XXI

IMn+A

n-1+

XXR

IMn

nA H+A

I+ +M

IM+

XI

XA

A

A

IMn+ A─ + M IMn+1

+ A─ p = kp[M+][M]

XXR

n-1+

M

X XXR

n

IMn+A IMn+1

+A

General kinetic scheme for cationic polymerisation(continuation)

Steady-state approximation:

i = t

kic[M] = kt[M+]

[M+] = kic[M]/kt

p = kp[M+][M] = (kp ki /kt)c[M]2

Xn = vp/vt = (kp /kt) [M]

Common steps of anionic polymerization: (i, ii) initiation, propagation

The mechanism of anionic polymerization is a kind of repetitive conjugate addition reaction (the "Michael reaction" in organic chemistry).

Electron withdrawing groups (ester, cyano) or groups with double bonds (phenyl, vinyl) are needed as the R groups because these can stabilize the propagating species by resonance. Examples:

Anionic initiators:For initiation to be successful, the free energy of the initiation step must be favorable. Therefore, it is necessary to match the monomer with the appropriate strength of initiator so that the first addition is "downhill." If the propagating anion is not very strongly stabilized, a powerful nucleophile is required as initiator. On the other hand, if the propagating anion is strongly stabilized, a rather weak nucleophile will be successful as initiator. (Of course, more powerful ones would work, too, in the latter case.)

But two EWGs are so effective in stabilizing anions that even water can initiate cyanoacrylate ("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 with styrene and related monomers. The actual initiating species is derived from an alkalai metal like sodium. An aromatic compound is required to catalyze the process by accepting an electron from sodium to form a radical anion salt with Na+ counterion. A polar solvent is required to stabilize this complex salt. The electron is subsequently transferred to the monomer to create a new radical anion which quickly dimerizes by free radical combination (similar to the termination reaction in free radical polymerization). The eventual result is a dianion, with reactive groups at either end. Propagation then occurs from the middle outwards. This system is especially useful for producing ABA block copolymers, which have important technological uses as thermoplastic elastomers.

Common steps of anionic polymerization: (iii) chain transfer

Acrylates have problems in anionic propagation because of chain transfer to polymer. The hydrogen atoms adjacent to the ester groups are slightly acidic, and can be pulled off by the propagating anion. The new anion thus created can reinitiate, leading to branched polymers. This side reaction is difficult to suppress.

Common steps of anionic polymerization: (iv) termination (continuation)

When carried out under the appropriate conditions, termination reactions do not occur in anionic polymerization. One usually adds purposefully a compound such as water or alcohol to terminate the process. The new anionic species is too weak to 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

The beauty of anionic polymerization lies in the lack of termination reactions when carried out under the appropriate conditions (living polymerization). This means that the propagating species remains unchanged at the chain end when the monomer is consumed, so subsequent chemical reactions can be carried out. (The chain end is a carbanion, and the organic chemistry of carbanions is diverse.) Here are a few examples among many possible:

Carboxylation of end groups:

Alcohol end groups via ethylene oxide:

Coupling agents:

Living anionic polymerization

• Chains are initiated all at once (fast initiation) • Little or no termination (except purposeful). • Little or no depolymerization. • All chains grow under identical conditions.

The usual circumstances:

The result is that the monomers get divided evenly among chains.• Narrow MW distribution (PD approaches 1.0, typically 1.05 - 1.2). • The MW is predictable (unlike other polymerizations).

For monofunctional initiators, the chain length is simply x = [monomer] / [initiator]. For difunctional initiators (electron transfer), the chain length is twice as large.

B: + CH2=CHR → BCH2C:-HR carbanion

•The strength of the base depends upon monomer reactivity.

• Monomers with strongly electron-withdrawing substituents require relatively weak bases (low pKa).

• Ability of substituents to stabilize carbanions decreases as: -NO2 > -C=O > -SO2 > -CO2 ~ -CN > -SO > Ph ~ -CH=CH2 >>> -CH3

Anionic Initiation: Direct Attack by Base

Types of Base Initiators:

•Base Initiators are often organometallic compounds or salt of a strong base, such as an alkali metal alkoxide.Examples:

•Potassium with liquid ammonia. •Stable alkali metal complexes may be formed with aromatic

compounds (e.g. Na/naphthalene) in ether.

•Sodium metal in tetrahydrofuran.

M• + CH2=CHR → [CH2=/•CHR]-M+

monomer radical anion

2[CH2=/•CHR]-M+ → M+-RHCCH2CH2CHR-+M dianion

The dianion allows propagation from both ends of the initiator.Highly reactive radical anions usually dimerize.

Anionic Initiation:Direct Electron Transfer from Alkali Metal

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-+NaPropagation from both ends! dianion

Anionic Initiation:Transfer of an Electron to an Intermediate

• For Ri >> Rp, all chains start at almost the same time.If there is no chain transfer and no termination, chains will have equal lifetimes and grow to about the same size.

[M] = monomer concentration [C] = aromatic complex concentration

•To obtain instantaneous initiation, the electron affinity of the monomer must be much greater than that of the aromatic compound.

Anionic Initiation:Transfer of an Electron to an Intermediate

Initiation could be instantaneous, of comparable rate, or much slower than propagation. If termination is absent,

Termination

By impurities and transfer agents:• Oxygen and carbon dioxide can react with propagating anions, and water will terminate the chain by proton transfer. Thus, the reactions must be carried out under high vacuum or in an inert atmosphere.

By nucleophilic attack of initiator on polar monomer• Polar monomers such as methyl methacrylate, methyl vinyl ketone, and acrylonitrile have substituents that will react with nucleophiles. These side reactions broaden the molecular weight distribution. To minimize the effect, use a less nucleophilic initiator, lower reaction temperatures, and more polar solvents.

Mechanism of Base Initiation:Relative Initiator Activity

Solvent Dielectric Constant kp (liter/mole sec)

Benzene 2.2 2Dioxane 2.2 5Tetrahydrofuran 7.6 550

1,2-Dimethoxyethane 5.5 3,800

•As the dielectric constant increases, the solvating power of the reaction medium increases and there is an increased fraction of free ions (which are highly reactive).

Effect of Reaction Medium: Solvent

The separation between the counterion and the carbanion end group on the polymer is the major factor determining the rate, equilibrium, and stereochemistry. Counterion kp, liter/mole sec in tetrahydrofuran in dioxaneCationsize Li+ 160 0.94 Na+ 80 3.4 K+ 60-80 19.8 Rb+ 50-80 21.5 Cs+ 22 24.5 Free anion 65,000!

Tetrahydrofuran is a good solvating solvent (ε = 7.4)Dioxane is a poor solvating solvent (ε = 2.2)

Effect of Reaction Medium: Counterion

Reaction SetInitiation: GA → G+ + A-

G+ + A- + M → G+ + AM-

Note that the nature of the solvent will determine whether the propagating anion 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.

Kinetics of Anionic Polymerization:

[A-] = total concentration of anions of all lengths=[GA]o = concentration of initiator before dissociation

Integrate to obtain:

Rate of Polymerization

Solid-State Properties

POLYMERS IN THE SOLID STATE

Semi-crystalline Amorphous

Glassy Rubbery

Questions: Relationship to microstructure Relationship of structure to properties

• 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 the strength of the secondary bonds between chains in a polymer; the stronger the secondary bonds; the higher the glass transition temperature.

Polyethylene Tg = 0°C; Polystyrene = 97 °CPMMA (plexiglass) = 105 °C.Since room temp. is < Tg for PMMA, it is brittle at room temp.For rubber bands; Tg = - 73°C…. So to make rubber brittleyou need to cool it. Had the Challenger taken off on a warm day the disaster may never have happened!

Glass Transition Temperature

Determination of the glass transition temperature:

Dynamic Mechanical tests: E', E", Tan Torsion pendulum Tensile or flexural vibration vs T, Torsional braidDilatometry, DSC, Dielectric loss, Bouncing ball 

Glass Transition Temp.1. Breakdown of Van Der Waals Forces2. Onset of large scale molecular motions3. Polymer goes from Glassy/Rigid to rubbery behavior4. Upper service temperature in amorphous polymers

Molecular Factors and TgMolecular Factors and Tg

Free VolumeFree Volume Backbone StiffnessBackbone Stiffness Steric effects (side groups)Steric effects (side groups) Network structure (thermosets)Network structure (thermosets) Anything which makes movement more difficult will increase TgAnything which makes movement more difficult will increase Tg

Crystallization in linear polymers involves the folding back and forth of the long chains upon themselves to achieve a very regular arrangement of the mersCrystalline polymers stereoregular/ linear/ strong dipole-dipole interaction

Crystallites Crystalline and ordered microdomains; fringed micelle

Induction of crystallinity● cooling of molten polymer● evaporation of polymer solution● annealing heating of polymer at a specific temperature● drawing stretching at a temperature above Tg

Crystallinity

Crystalline regions

● a plateletlike structure (~ 100 Å thick)● folded-chain lamella model

Extended-chain crystals● less common; and often take a needle form● usually formed with low MW polymer by slow crystallization or under pressureNucleation onset of crystallinity• homogeneous nucleation occur randomly throughout the matrix• heterogeneous nucleation occur at the interface of a foreign impurity (e.g. a finely divided silica)

Crystalline morphologies Spherulite aggregates of small fibrils in a radial pattern (crystallization under no stress) Drawn fibrillar obtained by drawing the spherulitic fibrils Epitaxial one crystallite grown on another; lamella growth on long fibrils; the so-called shish-kebab morphology (crystallization under stirring)

Crystalline polymers (vs amorphous polymers)

● tougher, stiffer (due to stronger interactions)● higher density, higher solvent resistance (due to closely packingmorphology)● more opaque (due to light scattering by crystallites)

Detection of crystallinity degree insoluble fraction / density / XRD / thermal analysis / (IR)

Factors Influencing Crystallinity

• Backbone stiffness• Backbone symmetry• Absence or presence of branches• Pendant group size• Pendant group polarity• Pendant group regularity

A number of factors determine the capacity and/or tendency of a polymer to form crystalline regions within the material.

As a general rule, only linear polymers can form crystals Stereoregularity of the molecule is critical Copolymers, due to their molecular irregularity, rarely form crystals Slower cooling promotes crystal formation and growth

Effect of Crystallization

• Increased Density• Increases Stiffness (modulus)• Reduces permeability• Increases chemical resistance• Reduces toughness

Thermal & Mechanical Properties

Thermodynamics of Tm and Tg

dG = - SdT + Vdp

V

TFirst-order Transition

Cp

TSecond order Transition

Crystalline vs. Amorphous

Phase transitions for long-chain polymers.

=>

Detect the occurrence of glass transition dilatometry measure volume increase calorimetry measure the enthalpy change mechanical measurements modulus and stiffness

Semi-crystalline Amorphous

V orH

Tm

V

Tg

Modulus & Temperature

Rheology

Rheology the science of deformation and flowTo cause a polymer to deform or flow ● need a force (a) if the force is withdrawn quickly) polymer will rebound (a relaxation process) (b) if the force is applied consistently polymer will flow irreversibly● the flowing polymer liquid will be very viscous due to chain entanglement and frictional effects● amorphous polymers are viscoelastic materials combination of elasticity and viscous flow

Shear (tangential stress) the most concerned force type Shear stress

AF

(dyne/cm2; newton/m2)F: force (dynes; newtons) A: surface area (cm2;

m2)

YX

Shear modulus (Resistance to shear)

G

(: shear strain) ( = G )

dtd

(s-1)

Shear strain (amount of deformation of one plane with respect to another)

Shear rate (velocity gradient)

An ideal (or Newtonian) liquid follows Newton’s law of viscosity (i.e. shear stress increases linearly with shear rate)

: viscosity (a measure of resistance to flow) poises (dyne s/cm2) SI system: Pascal-seconds (Pa s = newton s/m2)

Viscosity: air (10-5 Pa s), H2O (10-3 Pa s), glycerin (1 Pa s),

molten polymer (102 － 106 Pa s)

Viscosity can be related to temperature by an Arrhenius-type equationRTEaAe /

A: related to molecular motionEa: activation energy for forming viscous flow

Ea

● determined mainly by local chain segmental motion ● relatively insensitive to MW● highly depending on chain structure and branching● bulkier chain branch or substituent higher Ea

● bulkier group makes viscosity more sensitive to temperature

Bingham Newtonian fluid (Eugene Cook Bingham)

γηττ c c : critical shear stress; threshold stress

• Probably caused by some special type of structural arrangement, arising from conformational and secondary bonding forces

Non-Newtonian shear stress is not linearly proportional to shear rate shear thinning (pseudoplastic) more common shear thickening (dilatant) less common shear viscosity at a specified shear rate (i.e., the slope of a secant drawn from the origin)

γτη

Increasing shear rate make disentangling faster than reentangling

thixotropic liquid ● has gel-like properties or a high viscosity under low stress, but thin out on stirring● depending on shear time, but not shear rate (different from shear thinning)● commercial paints are typical examples

General expression B

A

logBAloglog

• for a Newtonian fluid B = 1 and A = ( =

)• plot log vs log

γ slope = B; intercept = log A

General expression B

A

logBAloglog

• for a Newtonian fluid B = 1 and A = ( =

)

• plot log vs log

γ slope = B; intercept = log A

MW effect

cM critical molecular weight for entanglement to begin● typical range 4,000 to 15,000● typical chain length DP about 600

MW distribution effect

Chain branching effect● lower hydrodynamic volume and lower entanglement lower viscosity at a given shear rate and MW● weaker secondary bonding forces poorer mechanical properties

Polymer conformation (or shape) effect

● a 0.5 for a random coil; a 1 for a more rodlike extended shape● more rigid polymers are significantly more viscous

avKM

Determine viscosity of a polymer melt

● using a cone-plate rotational viscometer● shear stress

M: torque; dynes/cm (CGS) or newtons/m (SI) R: cone radius; cm or m

323

RM

3

2 )/(

RM

RRM

AF

RFM

shear rate

: angular velocity; degrees/s (CGS) or radians/s (SI): cone angle; degrees or radians

viscosity

kMRM32

3

32

3R

k

(k is a constant defined by viscometer design)

Other types of viscometers● rotating cylinders immersed in the viscous fluid● steel capillaries through which the molten polymer is forced at constant pressure or constant flow