polymerization kinetics.doc

7/27/2019 Polymerization Kinetics.doc

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KINETICS OF

POLYMERISATIONREACTION

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POLYMERISATION

Inpolymer chemistry,polymerization is a process of

reacting monomermoleculestogether in a chemical reactionto formpolymerchains or

three-dimensional networks.[1][2][3] There are many forms of polymerization and differentsystems exist to categorize them.

Introduction

In chemical compounds, polymerization occurs via a variety of reaction mechanisms that

vary in complexity due to functional groups present in reacting compounds[3] and their

inherent steric effects. In more straightforward polymerization,alkenes, which are

relatively stable due to bondingbetween carbon atoms, form polymers through

relatively simple radical reactions; in contrast, more complex reactions such as those that

involve substitution at the carbonyl group require more complex synthesis due to the way

in which reacting molecules polymerize.[3]

As alkenes can be formed in somewhat straightforward reaction mechanisms, they form

useful compounds such aspolyethylene andpolyvinyl chloride(PVC) when undergoing

radical reactions,[3] which are produced in high tonnages each year[3] due to their

usefulness in manufacturing processes of commercial products, such as piping, insulation

and packaging. In general, polymers such as PVC are referred to as "homopolymers," as

they consist of repeated long chains or structures of the same monomer unit, whereas

polymers that consist of more than one molecule are referred to ascopolymers (or co-

polymers).[4]

Other monomer units, such as formaldehyde hydrates or simple aldehydes, are able to

polymerize themselves at quite low temperatures (ca. 80 C) to form trimers;[3] molecules consisting of 3 monomer units, which can cyclize to form ring cyclic

structures, or undergo further reactions to formtetramers,[3] or 4 monomer-unit

compounds. Further compounds either being referred to as oligomers[3] in smaller

molecules. Generally, because formaldehyde is an exceptionally reactive electrophile it

allowsnucleophillic addition of hemiacetal intermediates, which are in general short-

lived and relatively unstable "mid-stage" compounds that react with other molecules

present to form more stable polymeric compounds.

Polymerization that is not sufficiently moderated and proceeds at a fast rate can be very

hazardous. This phenomenon is known ashazardous polymerization and can cause fires

and explosions.Step-growth

Step-growth polymerization

Step-growth polymers are defined as polymers formed by the stepwise reaction between

functional groups of monomers, usually containing heteroatoms such as nitrogen or

oxygen. Most step-growth polymers are also classified ascondensation polymers, but not

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all step-growth polymers (likepolyurethanesformed from isocyanate and alcohol

bifunctional monomers) release condensates; in this case, we talk about addition

polymers. Step-growth polymers increase in molecular weight at a very slow rate at lower

conversions and reach moderately high molecular weights only at very high conversion

(i.e., >95%).

To alleviate inconsistencies in these naming methods, adjusted definitions for

condensation and addition polymers have been developed. A condensation polymer is

defined as a polymer that involves loss of small molecules during its synthesis, or

contains heteroatoms as part of itsbackbone chain, or its repeat unit does not contain all

the atoms present in the hypothetical monomer to which it can be degraded.

Chain-growth

Chain-growth polymerization

Chain-growth polymerization (or addition polymerization) involves the linking together

of molecules incorporating double or triple carbon-carbonbonds. These

unsaturated monomers (the identical molecules that make up the polymers) have extrainternal bonds that are able to break and link up with other monomers to form a repeating

chain, whose backbone typically contains only carbon atoms. Chain-growth

polymerization is involved in the manufacture of polymers such

aspolyethylene,polypropylene, andpolyvinyl chloride (PVC). A special case of chain-

growth polymerization leads to living polymerization.

In the radical polymerization ofethylene, its bond is broken, and the two electrons

rearrange to create a newpropagating centerlike the one that attacked it. The form this

propagating center takes depends on the specific type of addition mechanism. There are

several mechanisms through which this can be initiated. The free radical mechanism is

one of the first methods to be used. Free radicals are very reactive atoms or moleculesthat have unpaired electrons. Taking the polymerization of ethylene as an example, the

free radical mechanism can be divided in to three stages: chain initiation,chain

propagation, and chain termination.

Polymerization ofethylene

Free radical addition polymerization of ethylene must take place at high temperatures and

pressures, approximately 300 C and 2000 atm. While most other free radical

polymerizations do not require such extreme temperatures and pressures, they do tend to

lack control. One effect of this lack of control is a high degree of branching. Also, as

termination occurs randomly, when two chains collide, it is impossible to control the

length of individual chains. A newer method of polymerization similar to free radical, but

allowing more control involves the Ziegler-Natta catalyst, especially with respect

topolymer branching.

Other forms of chain growth polymerization include cationic addition

polymerization and anionic addition polymerization. While not used to a large extent in

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http://en.wikipedia.org/wiki/Polyurethanehttp://en.wikipedia.org/wiki/Polyurethanehttp://en.wikipedia.org/wiki/Isocyanatehttp://en.wikipedia.org/wiki/Addition_polymerhttp://en.wikipedia.org/wiki/Addition_polymerhttp://en.wikipedia.org/wiki/Backbone_chainhttp://en.wikipedia.org/wiki/Backbone_chainhttp://en.wikipedia.org/wiki/Structural_unithttp://en.wikipedia.org/wiki/Chain-growth_polymerizationhttp://en.wikipedia.org/wiki/Chemical_bondhttp://en.wikipedia.org/wiki/Chemical_bondhttp://en.wikipedia.org/wiki/Chemical_bondhttp://en.wikipedia.org/wiki/Polyethylenehttp://en.wikipedia.org/wiki/Polypropylenehttp://en.wikipedia.org/wiki/Polypropylenehttp://en.wikipedia.org/wiki/Polyvinyl_chloridehttp://en.wikipedia.org/wiki/Living_polymerizationhttp://en.wikipedia.org/wiki/Living_polymerizationhttp://en.wikipedia.org/wiki/Radical_polymerizationhttp://en.wikipedia.org/wiki/Ethylenehttp://en.wikipedia.org/wiki/Pi_bondhttp://en.wikipedia.org/wiki/Reactive_centerhttp://en.wikipedia.org/wiki/Reactive_centerhttp://en.wikipedia.org/wiki/Reactive_centerhttp://en.wikipedia.org/wiki/Free_radicalhttp://en.wikipedia.org/wiki/Chain_initiationhttp://en.wikipedia.org/wiki/Chain_propagationhttp://en.wikipedia.org/wiki/Chain_propagationhttp://en.wikipedia.org/wiki/Chain_propagationhttp://en.wikipedia.org/wiki/Chain_propagationhttp://en.wikipedia.org/wiki/Chain_terminationhttp://en.wikipedia.org/wiki/Ethylenehttp://en.wikipedia.org/wiki/Ziegler-Natta_catalysthttp://en.wikipedia.org/wiki/Ziegler-Natta_catalysthttp://en.wikipedia.org/wiki/Branching_(chemistry)http://en.wikipedia.org/wiki/Branching_(chemistry)http://en.wikipedia.org/wiki/Cationic_addition_polymerizationhttp://en.wikipedia.org/wiki/Cationic_addition_polymerizationhttp://en.wikipedia.org/wiki/Anionic_addition_polymerizationhttp://en.wikipedia.org/wiki/Anionic_addition_polymerizationhttp://en.wikipedia.org/wiki/Polyurethanehttp://en.wikipedia.org/wiki/Isocyanatehttp://en.wikipedia.org/wiki/Addition_polymerhttp://en.wikipedia.org/wiki/Addition_polymerhttp://en.wikipedia.org/wiki/Backbone_chainhttp://en.wikipedia.org/wiki/Structural_unithttp://en.wikipedia.org/wiki/Chain-growth_polymerizationhttp://en.wikipedia.org/wiki/Chemical_bondhttp://en.wikipedia.org/wiki/Polyethylenehttp://en.wikipedia.org/wiki/Polypropylenehttp://en.wikipedia.org/wiki/Polyvinyl_chloridehttp://en.wikipedia.org/wiki/Living_polymerizationhttp://en.wikipedia.org/wiki/Radical_polymerizationhttp://en.wikipedia.org/wiki/Ethylenehttp://en.wikipedia.org/wiki/Pi_bondhttp://en.wikipedia.org/wiki/Reactive_centerhttp://en.wikipedia.org/wiki/Free_radicalhttp://en.wikipedia.org/wiki/Chain_initiationhttp://en.wikipedia.org/wiki/Chain_propagationhttp://en.wikipedia.org/wiki/Chain_propagationhttp://en.wikipedia.org/wiki/Chain_terminationhttp://en.wikipedia.org/wiki/Ethylenehttp://en.wikipedia.org/wiki/Ziegler-Natta_catalysthttp://en.wikipedia.org/wiki/Branching_(chemistry)http://en.wikipedia.org/wiki/Cationic_addition_polymerizationhttp://en.wikipedia.org/wiki/Cationic_addition_polymerizationhttp://en.wikipedia.org/wiki/Anionic_addition_polymerization


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industry yet due to stringent reaction conditions such as lack of water and oxygen, these

methods provide ways to polymerize some monomers that cannot be polymerized by free

radical methods such aspolypropylene. Cationic and anionic mechanisms are also more

ideally suited forliving polymerizations, although free radical living polymerizations

have also been developed.

Esters ofacrylic acid contain a carbon-carbon double bond which is conjugated to an

ester group. This allows the possibility of both types of polymerization mechanism. An

acrylic ester by itself can undergo chain-growth polymerization to form

ahomopolymerwith a carbon-carbon backbone, such aspoly(methyl methacrylate).

Also, however, certain acrylic esters can react with diamine monomers by nucleophilic

conjugate addition of amine groups to acrylic C=C bonds. In this case the polymerization

proceeds by step-growth and the products are poly(beta-amino ester) copolymers, with

backbones containing nitrogen (as amine) and oxygen (as ester) as well as carbon.[5]

Polymerization Kinetics

Chain Polymerization

Process

Activated monomer, M*, attacks another monomer and adds to it Resultant species then attacks new monomer and adds, etc.

Monomer used up slowly High polymers formed rapidly

Average molar mass increased by long reaction times Step Polymerization

Any two monomers can link at any time

Monomer used quickly

Chain Polymerization

Examples ethene, metyl methacrylate and styrene -CH2CHXl + CH2=CHX -> -CH2CHXCH2CHXl

Rate of polymerization, v is proportional to the square root of the initiator

concentration, v = k[I]1/2[M] Proof:

Steps:

{Initiation} I -> Rl + Rl v = ki[I] (I= initiator, R = radical)M + Rl -> M1lfast(M=monomer, M1l monmer radical)

{Propagation} M + Mn-1l -> Mnl v = kp[M][Ml]

Rate of monomer radical production is determined by initiation

step so

d[Ml]/dt = 2f ki[I]

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http://en.wikipedia.org/wiki/Polypropylenehttp://en.wikipedia.org/wiki/Living_polymerizationhttp://en.wikipedia.org/wiki/Esterhttp://en.wikipedia.org/wiki/Acrylic_acidhttp://en.wikipedia.org/wiki/Acrylic_acidhttp://en.wikipedia.org/wiki/Conjugated_systemhttp://en.wikipedia.org/wiki/Homopolymerhttp://en.wikipedia.org/wiki/Homopolymerhttp://en.wikipedia.org/wiki/Poly(methyl_methacrylate)http://en.wikipedia.org/wiki/Poly(methyl_methacrylate)http://en.wikipedia.org/wiki/Poly(methyl_methacrylate)http://en.wikipedia.org/wiki/Diaminehttp://en.wikipedia.org/wiki/Nucleophilic_conjugate_additionhttp://en.wikipedia.org/wiki/Nucleophilic_conjugate_additionhttp://en.wikipedia.org/wiki/Copolymerhttp://en.wikipedia.org/wiki/Polymerization#cite_note-5http://en.wikipedia.org/wiki/Polypropylenehttp://en.wikipedia.org/wiki/Living_polymerizationhttp://en.wikipedia.org/wiki/Esterhttp://en.wikipedia.org/wiki/Acrylic_acidhttp://en.wikipedia.org/wiki/Conjugated_systemhttp://en.wikipedia.org/wiki/Homopolymerhttp://en.wikipedia.org/wiki/Poly(methyl_methacrylate)http://en.wikipedia.org/wiki/Diaminehttp://en.wikipedia.org/wiki/Nucleophilic_conjugate_additionhttp://en.wikipedia.org/wiki/Nucleophilic_conjugate_additionhttp://en.wikipedia.org/wiki/Copolymerhttp://en.wikipedia.org/wiki/Polymerization#cite_note-5


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{2 because 2 radicals produced and f is the fraction of radicals

which initiate a chain} {Termination} Mnl + Mml -> Mm+n v = kt[Ml]2 ; d[Ml]/dt =

-2kt[Ml]2

Proof (continued)

Apply steady state approximation

d[Ml]/dt = 2f ki[I] -2kt[Ml]2 = 0

2f ki[I] =2kt[Ml]2 or 2f ki[I] =2kt[Ml] 2 [Ml] = (2f ki[I]/2kt)0.5 = (f ki[I]/kt)0.5 ([I] )0.5

Rate of propagation = - rate of monomer consumption = kp[M][Ml]

Rate of monomer consumption=-v = -kp[M] (f ki[I]/kt)0.5 ([I] )0.5

This is same as v = k[I]1/2[M] where k = kp(f ki[I]/kt)0.5

Chain length

Kinetic chain length, n, ratio of the number of monomer units consumed per

active center in the initiation step

Measure of the efficiency of chain propagation

n = # of monomer units consumed/#number of active centers n = propagation rate/initiation rate

Since initiation rate = termination rate, n =kp[M][Ml]/ -2kt[Ml]2 or n =kp[M]/ 2kt[Ml]

But from steady state approximation, [Ml] = (f ki[I]/kt)0.5([I] )0.5 so

n =kp[M][Ml]/ -2kt[Ml]2 becomes n =kp[M]/ -2kt (fki[I]/kt)0.5 ([I] )0.5

n =k [M ][I]-0.5 where k = kp/ -2kt (f ki[I]/kt)0.5 ([I] )0.5

The slower the initiation, the greater the kineticchain length

Average Number of Monomers in a Chain Example

Average Number of Monomers in a Chain, depends on termination

mechanism

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If it is two radicals combining, Mnl + Mml -> Mm+n, is twice thekinetic chain length since two combine to terminate the reaction

= 2n = 2k [M ][I]-0.5

If it is disproportionation, Ml + Ml -> M + :M, is the kinetic chainlength termination results in two chains = n = k [M ][I]-0.5

Stepwise Polymerization

Any monomer can react at any time

Proceeds via a condensation reaction in which a small molecule is eliminated

in the step

Usually water

Example polyesters HO-M-COOH + HO-M-COOH -> HO-M-COO-M-COOH

Rate (A is COOH)

d[A]/dt = -k[OH][A] = k[A]2 {there is one OH for every A} Solution [A] = [A0]/(1 + kt[A0])

Fraction of groups condensed at t is p p = [A0]- [A]/ [A0] = kt [A0]/(1+kt [A0])

= [A0]/[A] = 1/(1-p) = 1 + kt [A0]

Catalysis Catalyst accelerates the reaction

Undergoes no change Lowers the activation energy

Provides alternate pathway for reaction

Homogeneous catalyst is in the same phase as the reaction mixture

Heterogeneous catalyst is a different phase

In auto catalysis, products accelerate the reaction

Example A-> P v= k[A][P] Rate initially slow. As P increases, rate increases. As [A] gets

small, reaction slows down

Demonstrated by integration of rate law:

Oscillating Reactions

Because of autocatalysis, reactants and products may vary periodically

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Important in biochemistry

Maintain heart rhythm

Glycolytic cycle

Lotka-Volterra mechanism Steps

(1) A + X -> X + X d[A]/dt = -ka[A][X]

(2) Y + X -> Y + Y d[X]/dt = -kv[X][Y] (3) Y -> B d[B]/dt = kc[Y]

(1) & (2) Autocatalytic Conditions: [A] is constant {steady state condition not

approximation}

Numerical solution of [X] and [Y] gives periodic variation

Bibliography Books

Physical Chemistry

-Keith Lailder Physical Chemistry

- Atkins

Website

www.google.com

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