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Hasirci V., Yilgor P., Endogan T., Eke G., and Hasirci N. (2011) Polymer Fundamentals: Polymer Synthesis. In: P. Ducheyne, K.E. Healy, D.W. Hutmacher, D.W. Grainger, C.J.

Kirkpatrick (eds.) Comprehensive Biomaterials, vol. 1, pp. 349-371 Elsevier.

© 2011 Elsevier Ltd. All rights reserved.

1.121. Polymer Fundamentals: Polymer SynthesisV Hasirci, P Yilgor, T Endogan, G Eke, and N Hasirci, Middle East Technical University, Ankara, Turkey

ã 2011 Elsevier Ltd. All rights reserved.

1.121.1. Introduction to Polymer Science 3501.121.1.1. Classification of Polymers 3511.121.1.2. Polymerization Systems 3521.121.2. Polycondensation 3531.121.2.1. Characteristics of Condensation Polymerization 3531.121.2.2. Kinetics of Linear Polycondensation 3541.121.2.2.1. Molecular weight control in linear polycondensation 3551.121.2.3. Nonlinear Polycondensation and Its Kinetics 3561.121.2.3.1. Prediction of the gel point 3561.121.2.4. Mechanisms of Polycondensation 3561.121.2.4.1. Carbonyl addition–elimination mechanism 3561.121.2.4.2. Other mechanisms 3561.121.2.5. Typical Condensation Polymers and Their Biomedical Applications 3571.121.3. Addition Polymerization 3571.121.3.1. Free Radical Polymerization 3581.121.3.1.1. Initiation 3581.121.3.1.2. Propagation 3581.121.3.1.3. Termination 3591.121.3.1.4. Kinetics of radical polymerization 3591.121.3.1.5. Degree of polymerization 3591.121.3.1.6. Thermodynamics of polymerization 3601.121.3.2. Ionic Polymerization 3601.121.3.2.1. Cationic polymerization 3601.121.3.2.2. Anionic polymerization 3601.121.3.3. Coordination Polymerization 3601.121.3.4. Typical Addition Polymers and Their Biomedical Applications 3611.121.3.5. Comparison of Addition and Condensation Polymerization 3611.121.3.6. New Polymerization Mechanisms 3611.121.3.6.1. Atom transfer radical polymerization 3611.121.3.6.2. Nitroxide-mediated polymerization 3621.121.3.6.3. Reversible addition–fragmentation chain transfer polymerization 3621.121.4. Polymer Reactions 3631.121.4.1. Copolymerization 3631.121.4.1.1. Types of copolymerization 3641.121.4.1.2. Effects of copolymerization on properties 3651.121.4.1.3. Kinetics of copolymerization 3651.121.4.2. Cross-Linking Reactions 3671.121.4.2.1. Effect of cross-linking on properties 3671.121.4.2.2. Cross-linking of biological polymers 3671.121.4.2.3. Cross-linking agents 3681.121.5. Conclusion 369References 370

GlossaryAddition polymerization Rapid polymerization basedon initiation, propagation, and termination of doublebonded monomers and no small molecules areeliminated.Anionic polymerization Polymerization initiated bya anion.

Cationic polymerization Polymerization initiated bycation and propagated by a carbonium ion.Condensation polymerization Polymerization in whichpolyfunctional reactants produce larger units in acontinuous, stepwise manner.Coordination polymers Polymers based on coordinationcomplexes.

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Comprehensive Biomaterials (2011), vol. 1, pp. 349-371

Copolymer Polymers composed of chains containing morethan one monomer unit.Degree of polymerization Average number of repeatingunits in main chains.Gel point Point at which cross-linking begins toproduce polymer insolubility.Glass transition temperature (Tg) Temperature atwhich a polymer gains local or segmentalmobility.Initiation Start of polymerization.

Kinetic chain length Average length of the polymerchain initiated by one free radical.Propagation Continuous successive chain extension in achain reaction.Repeating unit Basic molecular unit that can represent apolymer backbone chain.Tacticity Arrangement of the pendant groups in space; thatis, isotactic, syndotactic, atactic.Termination Destruction of active growing chains in achain reaction.

1.121.1. Introduction to Polymer Science

A polymer is a macromolecule composed of a combination ofmany small units that repeat themselves along the long mole-cule. The small starting molecules are called monomers, andthe unit which repeats itself along the chain is called therepeating unit. In general, polymer chains have several thou-sand repeat units. The length of the polymer chain is specifiedby the number of repeating units in the chains and thisnumber is called the degree of polymerization. Most of themonomers are composed of carbon, hydrogen, oxygen, andnitrogen. Few other elements such as fluorine, chlorine, sul-fur, etc. may also exist. Syntheses of polymers are carried outin vessels or large reactors, sometimes with application ofheat and pressure, and the small monomeric units connectto each other through the chemical reactions. The chemicalprocess used for the synthesis of polymers is called the poly-merization process.

Polymers which have the ability to melt and flow are usedin manufacturing and are generally identified with the com-mon name, plastics. In general, plastic products contain otheradded ingredients such as antioxidants and lubricants to givethe desired properties to the object produced.

Most of the macrochains obtained in polymerization reac-tions are linear polymers and are formed by the reactions ofmonomers containing either carbon–carbon double bondsor have two active functional groups or difunctionality.Many monomers have different active groups on the samemolecule such as one end of the monomer contains a carbox-ylic acid and the other end contains an alcohol, and thereaction of the acid group of one molecule with the alcoholgroup of the other forms polyesters. Polymerization reactionsalso take place when one of the monomers contains two acidgroups and the other contains two alcohol or two aminegroups. If there are some monomers which have more thantwo functionalities (e.g., 3- or 4-functionality), their presencein the chain cause the formation of extra chains linked to themain backbone. In this case, branched polymers are obtained.If the extent of branching is very high and all the macrochainsare connected to each other, then they form a highly cross-linked, three-dimensional structure which is called a network.These networks have infinite molecular weights since allchains are connected to each other. In a polymer structure,all chains are tangled around each other forming the bulkstructure. At low temperatures they are solid, but in a good

solvent, the chains start to separate from each other and forlinear and branched polymers this separation leads to com-plete solubility. The cross-linked network polymers, however,cannot dissolve in a solvent; they swell, forming gels.

The process of creating macromolecules from monomers iscalled polymerization. If only one type of monomer is used inpolymerization, there will be only one type of repeating unitin the chain. In this case, the macromolecule is a homopoly-mer. If the polymer is formed from two different monomers(have two different repeating units), it is known as a copoly-mer. If a chain is formed from only ethylene, the polymer is ahomopolymer and named as polyethylene. On the otherhand, the copolymer of ethylene and vinyl acetate has twomonomers and, therefore, has two different repeating units.If three different monomers are used to produce a polymer,the product is a terpolymer. Biological polymers, such asenzymes, are formed from many different amino acids, andtherefore, their structures contain a variety of repeating units.

Since a large number of combinations of these moleculesare available, it becomes possible to design and synthesizepolymers with the desired properties ranging from fibersto films, sponges to elastomers. This versatility makes themessential materials to be used in various applications rangingfrom macro-sized products used in the households to nano-scale devices used in nanotechnological and biomedicalapplications.

Polymers such as cellulose, silk, and chitin can be obtainedfrom natural sources and polymers such as polyethylene, poly-styrene, and polyurethanes can be synthesized in the labora-tories and plants. The macrochains such as DNA, RNA, andenzymes have biological importance and are crucial for life.In general, the backbone of a polymer is formed mainly ofcarbon atoms. These are called the organic polymers. There arealso a few inorganic polymers, and the atoms in their back-bones are different than carbon. An example is silicone, thebackbone of which is constituted of silicon and oxygen.

One very important property which strongly influencesthe mechanical strength of the polymer is its molecular weight.Hydrocarbon molecules with increasing number of carbonsare methane, ethane, propane, etc. The ones containing up tofive carbons are in the gaseous state. As the number of carbons,and therefore, the molecular weight increases, they becomeliquids, wax type solids, and eventually hard solids. The onescalled polymers contain more than 100 carbons along thechain. Most polymers which are useful as plastics, rubbers,

350 Polymers



fibers, etc. have at least 50 repeating units and have molecularweights between 104 and 106 gmol!1. Most of the propertiesof the polymers (plastics) are dependent on the chain length.As it increases, the softening point, melting point, or mechani-cal strength of the polymers also increase. Molecular weightsof polymers are defined with average molecular weight valuessince there is always a distribution in chain lengths and noconstant length for chains during the polymerization process.Although there are various averaging approaches, the mostcommonly used ones are the number averagemolecular weight(Mn) and the weight average molecular weight (Mw). Theequations for these parameters are given below:

Mn ¼P

MiNiPNi

[1]

Mw ¼P

M2i NiP

MiNi[2]

whereNi is the number of moles of molecules with a molecularweight of Mi.

The simplest polymer is polyethylene which has the repeat-ing unit of (–CH2–CH2–). The repeating units of polyethylenehave high regularity and the chains come close to each otherand cause high intermolecular interactions. If one of thehydrogen atoms of polyethylene repeating unit is changedwith a different atom or molecule such as a halogen atomor R group, the arrangement of the chain may have differ-ent possibilities. The arrangement of atoms or groups fixedby chemical bonding in a molecule is called the configura-tion. Some examples are cis and trans isomers, and D and L

forms of molecules. Chains may have different orientationsarising from rotation of the chain about single bonds. Thesetypes of arrangements which are continuously changingare called conformations. A chain can have many differentconformations.

In vinyl polymers isomerism is also defined with head-to-tail configuration. If there is a substitute attached to onecarbon atom of the double bond, this carbon side can benamed as the head, and the other carbon will then be thetail. During polymerization, the carbon atoms containing asubstitute come together in either head-to-tail configurationor head-to-head and tail-to-tail configurations.

Carbon atoms make four bonds in a tetrahedral geometry.If the –C–C– main backbone which forms a zigzag structureis assumed to be on a plane, the other two bonds of eachcarbon, linked to an atom or a group, are either on one side orthe other side of this plane. Depending on the organization ofthe side groups linked to the adjacent chiral center carbons, astereochemistry is created and this is named tacticity. Ifthe polymer is isotactic, it means that all the substituted sidegroups on each successive chiral center are on the same side ofthe backbone plane and have the same stereochemical con-figuration. For syndiotactic polymers, the side groups takeplace alternatingly on opposite sides of the backbone plane,and each successive chiral center has the alternating stereo-chemical configuration. There is no regular arrangement ofthe subgroups in atactic polymers. The substituents are placedrandomly along the chain. Different placements of substituentgroup R in vinyl polymers are shown in Figure 1. Since tacticity

creates highly ordered organization of repeating units along thechains, those polymers are more rigid with higher crystallinityand strength compared to atactic ones. Although this is the casein the industry for most of the processes, atactic polymers arepreferred because of their ease of processing.

As defined previously, long chains are entangled witheach other and stay together in a polymer structure forminga solid mass. This type of polymers have no ordered inter-molecular arrangements and are called amorphous polymers.The vinyl polymers which contain bulky substitutes such aspoly(methyl methacrylate) or polystyrene are amorphouspolymers. On the other hand, in some polymers, intermolec-ular attractions are very strong and many backbone chainsform closely packed structure as a result of these strongintermolecular forces. In these cases, they form crystallinepolymers. Some polymers are partially crystalline, and someregions of the different or the same chains are closely packedand have strong attractions. These highly ordered domainsare distributed in the amorphous matrix. In this case, thematerial is a semicrystalline polymer. Since crystallinity indi-cates highly ordered arrangement of macrochains with strongintermolecular forces, these polymers are stronger and havehigher mechanical and thermal properties compared to theiramorphous counterparts.

1.121.1.1. Classification of Polymers

During the early years of polymer science, two types of classi-fications have come into use. One was based on polymerstructure (backbone) and divided polymers into Condensa-tion and Addition polymers1 and the other was based on

R(a)

(b)

(c)

R R

R R

R

R R RR

R R R

R R R R R

Figure 1 Tacticity of vinyl polymers: (a) isotactic, (b) syndiotactic, and(c) atactic.

Polymer Fundamentals: Polymer Synthesis 351



polymerization kinetics and mechanism and divided polymer-izations into Step and Chain polymerizations.2 Although theseterms are often used interchangeably, because most condensa-tion polymers are produced by step polymerizations and mostaddition polymers are produced by chain polymerizations, thisis not always the case.

Polymers can be synthesized fromhundreds ofmonomers innumerous combinations in very different forms ranging fromsolid elastomers to fibers, from films to sponges, from tubesto gels. Therefore, they are very important in our daily life.Polymers can be classified in many different ways dependingon their various properties. Some of them are given below.

Polymer classification according to:

1. The origina. Natural polymers: Proteins, starch, cellulose, natural

rubber, etc. are of natural origin.b. Synthetic polymers: These are man-made polymers

synthesized in the laboratories.2. The polymerization process

a. Condensation polymers: These polymers are formed whentwo di- or polyfunctional molecules react and condenseforming macromolecules and with the possible elimina-tion of a small molecule such as water in the case ofpolyester formation. All the natural polymers are con-densation polymers.

b. Addition polymers: These polymers are produced by chainreactions of double-bonded monomers in which thechain carrier can be a radical or an ion. Free radicals areusually formed by the decomposition of a relativelyunstable compound, called the initiator.

3. The structural forms of the chainsa. Linear polymers: These polymers are composed of long

chains and their monomers have only two functionalgroups if the polymer is a condensation polymer or asingle double bond if it is an addition polymer.

b. Branched polymers: Similar to linear polymers, but theyhave long chains with shorter side chains (branches)caused by the presence of small amounts of tri-functional monomers for condensation or two unsa-turations for addition polymers.

c. Network polymers: These are cross-linked three-dimensionalpolymers. They consist of long chains connected to eachother with multifunctional units and form a network.

4. The composition of the main backbone of the polymersa. Homopolymers: These polymers contain only carbon–

carbon bonds in their backbone.b. Heteropolymers: These polymers contain atoms other

than carbon in their main chain. The most commonnoncarbon atoms are oxygen and nitrogen.

5. The structurea. Organic polymers: These polymers contain mainly carbon

atoms in their main chain.b. Inorganic polymers: The main chain of these polymers is

not composed of carbon but mainly of inorganic atomssuch as silicon in silicone rubbers.

c. Coordination (chelate) polymers: In this type of polymers,a chelate ring is formed from an ion or metal and differ-ent organic ligands which have donor–acceptor bondsbetween.

6. The molecular weighta. Oligomers: These are the polymers with a molecular

weight in the range of 500–5000 gmol!1.b. High polymers: These are the polymers used in the indus-

try in the production of materials and have a molecularweight in the range of 104–106 gmol!1.

7. The thermal behaviora. Thermoplastics: These are linear or slightly branched

chains containing polymers and they soften and flowwhen the temperature is increased. If they are loaded ina mold in this soft form and cooled, they solidify form-ing the product. Since there is no new chemical bondformation during the heating and cooling, they can bereshaped with further application of heat and pressure.

b. Thermoset polymers: During the processing of these poly-mers, cross-linking reactions take place upon increaseof temperature and they set in the shape of the moldthey are in. Therefore, they cannot be melted andreshaped with the application of heat. At high tempera-tures, they decompose.

8. The arrangement of the repeating unitsa. Homopolymers: They are formed from single type of

monomers.b. Copolymers: They are made of two or more types of

monomers. The arrangements of the different repeatingunits in the chain can be different, and therefore, copo-lymers can be further divided into groups as given below.i. Alternating copolymers: the repeating groups of two

different monomers alternatingly follow each otheralong the macrochain.

ii. Random copolymers: there is no order in the positionsof the repeating units of different monomers.

iii. Block copolymers: in these polymers, one type of themonomer reacts and forms a long chain (ablock) andthen reacts with the other type of monomer forminga different block. These block copolymers can bediblock copolymers which are formed as AB typeblocks, three-block copolymers which are formedas ABA type blocks, or graft copolymers in whichthe main chain is one type of block and the othertype is attached to the main chain as side chains.

9. The linkages repeating in the chains: These polymers are clas-sified according to the chemical linkages between themonomeric units which repeat along the chain. For exam-ple, polyethers have ether linkages, polyesters have esterlinkages, polyurethanes have urethane linkages, etc.

1.121.1.2. Polymerization Systems

Polymerization reactions are carried out in vessels or reactorsgenerally with application of heat and with the addition ofdifferent substituents. Depending on the phases that exist andthe forms of the medium, the polymerization processes areclassified as homogeneous and heterogeneous systems, whichinclude different techniques as given below:

1. Homogeneous polymerization systems: All chemicals added intothe reaction medium create a homogeneous mixture inwhich polymer formation occurs. These processes are eitherbulk or solution polymerization processes.

352 Polymers



a. Bulk polymerization: In these polymerizations, there areonly monomers and initiators in the reaction medium.These processes are generally used in the productionof condensation polymers in which the reactions aremildly exothermic, less viscous, and therefore, mixing,heat transfer, and control of the process is easier com-pared to chain polymerization of vinyl polymers.

b. Solution polymerization: A monomer and a initiatorare added in a solvent and the reaction takes place inthis solution medium. This approach can be used foraddition or condensation polymerizations since themedium does not get too viscous which makes mixing,heat transfer, and control of the process easy. On theother hand, it requires purification and removal ofthe solvent.

2. Heterogeneous polymerization systems: In these systems thereare more than one phase creating heterogeneous mediafor the monomer, polymer, and initiator.a. Gas phase polymerization: In these systems, the monomer

is in gaseous form and the polymer formed is eitherin liquid or solid form. Ethylene polymerization is anexample (Figure 2).

b. Precipitation polymerization: This is similar to bulk orsolution polymerization, but the polymer formed pre-cipitates as soon as it forms. This polymer is not solublein its monomer and the solvent of the monomer is alsonot a solvent for the polymer (Figure 3).

c. Solid phase polymerization: Some solid crystalline olefinsor cyclic monomers polymerize by solid state polymeri-zation. In these systems, polymerization generally startswith radiation such as X-rays or g-rays (Figure 4).

d. Suspension polymerization: In these systems, organicphase containing monomer and initiator is dispersedas droplets in the aqueous phase containing the stabili-zers such as cellulose or polyvinyl alcohol. Initiator issoluble in the monomer phase, and therefore, in the

droplet the mechanism is very similar to bulk polymeri-zation. Size of the droplets is in the range of 0.01–0.50 cmand the polymer forms as dispersed solid particles of thissize (Figure 5).

e. Emulsion polymerization: This system is similar tosuspension system, but the initiator is soluble in theaqueous phase. As the polymerization starts in the aque-ous phase, emulsifier molecules surround the growingchain forming micelles. As the polymerization proceeds,chains in the micelles elongate to get the monomer fromthe organic phase. Therefore, the monomer droplets getsmaller and polymer micelles get larger. Still, these par-ticles are very small (about 0.1 mm) (Figure 6).

There are numerous types of synthetic polymers or copoly-mers which are produced in the laboratories and every yearnew ones are added to the list. In addition, some newbiological polymers are also added to the list obtained bysome novel molecular techniques. These can be derived fromrenewable biomass sources, such as vegetable oil, corn starch,or microbiota. Some examples for these polymers are starch-based polymers (used for the production of drug capsules inthe pharmaceutical sector), polylactic acid (PLA; producedfrom cane sugar or glucose, and used in the production offoil, molds, tins, cups, bottles, and as bone plates in the medi-cal sector), poly(3-hydroxybutyrate) (PHB; is biodegradableand produced by certain bacteria), polyamide-11 (PA11; isderived from natural oil and not biodegradable), bioderivedpolyethylene (can be produced by fermentation of agricul-tural feed stocks such as sugar cane or corn, and is chemicallyand physically identical to traditional polyethylene), and bio-plastics (produced by genetically modified organisms such asGM crops).

1.121.2. Polycondensation

1.121.2.1. Characteristics of Condensation Polymerization

Condensation polymerization is used for polymerizationof monomers with functional groups and involves a series of

Monomer (gas) Solid polymer

Monomer (gas)

Liquid

Figure 2 Gas phase polymerization.

Solid polymerLiquid

Figure 3 Precipitation polymerization.

Solid crystal monomer Solid polymer

hn

Figure 4 Solid phase polymerization.

Organicphase

Aqueousphase

Monomerdroplets

Polymerparticles

Figure 5 Suspension polymerization.




chemical condensation reactions progressing generally withthe elimination of side products with low molar weight, suchas water, alcohol, or hydrogen.

In condensation polymers, the elemental composition ofthe repeating unit differs from that of the two monomers bythe elements of the eliminated small molecule. Condensationpolymers can, therefore, be degraded to their monomers uponthe addition of the eliminated small molecules.

1.121.2.2. Kinetics of Linear Polycondensation

The type of product formed in a condensation reaction isdetermined by the functionality of the monomers, that is, bythe number of reactive functional groups per monomer.Bifunctional monomers form long linear polymers but mono-functional monomers when used with bifunctional monomersform only low molecular weight products.

The monomers can have the same type or different type offunctional groups, and in the former case, two different difunc-tional monomer types are necessary for product formation.Polyesters are formed by typical condensation reactions withthe elimination of water. If a polyester is synthesized from adiol and a diacid, the first step is the reaction of the diol anddiacid monomers to form a dimer:

HOwRwOHþHOOCwR1

wCOOH !

HOwRwOCOwR1

wCOOHþH2O [I]

The dimer then might form a trimer by reaction with a diolmonomer:

HOwRwOCOwR1

wCOOHþHOwRwOH !

HOwRwOCOwR1

wCOOwRwOHþH2O [II]

or with a diacid monomer:

HOwRwOCOwR1

wCOOHþHOOCwR1

wCOOH!

HOOCwR1

wCOOwRwOCOwR1

wCOOHþH2O [III]

Dimer could also react with itself to form a tetramer:

2HOwRwOCOwR1

wCOOH ! HOwRwOCOwR1

wCOOwRwOCOwR

1

wCOOHþH2O [IV]

The tetramer and trimer proceed to react with themselves,with each other, with the monomer and the dimer.3

The polymerization proceeds in this stepwise manner withthe molecular weight of the polymer gradually increasingwith time. Condensation polymerizations are characterizedby the disappearance of monomer early in the reaction forbefore the production of any polymer of sufficiently highmolecular weight to be of practical use.

The rate of a condensation polymerization is the sumof the rates of reactions between molecules of various sizes.The kinetics of such a situation with innumerable separatereactions is normally very difficult to analyze. However, it isgenerally assumed that the rate of reaction of a group is inde-pendent of the size of the molecule to which it is attached;in other words, the functional group reactivity is assumed tobe independent of the molecular weight. These simplifyingassumptions, often referred to as the concept of equal reactiv-ity of functional groups, make the kinetics of condensationpolymerization identical to those for the analogous smallmolecule reaction. There is both theoretical4 and experimen-tal2 justification of these simplifying assumptions.

The kinetics of condensation polymerization can beexplained by taking the formation of a polyester from a dioland a diacid as a model system. Condensation polymerizationtypically involves equilibrium reactions of the type

A þ B⇄kf

krCþD [V]

and the rates of the forward and reverse reactions arekf[A][B] and kr[C][D], respectively. At equilibrium these ratesare equal, therefore

K ¼ kfkr

¼ C½ % D½ %A½ % B½ %

[3]

If the system is not at equilibrium, as in the initial stagesof polymerization, the reverse reaction is negligibly slowand changes in the concentrations of the reactants may beconsidered to result from the forward reaction alone. Thisreaction is normally catalyzed by acids, however, in theabsence of a strong acid, the diacid monomer acts as its owncatalyst for the esterification reaction and the reaction is fol-lowed by measuring the rate of disappearance of carboxylgroups:

!d COOH½ %dt

¼ k COOH½ %2 OH½ % [4]

where one of [COOH] represent the catalysis phenomenon.

Emulsifier Micelles

Organicphase

Aqueousphase

Monomerdroplets

Polymerparticles

Figure 6 Emulsion polymerization.

354 Polymers



If the starting concentrations of carboxyl and hydroxylgroups are equal

!d COOH½ %dt

¼ k COOH½ %3 [5]

rearrangement and integration gives:

2kt ¼ 1

COOH½ %2tþ constant [6]

The extent of reaction, p, is defined as the fraction of func-tional groups that has reacted at time t. Therefore,

p ¼ COOH½ %o ! COOH½ %tCOOH½ %o

[7]

Substitution of p into eqn [6] and rearrangement gives:

1

1! pð Þ2¼ 2k COOH½ %2ot þ constant [8]

or a plot of 1/(1! p)2 versus t should be linear with a slope of2k½COOH%2o from which k can be determined (Figure 7).3

It was shown with experimentation that uncatalyzed ester-ifications require quite long times to reach high degrees ofpolymerization. Greater success is achieved by adding a smallamount of acid catalyst to the system, whose concentration isconstant throughout the reaction. In this case, the concentra-tion of the catalyst has to be included in the rate constant (k0):

!d COOH½ %dt

¼ k0COOH½ % OH½ % [9]

If the initial concentrations of carboxyl and hydroxylgroups are equal,

!d COOH½ %dt

¼ k0COOH½ %2 [10]

COOHo½ %k0t ¼ 1

1! pð Þ þ constant [11]

If only bifunctional reactants are present in the reactionsystem and no side reactions occur, the number of unreactedcarboxyl groups equals the total number of molecules (N) inthe system. If acid or glycol groups separately (not in pairs)

are defined as structural units, the initial number of carboxylspresent is equal to the total number of structural units presentN0. The number average degree of polymerization, !Xn, is:

!Xn ¼Number of original molecules

Number of molecules at time t¼N0

N¼ ½COOH%o

COOH½ %t¼ 1

1!p

[12]

1.121.2.2.1. Molecular weight control in linearpolycondensationIt is important to control the change in polymer molecularweight with reaction time since molecular weight determinesthe properties of the polymer. One method of stopping thereaction at the desired molecular weight is cooling. But, this isnot preferable since the polymer could restart growing uponsubsequent heating because the ends of the polymer moleculescontain unused functional groups.

The easiest way to avoid this situation is to adjust thestarting composition of the reaction mixture slightly awayfrom stoichiometric equivalence, by adding either a slightexcess of one bifunctional reactant or by introducing a smallamount of a monofunctional reagent. Eventually, the mono-mer which is low in amount is completely used up and allchain ends consist of the excess group. If only bifunctionalreactants are present and the two types of groups are initiallypresent in numbersNA andNB with a ratio r¼NA/NB, the totalnumber of monomers present is

NA þNB

2¼ NA 1þ 1=rð Þ

2[13]

At a given time, if p is the extent of reaction defining thefraction of reacted groups, (1! p) will show the fraction ofunreacted groups. Therefore, the total number of chain endswill be

NA 1! pð Þ þNB 1! rpð Þ ¼ NA 1! pþ 1! rp

r

! "[14]

Since each monomer is difunctional, the number ofgroups is twice the number of molecules present. Therefore,!Xn will be

Xn¼NA

1þ1rð Þ

2

NA1!pþ1!rp

rð Þ2

¼ 1þ r

1þ r ! 2p[15]

This equation shows the variation of the degree of polymeriza-tion with the stoichiometric imbalance r and the extent ofreaction p. When the two bifunctional monomers are presentin equal amounts (r¼ 1), the equation reduces to

Xn¼1

1! pð Þ [16]

On the other hand, for 100% conversion the !Xn becomes

Xn¼1þ r

1þ r ! 2¼ 1þ r

r ! 1[17]

In actual practice, pmay approach but never becomes equalto unity. This means there are always some functional groupsthat are left unreacted.5

t

1/(1

-p)2

Slope = 2k[COOH]02

Figure 7 Plot of 1/(1! p)2 versus t in the determination of rateconstant of linear polycondensation.




Stoichiometric balance should be precisely maintained inorder to obtain high degrees of polymerization. Loss of oneingredient, side reactions, or the presence of monofunctionalimpurities may severely limit the degree of polymerization.6

1.121.2.3. Nonlinear Polycondensation and Its Kinetics

Polyfunctional monomers with more than two functionalgroups per molecule yield branched or hyperbranched conden-sation polymers. With certain monomers, cross-linking willalso take place with the formation of network structures inwhich branches from one polymer molecule become attachedto other molecules and eventually yield insoluble molecules.

The structures of these nonlinear condensation polymersare more complex than those of linear ones. Nonlinear poly-condensation occurs with gelation, the formation of essentiallyinfinitely large polymer networks. The sudden onset of gela-tion marks the division of the mixture into two parts: the gel,which is insoluble in all nondegrading solvents; and the sol,which remains soluble and can be extracted from the gel. As thepolymerization proceeds beyond the gel point, the amount ofgel increases at the expense of sol and the mixture rapidlytransforms from a viscous liquid to an elastic material ofinfinite viscosity. An important feature of the onset of gelationis that the number average molecular weight stays very lowwhile the weight average molecular weight becomes infinite.7

1.121.2.3.1. Prediction of the gel pointIn order to calculate the point in the reaction at which gela-tion takes place, a branching coefficient (a) is defined as theprobability that a given functional group on a branch unit toconnect to another branch unit. In the case where polyfunc-tional Af units are present with functionality f, the criterionfor gel formation is that at least one of the f! 1 segmentsradiating from the end of a segment is in turn connected toanother branch unit. Therefore, the critical value of a forgelation (ac) is given as:

ac ¼1

f ! 1[18]

The gel point can also be observed experimentally whenthe polymerizing mixture suddenly loses fluidity. If theextent of reaction is followed as a function of time by deter-mining the number of functional groups present, the valueof p (extent of reaction) at the gel point can be experimentallydetermined.8

1.121.2.4. Mechanisms of Polycondensation

As was stated earlier, all condensation polymerizations takeplace either by using a monomer with two unlike groupssuitable for polycondensation (AB type, e.g., polycondensationof hydroxycarboxylic acids) or two different monomers, eachpossessing a pair of identical reactive groups that can react witheach other (AA and BB type, e.g., polycondensation of diolswith dicarboxylic acids).

These monomers polymerize following different routessuch as carbonyl addition–elimination, carbonyl addition–substitution, nucleophilic substitution, double bond addition,or free radical coupling.5

1.121.2.4.1. Carbonyl addition–elimination mechanismCarbonyl addition–elimination is the most important reactionwhich has been used for the preparation of polyamides, poly-acetals, phenol–, urea–, and melamine–formaldehyde poly-mers. Some typical examples of this reaction include:

Direct reaction: The reaction of a dibasic acid and a glycol (toform a polyester) or a dibasic acid and a diamine (to form apolyamide) are some examples of direct reaction. A strongacid or acidic salt often serves as a catalyst. The reaction maybe carried out by heating the reactants together and remov-ing water (to draw the reaction toward product formation)usually by applying vacuum in the later stages.

Interchange: The reaction between a glycol and an ester yieldspolyesters and is preferred especially when the dibasic acidhas low solubility. Frequently the methyl ester is used, as inthe production of poly(ethylene terephthalate) from eth-ylene glycol and dimethyl terephthalate. The reactionbetween a carboxyl and an ester is much slower, but otherinterchange reactions, such as amine–amide, amine–ester,and acetal–alcohol are well known.

Acid chloride or anhydride: Either of these can be reacted with aglycol or an amine. Polyamides are prepared by the reactionof an acid chloride with a diamine.

Interfacial condensation: The reaction of an acid halide with aglycol or a diamine proceeds rapidly to high molecularweight polymer if carried out at the interface between twoimmiscible liquid phases each containing one of the reac-tants. Very high molecular weight polymers can be prepared.Typically, an aqueous phase containing the diamine or glycoland an acid acceptor is layered at room temperature overan organic phase containing the acid chloride. The polymerformed at the interface can be pulled off as a continuous filmor filament. The method is applied to the formation of poly-amides, polyurethanes, and polyureas. It is particularly usefulfor preparing polymers which are unstable at the highertemperatures.

Ring versus chain formation: Bifunctional monomers may reactintramolecularly to produce a cyclic product. Thus, hydro-xyacids may give either lactones or polymers on heatingand amino acids may give lactams or linear polyamides.The type of the product is generally dependent on the sizeof the ring that can be formed.

1.121.2.4.2. Other mechanismsCarbonyl addition–substitution reactions: The reaction of aldehydes

with alcohols involving addition followed by substitutionat the carbonyl group leads to the formation of polyacetals.

Nucleophilic substitution reactions: Nucleophilic substitution isthe reaction of an electron pair donor (the nucleophile)with an electron pair acceptor (the electrophile). These reac-tions are used in the polymerization of epoxides. Nucleo-philes attack the electrophilic C of the C–O bond causing itto break, resulting in ring opening. Opening the ring relievesthe ring strain and epoxides can react with a large rangeof nucleophiles (such as H2O, ROH, R–NH2). Nucleophilicsubstitution reactions are also the basis for the formationof natural polysaccharides and polynucleotides.

Double bond addition reactions: Although addition reactionsat double bonds are often associated with addition

356 Polymers



polymerization, this is not always the case. The ionic addi-tion of diols to diisocyanates in the production of polyur-ethanes is an example of condensation polymerization.

Free radical coupling: These reactions are used in the preparationof arylene ether polymers, polymers containing acetyleneunits, and arylenealkylidene polymers.

Aromatic electrophilic substitution reactions: This type of reactionsincluding the use of Friedel–Crafts catalysts produces poly-mers by condensation polymerization.

1.121.2.5. Typical Condensation Polymers and TheirBiomedical Applications

Polyesters, polyurethanes, polyamides, polyanhydrides, poly-carbonates, and polyureas are among the condensationpolymers that find broad use in medical applications in vari-ous forms. Some naturally occurring polymers such as proteins(collagen) and polysaccharides (hyaluronic acid) as well asbacterial polyesters (polyhydroxyalkanoates) are classifiedas condensation polymers, since their synthesis from theirreactants are achieved by the elimination of water.3,9 Sometypical examples of condensation polymers and their biomed-ical applications are listed in Table 1.

1.121.3. Addition Polymerization

Polymerization in which the polymer forms by addition ofmonomeric unit to the growing chain is called as addition poly-merization. Generally, a monomer containing double bondand an initiator creates the first active unit; they are needed tostart the chain growth. The active group, which is the chaincarrier group, may be a free radical, an anion, or a cation.

In addition polymerization reaction takes place by openingof the double bond and the created active group adds themonomer at a very high rate so that immediately highmolecular-weight polymer chains form. Therefore, the reaction

medium consists of large polymers and monomers unlike incondensation polymerization. Depending on the type of initi-ator a radical, anion, or cation is created and depending onthe chemistry, adds monomers and eventually form a largemolecule. The molecular weight of the polymer chains ispractically unchanged during polymerization, but in timemore of the monomer is converted into polymers and mono-mer concentration decreases.3

Monomers show varying degrees of selectivity with regardto the type of reactive center that will lead to polymerization.Most monomers are polymerized by free radicals, but they aremore selective to the ionic mechanisms. For example, acrylam-ide polymerizes anionically but not cationically, whereasN-vinyl pyrrolidone polymerizes by cationic but not anionicroute.6 For both monomers, free radical polymerization ispossible. Another type of polymerization is coordination poly-merization in which special catalysts are used and highlyordered polymers with stereospecific properties are obtained.

Table 2 shows the types of initiation that polymerizevarious monomers. Although the polymerization of the mono-mers in Table 2 is thermodynamically feasible by havingDG< 0, practically polymerization is achieved only with acertain type of initiator.3 The key to this phenomenon liesin the polarity of the monomer and the strength of the ionformed. Monomers with electron-donating groups (alkoxy,alkyl, alkenyl, and phenyl) attached the carbons of the unsa-turation, increase the electron density on the carbon–carbondouble bond and when these electrons react with a cationicinitiator, a stable carbenium ion forms on the growing unit.In this case, chain polymerizes with cationic catalysts. On theother hand, monomers with electron-withdrawing substitu-ents (aldehyde, ketone, acid, ester) decrease the electron den-sity on the double bond and facilitate the attack of anioniccatalysts leading to anionic polymerization. Free radical poly-merization takes place in most cases but may be considered tobe an intermediate case and a radical created on the growingchain leads to the formation of macromolecules. Many

Table 1 Typical condensation polymers and their biomedical applications

Type Characteristic linkage Sample polymer Biomedical application

Polyacetal – O – CH – O –

R

Poly(ethyl glyoxylate) Hard tissue replacement

Polyamide

– NH – C –

O Nylon Intracardiac catheters, sutures, dialysis device components,heart mitral valves, hypodermic syringes

Polycarbonate

– O – CO –

O Bisphenol-A polycarbonate Intraocular lenses, dialysis device components, heart/lungassist devices, blood collection, arterial tubules

Polyester

– CO –

O Poly(lactic acid-co-glycolic acid) Grafts, sutures, implants, prosthetic devices, micro andnanoparticles

Polypeptides

– NH – C –

O Proteins, enzymes Tissue engineering scaffolds, wound dressings

Polyurea

– NH – C – NH –

O Polyisobutylene-based polyurea Blood contacting surfaces

Polyurethane

– O – C – NH –

O Poly(ether urethane) Aortic patches, heart assist devices, adhesives, dentalmaterials, blood pumps, artificial heart and skin




monomers can polymerize by free radical mechanism in addi-tion to an ionic mechanism.3,5

1.121.3.1. Free Radical Polymerization

Free radicals are unpaired electrons that are highly reactive andhave short lifetimes. In free radical polymerizations, each poly-mer chain grows by addition of monomer to the free radicalof the growing chain. Upon addition of the monomer, thefree radical is transferred to the new chain end. Free radicalpolymerization has three stages: initiation, propagation, andtermination.

1.121.3.1.1. InitiationIn the initiation step free radicals are formed from an initiatorand then these free radicals bind to a monomer. Initiators canbe peroxides or azo compounds in which scission of a singlebond creates radicals, or a redox reaction in which radicals arecreated by an electron transfer to or from an ion or molecule.

Dissociation can be affected by the application of heat orelectromagnetic radiation (e.g., UV, g). Peroxides and hydro-peroxides are frequently used as initiators because of theinstability of the O–O bond. In the case of azo compounds,the process is driven by the release of N2. Redox reactions arepreferred especially when the polymerization is needed to becarried out at low temperatures.6,10 Heat and electromagneticradiations can also start polymerization by breaking the dou-ble bond of the monomeric units and creating two activeradicals. In this case, the chain adds to monomeric unitsfrom both ends. Some of the most widely used initiator sys-tems are given in Table 3.

The free radical initiation step can be shown as follows:

Dissociation of an initiator (I) such as benzoyl peroxide yieldstwo radicals (R�) with a dissociation rate constant kd:

I!kd 2R� [VI]

This radical then attacks to a monomer molecule to create thefirst radical M�.

R�þM!ki RM� [VII]

where ki is the rate constant of initiation.

1.121.3.1.2. PropagationThe free radicals formed are very active and immediately addon monomer molecules leading to growing macroradicals.Each addition creates a new radical that has the same identityas the previous one, except that it is larger by one monomer

Table 2 Types of addition polymerization suitable for commonmonomers

Polymerization mechanism

Monomer Radical Cationic Anionic Coordination

Ethylene þ þ ! þPropylene and a-olefins ! ! ! þStyrene þ þ þ þVinyl chloride þ ! ! þTetrafluoroethylene þ ! ! þAcrylic and methacrylicesters

þ ! þ þ

Acrylonitrile þ ! þ þ

þ, high polymer formed; !, no reaction or oligomers only.

Modified from Billmeyer, F.W. Textbook of Polymer Science, Wiley: New York, 1984.

Table 3 Free radical initiation reactions

OOOD

CH3

CH3

CH3

CH3

CN CN CN

H H

H H

O

OH

O

OH

1. Acyl peroxides, alkyl peroxides or hydroperoxides Benzoyl peroxide:

Æ – C – O – O – C – Æ 2Æ – C – O•

t-butyl peroxide:

H3C – C – O – O – C – CH3 2H3C – C – O•

Cumyl hydroperoxide:

Æ – C – O – OH Æ – C – O• + •OH

2. Azo compounds

2,2!-Azobisisobutyronitrile (AIBN):

H3C – C – N = N – C – CH3 2H3C – C• + N2

3. Redox systems

H2O2 + Fe2+ ® OH– + Fe3+ + •OH

S2O82− + Fe2+ ® SO4

2− + Fe3+ + SO4–•

4. Electromagnetic radiation (photoinitiation) Styrene, Benzoin:

Æ – C = C Æ – C = C• + H•

Æ• + C = C•

Æ – C – C – Æ Æ – C• + •C – Æ

CH3

CH3

hn

hn

hn

CH3

CH3 CH3

CH3

CH3 CH3 CH3

H H H

H H

H

®

D®

D®

D®

358 Polymers



unit. In the polymerization mechanism, it is assumed that allgrowing chains have the same propagation constant (kp). Thesuccessive additions may be represented by:

Mn�þM!kp

Mnþ1� [VIII]

Propagation with growth of the chain takes place in milli-seconds and kp for most monomers is in the range of102–104 lmol!1 s!1.3

1.121.3.1.3. TerminationTermination usually occurs by combination or disproportion-ation reactions. Combination is coupling of two growingchains to form a single polymer molecule.

Mn�þMm�!ktc

Mnþm [IX]

where ktc is the rate constant for termination by combination.In disproportionation reaction, a hydrogen atom is

abstracted and exchanged between the growing chains leavingbehind two terminated chains:

Mn�þMm�!ktd

Mn þMm [X]

where ktd is the rate constant for termination bydisproportionation.

Termination by disproportionation forms one polymermolecule with a saturated end-group and another withan unsaturated end-group. Type of termination affects themolecular weight. If it is through combination, average molec-ular weight will be two times higher than that of polymersterminated by disproportionation. In general, both types oftermination reactions take place in different proportionsdepending upon the monomer and the polymerization condi-tion. For example, polystyrene chains terminate by combina-tion whereas poly(methyl methacrylate) chains terminate bydisproportionation, especially at temperatures above 60 (C.10

1.121.3.1.4. Kinetics of radical polymerizationIn radical polymerization reactions, decomposition of theinitiator (such as peroxides and azo compounds) proceedsmuch more slowly than the reaction of the free radical withthe monomer. This step is therefore the rate-determining step.The rate of initiation (Ri) is

Ri ¼d M�½ %dt

# $

i

¼ 2fkd I½ % [19]

where f is the initiator efficiency, the fraction of the radicalssuccessful in initiating chains, kd is the rate constant forinitiator dissociation, and [I] is the concentration of the initi-ator. The constant 2 defines that two radicals are formed fromone initiator molecule. The initiator efficiency is in the rangeof 0.3–0.8 due to side reactions. The initiator efficiencydecreases when side reactions terminates the radicals.6

For a redox initiation system, rate of initiation is given as

Ri ¼d M�½ %dt

# $

i

¼ f k Ox½ % Red½ % [20]

where [Ox] and [Red] are the concentrations of oxidizing andreducing agents and k is the rate constant.

For photochemical initiation, intensity of light affects therate and equation is given as

Ri ¼d M�½ %dt

# $

i

¼ 2FIabs [21]

where Iabs is the intensity of the light absorbed and the con-stant F is called quantum yield.

The rate of termination is represented as

Rt ¼ ! d M�½ %dt

# $

i

¼ 2kt M�½ %2 [22]

where kt is the overall rate constant for termination. The con-stant 2 shows that the two growing chains are terminated byeach termination reaction.

At the start of the polymerization, the rate of formation ofradicals greatly exceeds the rate of termination. As the reactionproceeds, the rate of formation and the rate of loss of radicalsby termination becomes equal and it can be stated that there isno change in the concentration of M�. This is the steady state(d[M�] /dt¼ 0). At steady state, the rates of initiation (Ri) andtermination (Rt) are equal, leading to

M�½ % ¼ f kd I½ %kt

# $1=2

[23]

The rate of propagation is represented as

Rp ¼ ! d M½ %dt

# $

t

¼ kp M½ % M�½ % [24]

so using eqn [23], Rp can be obtained as

Rp ¼ kpf kd I½ %kt

# $1=2

M½ % [25]

If the initiator efficiency is high (close to 1) and if f is indepen-dent of monomer, rate of polymerization is proportional to thefirst power of the monomer concentration.

In chain polymerization, one important phenomenon is‘gel effect’ or ‘ Trommsdorff – Norrish effect’ which is autoac-celeration of the polymerization. In these cases, viscosity of thereaction medium increases and the mobility of the growingchains are restricted. Chains continue to grow with additionof monomers, but they cannot terminate. Therefore, the systemis no longer in steady state. Fast polymerization causes heatevolution and local hot spots, leading to cross-linking and gelformation.11

1.121.3.1.5. Degree of polymerizationKinetic chain length n is defined as the number of monomermolecules used per active center. It is, therefore, represented asRp/Ri¼Rp/Rt. Therefore,

n ¼kp M½ %2kt M�½ % [26]

using eqn [24],

n ¼k2p M½ %2

2ktRp[27]

The number average degree of polymerization, !Xn, is theaverage number of monomer molecules added to the polymer




molecule. If the propagating radicals terminate by combi-nation !Xn¼2n, and if termination is by disproportionation!Xn¼n.

Chain transfer is the reaction of a growing chain withan inactive molecule to produce a dead polymer chain anda molecule with a radical. The transfer agent may be theinitiator, monomer, polymer, solvent, or an impurity. Whenthe transfer does not lead to new chain growth, it is calledinhibition. If the newly formed radical is less reactive thanthe propagating radical, then it is called retardation.3

1.121.3.1.6. Thermodynamics of polymerizationAddition polymerizations of olefinic monomers have negativeDH and DS. The exothermic nature of polymerization arisesbecause the process involves the formation of new bonds andthe negative DS arises from the decreased degree of freedom ofthe polymer compared to the monomer. DG depends on bothparameters and is given by

DG ¼ DH ! TDS [28]

The numerical value of DS is much smaller than DH. ThereforeDG is negative under ambient T conditions since |DH|> |TDS|.Polymerization is thermodynamically favorable. However,thermodynamic feasibility does not mean that the reactionis practically feasible. For the polymerization reaction totake place at appreciable rates, it may require specific catalystsystems. This is the case with the a-olefins, which requireZiegler–Natta or coordination-type initiators.3

1.121.3.2. Ionic Polymerization

Addition polymerization of olefinic monomers can also beachieved with active centers possessing ionic charges. Thesecan be either cationic polymerizations or anionic polymeriza-tions depending on the type of the chain carrier ion. The ioniccharge of the active center causes these polymerizations to bemore selective unlike free radical polymerization. They proceedonly with monomers that have appropriate substituent groupswhich can stabilize the active center. Since the required activa-tion energy for ionic polymerization is small, these reactionsmay occur at very low temperatures. High rate of polymerizationat low temperatures is a characteristic of ionic polymerizations.For cationic active centers, electron-donating substituent groupsare needed. For anionic polymerization, the substituent groupmust be electron withdrawing to stabilize the negative charge.Thus, most monomers can be polymerized either by cationic orby anionic polymerization but not by both. Only when thesubstituent group has a weak inductive effect and is capable ofdelocalizing both positive and negative charges (e.g., styreneand 1,3-dienes) both cationic and anionic polymerization canbe achieved.

Another important difference between free radicalic andionic polymerizations is that many ionic polymerizations pro-ceed at much higher rates than free radical polymerization,mainly because the concentration of propagating chains ismuch higher (by a factor of 104–106). Another difference isthat an ionic active center is accompanied by a counter ion ofopposite charge. Both the rate and stereochemistry of propa-gation are influenced by the counter ion and the strength of

interaction with the active center. Finally, termination does notoccur by a reaction between two ionic active centers becausethey are of similar charge.10

1.121.3.2.1. Cationic polymerizationTypical catalysts for cationic polymerization are strong electronacceptors and include Lewis acids, Friedel–Crafts halides,Bronsted acids, and stable carbenium-ion salts. Many ofthem require a cocatalyst, usually a proton donor, to initiatepolymerization. Those monomers with electron donating1-1-substituents that can form stable carbenium ions arepolymerized by cationic mechanisms. For these systems,the polymerization rate is very high; for isobutylene initiatedby AlCl3 or BF3, in few seconds at ! 100 (C, chains of severalmillion daltons can form. Both the rate and the molecularweight decrease with temperature and are much lower atroom temperature.5

In certain cationic polymerizations, a distinct terminationstep may not take place; therefore ‘living’ cationic polymersare formed. However, chain transfer to a monomer, polymer,solvent, or counterion can terminate the growth of chains.Cationic polymerizations are usually conducted in solution,at low temperature, typically !80 to !100 (C. The solvent isimportant because it determines the activity of the ion at theend of the growing chain. There is a linear increase in polymerchain length and an exponential increase in polymerizationrate as the dielectric strength of the solvent increases.12

1.121.3.2.2. Anionic polymerizationThe initiator in an anionic polymerization needs to be a strongnucleophile, including Grignard reagents and other organome-tallic compounds like n-butyl (n-C4H9) lithium. When thestarting reagents are pure and the polymerization reactor isfree of traces of oxygen and water, the chain can grow untilall the monomer is consumed. For this reason, anionic poly-merization is sometimes called ‘living’ polymerization. Ter-mination occurs only by the deliberate introduction ofoxygen, carbon dioxide, methanol, or water. In the absenceof a termination mechanism, the number average degree ofpolymerization, !Xn, is

!Xn ¼ M½ %oI½ %o

[29]

where [M]o and [I]o are the initial concentrations of the mono-mer and the initiator, respectively.

The absence of termination during a living polymerizationleads to a very narrow molecular weight distribution with aheterogeneity index (HI) as low as 1.06, whereas for free radicalpolymerization polydispersities as high as 2 were reported.12

1.121.3.3. Coordination Polymerization

Use of some special catalysts may lead to the formation of veryorderly structured polymers with high stereospecificity. Forexample, the processes used in the polymerization of bothisotactic polypropylene (i-PP) and high density polyethylene(HDPE) employ transition-metal catalysts called Ziegler–Nattacatalysts, which utilize a coordination type mechanism duringpolymerization. In general, a Ziegler–Natta catalyst is an

360 Polymers



organometallic complex with the cation from Groups I to IIIin the Periodic Table, (e.g., Al(C2H5)3), a hallide of transi-tion metal from Groups IV to VIII, (e.g., TiCl4). HDPE canbe prepared by bubbling ethylene gas into a suspensionof Al(C2H5)3 and TiCl4 in hexane at room temperature.Although the exact mechanism is still unclear, it is proposedthat the growing polymer chain is bound to the metal atomof the catalyst and that monomer insertion involves a coordi-nation of the monomer with the atom. It is this coordina-tion of the monomer that results in the stereospecificityof the polymer. Coordination polymerizations can be termi-nated by introduction of water, hydrogen, aromatic alcohol,or metals.12

1.121.3.4. Typical Addition Polymers and Their BiomedicalApplications

Addition polymers such as polyethylene, polypropylene, poly-styrene, polyacrylates can be easily fabricated in manyforms such as fibers, textiles, films, rods, and viscous liquidsand they are used in a variety of biomedical applications.Some are given in Table 4.13,14

1.121.3.5. Comparison of Addition and CondensationPolymerization

The main characteristic of step polymerization that distin-guishes it from chain polymerization is that the reactionoccurs between any of the different sized species present inthe reaction system. In step polymerization, the size of thepolymer molecules increases at a relatively slow pace and

the monomers disappear early in the reaction unlike chainpolymerization where the monomer concentration decreasesgradually (medium generally contains long and dead chainsand monomers) and growth occurs very rapidly by additionof one unit at a time to the end of the growing chain.Longer polymerization durations are essential in obtaininghigh molecular weight condensation polymers whereas withchain polymers long reaction times give high yields but donot affect the molecular weight significantly.

The typical step and chain polymerizations differ signifi-cantly in the relationship between polymer molecular weightand the percent conversion of monomer. The chain polymeri-zation will show the presence of high molecular weightpolymer molecules at all percent of conversions. There areno intermediate sized molecules in the reaction mixture(only monomer and high polymer). The only change thatoccurs with conversion is the continuous increase in the num-ber of polymer molecules. On the other hand, high molecularweight polymer is obtained in step polymerizations only nearthe very end of the reaction (at 98% conversion).3,15,16

1.121.3.6. New Polymerization Mechanisms

1.121.3.6.1. Atom transfer radical polymerizationAtom transfer radical polymerization (ATRP) is a controlled/living polymerization technique which is highly effective inobtaining well-defined polymers or copolymers with predeter-mined molecular weight, narrow molecular weight distribu-tion, and a high degree of chain end functionality. ATRP hasbeen used in the preparation of polymers with precisely con-trolled functionalities, topologies (linear, star/multiarmed,

Table 4 Some additional polymers used in biomedical applications

Synthetic polymers Monomeric unit Applications

Polyethylene (PE) −CH2−CH2−n

Pharmaceutical bottles, nonwoven fabrics, catheters, pouches, flexiblecontainers, orthopedic implants (e.g., hip implants)

Poly(2-hydroxyethyl methacrylate)(PHEMA) −CH2−C−

n

COOCH2CH2OH

CH3 Contact lenses, surface coatings, drug delivery systems

Poly(methyl 2-cyanoacrylate)

−CH2−C−n

CN

COOCH3

Surgical adhesive

Poly(methyl methacrylate) (PMMA)

−CH2−C−n

CH3

COOCH3

Blood pumps and reservoirs, membranes for dialyzers, intraocular lenses, bonecement, drug delivery systems

Polypropylene (PP) −CH2−CH−

CH3

nDisposable syringes, blood oxygenator membranes, sutures, nonwovenfabrics, artificial vascular grafts, reinforcing meshes, catheters

Polystyrene (PS) −CH2−CH−n

C6H5

Tissue culture flasks, roller bottles, filterwares

Poly(tetrafluoro ethylene) (PTFE) −CF2−CF2−n

Catheters, artificial vascular grafts, various separator sheets

Poly(vinyl chloride) (PVC) −CH2−CH−

Cln

Blood bags, surgical packaging, i.v. sets, dialysis devices, catheter bottles,connectors, and cannulae




comb, hyperbranched, and network polymers), and composi-tions (homopolymers, block copolymers, statistical copoly-mers, gradient copolymers, graft copolymers).

Monomer, initiator with a transferable atom (halogen), andcatalyst (transition metal with suitable ligands) are the maincomponents of ATRP. In some cases, an additive (metal salt ina higher oxidation state) may be used. Type of solvent and levelof temperature are important parameters for a successful ATRP.The most commonly used monomers are styrenes, methacry-lates, methacrylamides, dienes, and acrylonitriles.

Atom transfer step is the key elementary reaction leadingto the uniform growth of the polymeric chains. In ATRP,radicals are formed by a reversible redox reaction of a transi-tion metal complex, Mn

t -Y/ligand, where Mt is transition metaland Y may be another ligand or a counterion. Transfer of an Xatom (usually halogen) from a dormant species to the metalresults in an oxidized metal complex (X-Mnþ1

t -Y/ligand whichis the persistent species) and a free radical (R�). Activation anddeactivation processes occur with rate constants of kact andkdeact, respectively (Figure 8).

Even when the same ATRP conditions (same catalyst andinitiator) are used, each monomer has its own unique atomtransfer equilibrium constants for its active and dormant species.The rate of polymerization depends on Keq (Keq¼ kact/kdeact).If it is too small, polymerization reaction will occur slowly,and if it is too large, due to the high radical concentration,termination will occur and polymerizationwill be uncontrolled.

The new radical can initiate the polymerization by additionto a monomer with the rate constant of propagation kp. Termi-nation reactions (rate constant is kt) also occur in ATRP, bycombination or disproportionation, or the active species isreversibly deactivated by the higher oxidation state metal com-plex. In a well-controlled ATRP, no more than a few percent ofthe polymer chains undergo termination. During the initial,short, nonstationary stage of the polymerization, the concen-tration of radicals decays by the unavoidable irreversible selftermination, whereas, the oxidized metal complexes increasesteadily as the persistent species. As the reaction proceeds,the decreasing concentration of radicals causes a decrease inself-termination and cross-reaction with persistent speciestoward the dormant species. The decrease in the stationaryconcentration of growing radicals minimizes the rate of termi-nation which has a key role in the first-order kinetic.

The stabilizing group (e.g., phenyl or carbonyl) on themonomers produces a sufficiently large atom transfer equilib-rium constant. Typically, alkyl halides (RX) are used as theinitiator. The halide group (X) must rapidly and selectivelymigrate between the growing chain and the transition-metalcomplex to form polymers with narrow molecular weight

distributions. Catalyst is an important component of ATRPsince it determines the position of the atom transfer equilib-rium and the dynamics of exchange between the dormant andactive species. A variety of transition metal complexes havebeen used as ATRP catalysts such as transition metal complexesof copper, ruthenium, palladium, nickel, and iron. Polymeri-zation is conducted either in bulk or in solvents (benzene,water, etc.) at moderate temperatures (70–130 (C).17–21

1.121.3.6.2. Nitroxide-mediated polymerizationNitroxide-mediated polymerization (NMP) is another con-trolled radical polymerization method. NMP allows thepreparation of very well-defined polymers with controlledmolecular weight and narrow molecular weight distributionand to extend chains with different monomers to obtainmultiblock copolymers. Combination of a nitroxide and afree radical initiator or alkoxyamines serving as both initiatorsand controlling agents are used in this technique.

NMP is based on a reversible recombination between pro-pagating species (P�) and nitroxide (R2NO�, R¼ alkyl group)with the formation of alkoxyamine (R2NOP), resulting in alow radical concentration and decreases the irreversible termi-nation reactions. Polymer chains with equal chain lengths andreactive chain ends can be obtained because a majority ofdormant living chains can grow until the monomer is fullyconsumed.

NMP is metal free and not colored, and polymer does notrequire any purification after synthesis. The main limitation ofNMP is the range of monomers that can be effectively con-trolled. Some efficient alkoxyamines and nitroxides are ableto control most of the conjugated vinyl monomers such asstyrene and derivatives, acrylates (including some functionalacrylates), acrylamides, acrylonitrile, and methacrylates (withsome limitations) and also some dienes such as isoprene.22,23

1.121.3.6.3. Reversible addition–fragmentation chaintransfer polymerizationReversible addition–fragmentation chain transfer polymeriza-tion (RAFT) is one of the most versatile methods of controlledradical polymerization because it allows a wide range of func-tionalities in the monomers and solvents, including aqueoussolutions. The method is relatively new for the synthesis ofliving radical polymers and may be more versatile than ATRPor NMP. RAFT polymerization uses thiocarbonylthio com-pounds, such as dithioesters, dithiocarbamates, trithiocarbo-nates, and xanthates in order tomediate the polymerization viaa reversible chain-transfer process. The technique is applicableto a wide range of monomers including methacrylates, metha-crylamides, acrylonitrile, styrene and derivatives, butadiene,

Monomer kt

kp

Termination

P1•

kdeact

kact

R-X + Mtn-Y/Ligand X-Mt

n+1-Y/Ligand + R•

Figure 8 General mechanism of ATRP.

362 Polymers



vinyl acetate, and N-vinyl pyrrolidone. As a result of its excep-tional effectiveness and the wide range of monomers andsolvents, RAFT polymerization has developed into anextremely versatile polymerization technique. Especially, themolecular weight of the polymer can be predetermined and themolecular weight distribution can be controlled fairly well.

Typically, a RAFT polymerization system consists ofan initiator, monomer, chain transfer agent, and solvent. Thecontrol of temperature is crucial. It can be performed by simplyadding a certain quantity of an appropriate RAFT agent (i.e., athiocarbonylthio compound) to a conventional free radicalpolymerization medium. Radical initiators such as azobisiso-butyronitrile (AIBN) and 4,40-azobis(4-cyanovaleric acid)(ACVA) are widely used as initiators in RAFT polymerizations.RAFT agents (also called chain transfer agents) must be thio-carbonylthio compounds where the Z and R groups performdifferent functions (Figure 9). The Z group primarily controlsthe effectiveness with which radical species can add to the C¼Sbond. The R group must be a good homolytic leaving groupwhich is able to initiate new polymer chains.

There are four steps in a typical RAFT polymerization: initi-ation, addition–fragmentation, reinitiation, and equilibration(Figure 10).

In the initiation step, the reaction is started using radicalinitators (I) such as AIBN. The initiator reacts with a monomerto create a radical species which starts an actively polymerizingchain. During addition–fragmentation step, the active chain(Pn) reacts with the dithioester, which releases the homolyticleaving group (R�). This is a reversible step, with an intermedi-ate species capable of losing either the leaving group (R�) or the

active species (Pn�). Reinitiation occurs with the reactionbetween the leaving group radical and another monomer spe-cies, starting another active polymer chain. This active chain(Pm�) then goes through the addition–fragmentation or equili-bration steps. Equilibration is a fundamental step in the RAFTprocess which traps the majority of the active propagatingspecies into the dormant thiocarbonyl compound. This limitsthe possibility of chain termination. Active polymer chains (Pm�and Pn�) are in an equilibrium between the active anddormant stages. While one polymer chain is in the dormantstage (bound to the thiocarbonyl compound), the other isactive in polymerization.24–28

RAFT process allows the synthesis of polymers with spe-cific macromolecular architectures such as block, gradient,statistical, linear block, comb/brush, star, hyperbranched, andnetwork copolymers and dendrimers. Examples of architec-tures that can be synthesized by RAFT are given in Figure 11.

1.121.4. Polymer Reactions

1.121.4.1. Copolymerization

Copolymers are polymers formed from two or more mono-meric units. The arrangement of repeating units can be invarious ways along the chain. Some copolymers are very simi-lar to homopolymers, because they have one type of repeatingunits. But proteins and some polysaccharides are copolymersof a number of different monomers.

Copolymers constitute the vast majority of commerciallyimportant polymers. Compositions of copolymers may varyfrom only a small percentage of one component to comparableproportions of both monomers. Such a wide variation in com-position permits the production of polymer products withvastly different properties for a variety of end uses. The minorconstituent of the copolymer may, for example, be a dieneintroduced into the polymer structure to provide sites forsuch polymerization reaction as vulcanization; it may also bea trifunctional monomer incorporated into the polymer to

C

ZR

S

S

Figure 9 General structure of RAFT agents.

Initiation:

I•

Addition–fragmentation:

Pn•

Pn•

Reinitiation:

R• + Monomer (M) Pm•

Equilibration:

Pm• +SPn•

S +SR•

Z

C

S

C

Z

SR

•S

C

Z

SRPn Pn

Addition Fragmentation

MS

C

Z

S

Pn

•S

C

Z

SPm PmPm C

S

Z

M

+

+

Figure 10 RAFT mechanism.




ensure cross-linking, or possibly it may be a monomer contain-ing carboxyl groups to enhance product solubility, dyeability,or some other desired properties.12

1.121.4.1.1. Types of copolymerizationIn free radical polymerization, reactivity ratios of the mono-mers, r1 and r2, should be considered. Reactivity ratios repre-sent the relative preference of a given radical that is addingits own monomer to the other monomer.

r1¼k11k12

[30]

where k11 and k22 are the rate constants for radicals addingtheir own type of monomer and k12 and k21 are the rate con-stants for adding the opposite kind.

r2¼k22k21

[31]

Depending on the r values, copolymerization reaction canform ideal, random, alternating, or block copolymers. Anothertype is graft copolymers.

In ideal copolymerization (r1r2¼ 1), the growing chainend reacts with one of the monomeric unit with a statisticallypossible preference. The multiplication of reactivity ratiosshould be equal to 1.

When r1r2¼ 1 then,

r1 ¼ 1

r2or

k11k12

¼ k21k22

[32]

The relative amounts of the monomer units in the chain aredetermined by the reactivities of the monomer and the feedcomposition of the reaction medium.

r1r2¼ 1 occurs under two conditions:

1. r1> 1 and r2< 1 or r1< 1 and r2> 1.

One of the monomers is more reactive than the other. Thecopolymer will contain a greater proportion of the more

reactive monomer in the random sequence of monomerunits. In this case, production of copolymers with signifi-cant quantities of both monomers will be more difficult asthe difference in reactivities of the two monomers increases.

2. r1¼ r2¼ 1.

Under these conditions, the growing radicals cannot distin-guish between the two monomers. The composition of thecopolymer is the same as that of the input concentrationsand the monomers are arranged randomly along the chain.These copolymers show properties of both homopolymersof its constituents.Random copolymers are formed when r values of both

monomers are close to each other. A mixture of two or moremonomers is polymerized in one process and where thearrangement of the monomers within the chains is determinedby kinetic factors. If the reacting monomers are shown as A andB, the sequence will have no order in the chain, suchas –AABBAAABABAA–.

Random copolymers tend to average the properties of theconstituent monomers in the proportion to the relative abun-dance of the comonomers.

In the alternating copolymerization, r values of bothmonomers are equal to zero. When r1¼ r2¼ 0 (or r1r2¼ 0),each radical reacts exclusively with the other monomer;that is, neither radical can regenerate itself. Consequently,the monomer units are arranged alternately along the chain.These are called alternating copolymers and can be shownas –ABABAB–.

Polymerization continues until one of the monomers isused up and then it stops. Perfect alternation occurs whenboth r1 and r2 are zero. As the quantity r1r2 approaches zero,there is an increasing tendency toward alternation. This haspractical significance because it enhances the possibility ofproducing polymers with appreciable amounts of both mono-mers from a wider range of feed compositions.12 Alternatingcopolymers, while relatively rare, are characterized by combin-ing the properties of the two monomers along with structuralregularity. Crystalline polymers can be obtained if a very highdegree of regularity (stereoregularity extending along the allconfiguration of the repeat units) exists.

Block or segmented copolymers are usually prepared bymultistep processes. The blocks may be a homopolymer ormay themselves be copolymers. Diblock can be shown as–AAAABBB– and triblock can be shown as –AAABBBBAAAA–.In multiblock copolymers, the A and B segments repeat them-selves many times along the chain.

Block copolymers are generally prepared by sequentialaddition of monomers to living polymers, rather than bydepending on the improbable r1r2> 1 criterion in monomers.6

Graft copolymers and branched copolymers are formed bycopolymerization of macromonomers and can form as a con-sequence of intramolecular rearrangement. In general, thebackbone and the chain is formed from one type of monomer,and the chains of other type are attached as branches. This canbe shown as

–AAAAAAAA–

B BB BB B

A-A-A-B-B-B

A-A-A

Block copolymer Star polymer

A-A-A-A-ABBB

BBB

BBB

Comb polymer

BB

B

BB

B

BB

B

BB

B

B BB B

B B

B BB B

B B

BB

B

BB

B

AB2 star

A-A-A

Dumbbell (pom-pom)

A-A-ABB

BBBB

A-A-ABB

BBBB

AA

A

AA

A

Ring block

A

Figure 11 Examples of complex architectures prepared by RAFT.

364 Polymers



Special classes of branched copolymers are star polymers,dendrimers, hyperbranched copolymers, and microgels.29

1.121.4.1.2. Effects of copolymerization on propertiesCopolymer synthesis offers the ability to alter the properties ofhomopolymer in the desired direction by the introductionof an appropriately chosen second repeating unit. Since thehomopolymers are combined in the same molecule, copoly-mer demonstrates the properties of both homopolymers. Prop-erties, such as crystallinity, flexibility, Tm, Tg can be altered byforming copolymers. The magnitudes and sometimes even thedirections of the property alteration differ depending onwhether random, alternating, or block copolymer is involved.The crystallinity of a random copolymer is lower than that ofeither of the respective homopolymers (i.e., the homopoly-mers corresponding to the two different units) because of thedecrease in structural regularity. The melting temperature ofany crystalline material formed is usually lower than thatof either homopolymer. The Tg value will be in betweenthose for the two homopolymers.

Alternating copolymers have a regular structure, and theircrystallinity may not be significantly affected unless oneof the repeating units contains rigid, bulky, or excessivelyflexible chain segments. The Tm and Tg values of an alternatingcopolymer are in between the corresponding values forthe homopolymers. Block copolymers show the properties(e.g., crystallinity, Tm, Tg) present in the corresponding homo-polymer as long as the block lengths are not too short. Thisbehavior is typical since A blocks from different polymer mole-cules aggregate with each other and separately, B blocks fromdifferent polymer molecules aggregate with each other. Thisoffers the ability to combine the properties of two very differ-ent polymers into the one block copolymer. The exceptionto this behavior occurs infrequently when the tendency forcross-aggregation between A and B blocks is the same as forself-aggregation of A blocks with A blocks and B blocks withB blocks.

Most commercial utilization of copolymerization falls intoone of the two groups. One group consist of various randomcopolymers in which the two repeating units posses the samefunctional groups. The other groups of commercial copoly-mers consist of block copolymers in which two repeatingunits have different functional groups although only fewcommercial random copolymers in which the two repeatingunits have different functional groups exist. The reason for thesituation probably lies in the difficulty of finding one set ofreaction condition for simultaneously performing two differ-ent reactions.30

1.121.4.1.3. Kinetics of copolymerization1.121.4.1.3.1. Kinetics of addition copolymerizationKinetics of copolymerization reactions are very complicated.The copolymerization between two different monomers can bedescribed using four reactions, two homopolymerizations andtwo cross-polymerization additions. Reaction mechanism isgiven in Table 5. The specific rate constants for the differentreaction steps described are assumed to be independent ofchain length.11

At steady state, the concentrations of M1� and M2� areassumed to remain constant. Therefore the rate of conversion

of M1� to M2� necessarily equals that of conversion of M2�to M1�. Thus,

k21 M2�½ % M1½ % ¼ k12 M1�½ % M2½ % [33]

The rate of polymerization can be given with the rates ofdisappearance of monomers M1 and M2 as shown below:

!d M1½ %dt

¼ k11 M1�½ % M1½ % þ k21 M2�½ % M1½ % [34]

!d M2½ %dt

¼ k11 M1�½ % M2½ % þ k22 M2�½ % M1½ % [35]

From the division of the two equations, the copolymer equa-tion is obtained. The ratio of d[M1]/d[M2] gives the monomerratios present in the polymer chain.

d M1½ %d M2½ % ¼

M1½ %M2½ %

r1 M2½ % þ M2½ %M1½ % þ r2 M2½ % [36]

Here, r1 and r2 are monomer reactivity ratios and are defined by

r1 ¼ k11k12

[37]

and,

r2 ¼ k22k21

[38]

Monomer-radical reaction rates are also affected by sterichindrance. The role of steric hindrance in the reduction of thereactivity of 1,2-disubstituted vinyl monomers can be illu-strated by the fact that while these monomers undergo copoly-merization with other monomers (e.g., styrene), they do nottend to homopolymerize. Homopolymerization is preventedbecause of the steric effect of the 2-substituent on the attackingradical and the monomer. On the other hand, there is no 2- orb-substituent when the attacking radical is styrene; conse-quently, copolymerization is possible.12

The effect of steric hindrance in reducing reactivity may alsobe demonstrated by comparing the reactivities of 1,1- and 1,2disubstituted olefins with reference radicals. The addition of asecond 1-substituent usually increases reactivity three to ten-fold; however, the same substituent in the 2-position usuallydecreases reactivity 2- or 20-fold. The extent of reduction inreactivity also depends on the energy differences between cisand trans forms.5

1.121.4.1.3.2. Kinetics of condensation copolymerization:

• Random copolymers: The copolymerization of a mixture ofmonomers offers a route to randomcopolymers; for instance,a copolymer of overall composition XWYV is synthesizedby copolymerizing a mixture of the four monomers.

Table 5 Reaction mechanism, rate constants, and rate equation orcopolymerization

Reaction Rate constant Rate equation

M1 �þM1!M1M1 � k11 k11[M1 �][M1]M1 �þM2!M1M2 � k12 k12[M1 �][M2]M2 �þM2!M2M2 � k22 k22[M2 �][M2]M2 �þM1!M2M1 � k21 k21[M2 �][M1]




(X) HOOC—R—COOH

(Y) HOOC—R2—COOH

(W) H2N—R1—NH2

(V) H2N—R3—NH2

HOOC—CONH—R1—NHCO—R2—CONH—R3—NH2

Copolymer of XWYV

It is highly unlikely that the reactivities of the variousmonomers would be such that block or alternating copolymersare formed. The overall composition of the copolymerobtained in a step polymerization will almost always bethe same as the composition of the monomer mixture sincethese reactions are carried out to essentially 100% conversion(a necessity for obtaining high molecular weight polymer). Inthe step copolymerization of monomer mixtures, one oftenobserves the formation of random copolymers. This occurseither because there are no differences in the reactivities ofthe functional groups existing on different monomers or thepolymerization under reaction conditions where there isextensive interchange. The use of only one diacid or diaminewould produce a variation on the copolymer structure witheither R¼R2 or R1¼R3.

31

Statistical copolymers containing repeating units eachwith a different functional group can be obtained usingappropriate mixture of monomers. For example, a polyester-amide can be synthesized from a ternary mixture of a diol,diamine, and diacid or binary mixture of a diacid andamine–alcohol.

• Alternating copolymers: It is possible to synthesize an alter-nating copolymer in which R¼R2 by using a two-stageprocess. In the first stage, a diamine is reacted with an excessof diacid to form a trimer:

nHOOCwRwCOOHþmH2NwR1wNH2

! mHOOCwRwCONHwR1wNHCOwRwCOOH [XI]

The trimer is then reacted with an equamolar amount of asecond diamine in the second stage:

nHOOCwRwCONHwR1wNHCOwRwCOOHþnH2NwR3wNH2

!HOðwCOwRwCONHwR1wNHCOwRwCONHwR3wNHÞnwH

þ 2n!1ð ÞH2O

[XII]

Alternating copolymers with two different functional groupsare similarly synthesized by using preformed reactants.32–35

nOCNwRwCONHwR1wOSi CH3ð Þ3 !!HF

! CH3ð Þ3SiF

HFw CH3ð Þ3SiFðCOwNHwRwCOwNHwR1wOÞn [XIII]

nOCNwRwCONHwR1wNHCOwRwNCOþHOwR2wOH!HF

HFwðCONHwRwCONHwR1wNHCOwRwNHCOOwR2wOÞn[XIV]

The silyl ether derivative of the alcohol is used in reac-tion [XIII]. The corresponding alcohol OCNwRwCONHwR1wOH

cannot be isolated because of the high degree of reactivity ofisocyanate and alcohol groups toward each other.

• Block copolymers: There are two general methods forsynthesizing block copolymers. These two methods, the oneprepolymer and the two prepolymer methods, are describedbelow for block copolymers containing different functionalgroups in the repeating units. They are equally applicableto block copolymers containing the same functionalgroups in the two repeating units. The two prepolymermethod involves the separate synthesis of two differentprepolymers, each containing appropriate end groups,followed by the polymerization of two polymers viareaction of their end groups. Consider the synthesis ofa polyester-block-polyurethane. A isocyanate-terminatedpolyester prepolymer is synthesized from HO–R3–OHand HOOC–R1–COOH using an excess of diol reactant.An isocyannate-terminated polyurethane prepolymeris synthesized from OCN–R2–NCO and HO–R3–OHusing an excess of the diisocyanate reactant. Thea,o-dihydroxypolyester and a,o-diisocyanatapolyurethaneprepolymers, referred to as macrodiol and macrodiiso-cyanate, respectively, are subsequently polymerized witheach other to form the block copolymer:

HwðwOwRwOCCwR1wCOwÞnwOwROH

þOCNwðwR2wNHCOOwR3wOOCNHÞmwR2wNCO

!HwðwOwRwOOCwR1wCOwÞnwOwROwOCNHwR2wðNHCOOwR3wOOCNHwR2wÞmwNCO

[XV]

The block lengths n and m can be varied by adjustingthe stoichiometric ratio r of reactants and conversion ineach prepolymer synthesis. In typical systems, the prepoly-mers have molecular weights in the range of 500–6000Da.A variation of the two-prepolymer method involves the useof a coupling agent to join the prepolymers. For example, adiacyl chloride could be used to join together two differentmacrodiols or two different macrodiamines or a two differ-ent macrodiamines or a macrodiol with a macrodiamine.

The one-prepolymer method involves one of the aboveprepolymers with two ‘small’ reactants. The macrodiol isreacted with a diol and diisocyanate

HwðwOwRwOOCwR1wCOÞnORwOH

þ ðmþ 1ÞOCNwR2wNCOþmHOwR3wOH

! HwðOwRwOOCwR1wCOÞnORwOOCNHwðwR2wNHCOOwR3wOOCNHÞmwR2wNCO

[XVI]

The block lengths and the final polymer molecularweights are again determined by the details of the prepolymersynthesis and its subsequent polymerization. An often-usedvariation of the one-prepolymer method is to react themacrodiol with excess diisocyanate to form an isocyanate-terminated prepolymer. The latter is then chain-extended(i.e., increased in molecular weight) by reaction with a diol.

366 Polymers



The one- and two-prepolymer methods can in principle yieldexactly by the same final block copolymer. However, the dis-persity of the polyurethane block length is usually narrowerwhen the two-prepolymer method is used.32,35

1.121.4.2. Cross-Linking Reactions

Cross-linking is the predominant reaction upon irradiation ofmany polymers. It involves attachment of polymeric chainsto each other. When each molecule is bonded at least once,then the whole sample becomes insoluble. It is accompaniedby the formation of a gel and ultimately by the insolubiliza-tion of the specimen. Cross-linking has a beneficial effect onthe mechanical properties of polymers.

In commercial practice, cross-linking reactions take placeduring the fabrication of articles made with thermosettingresins. The cross-linked network is stable against heat anddoes not flow or melt. Most linear polymers are thermoplastic.They soften and take on new shapes upon the application ofheat and pressure.5

Cross-linking can be achieved by the action of electromag-netic radiation, heat, or catalysts and results in opening ofunsaturated groups on chains and reaction of multifunctional(>2) groups. Control of cross-linking is critical for processing.The period after the gel point, when all the chains are bondedat least to one other chain is usually referred to as the curingperiod.

1.121.4.2.1. Effect of cross-linking on propertiesThe change in properties is determined by the extent of cross-linking. Lightly cross-linked polymers swell extensively insolvents in which the uncross-linked material dissolves, butcovalently (irreversibly) cross-linked polymers cannot dissolvebut only swell in the solvent of the uncross-linked form. Uponextensive cross-linking, the sample may even not swell appre-ciably in any solvent.

Cross-linking has a significant effect on viscosity; itbecomes essentially infinite at the onset of gelation. The effectof chain branching and cross-linking on Tg are explained interms of free volume. A high amount of branches increase thefree volume and lower the Tg, whereas cross-linking lowersthe free volume and raises the Tg.

The addition of cross-links leads to stiffer, stronger, tougherproducts, usually with enhanced tear and abrasion resistance.However, extensive cross-linking of a crystalline polymer leadsto a loss of crystallinity, and this might decrease mechanicalproperties. When this occurs, the initial trend of propertiesmay be toward either enhancement or deterioration, depend-ing on the degree of crystallinity of the unmodified polymerand the method of formation and location (crystalline oramorphous regions) of the cross-links.5

1.121.4.2.2. Cross-linking of biological polymers1.121.4.2.2.1. Cross-linking of proteinsProteins are found to be chemically (permanent) or physically(reversibly) cross-linked. These cross-links can be intra or inter-molecular. For example the triple helix of collagen is intermo-lecularly cross-linked whereas many reversible cross-links

are observed in the secondary and tertiary structure ofthe proteins. Proteins are also cross-linked for various applica-tions (biotechnological, biomedical, etc.).

Physical cross-linking methods include drying, heating, orexposure to g or UV radiation. The primary advantage ofphysical methods is that they do not cause harm. However,the limitation of such methods is that obtaining the desiredamount of cross-linking is difficult. In chemical cross-linkingmethods, cross-linkers are generally used to bond the func-tional groups of amino acids. In recent years, there has beenan increase in interest in physical cross-linking methods.The main reason is that use of cross-linking agents is avoidedbecause most cause some toxic effects. However, the degree ofcross-linking is considerably lower and cross-links are weakerthan obtained by chemical methods.

Collagen is the major protein component of bone,cartilage, skin, and connective tissue and also the major con-stituent of all extracellular matrices in animals. Collagencan be chemically cross-linked by various compoundsincluding glutaraldeyde, carbodiimide, genipin, and transglu-taminase. 1-Ethyl-3-diaminopropyl carbodiimide (EDC) andN-hydroxysuccinimide (NHS) catalyze covalent bindingsbetween carboxylic acid and amino groups; thus, cross-linkingbetween collagen structures is possible (Figure 12). Furthermore,other extracellular matrix components containing carboxylgroups, such as glycosaminoglycans, can also be cross-linkedwith this approach.36,37

1.121.4.2.2.2. Cross-linking of polysaccharidesChemical and physical methods are used for cross-linking ofpolysaccharides. Physical cross-linking is achieved by physicalinteraction between different polymer chains.

In physical cross-linking, polysaccharides form cross-linked networks with the counterions on the surface. Highcounterion concentration requires long exposure times toachieve complete cross-linking of the polysaccharides. Chemi-cal cross-linking of polysaccharides leads to products withgood mechanical stability. During cross-linking, counterionsdiffuse into the polymer and reacts with polysaccharidesforming intermolecular or intramolecular linkages. Factorswhich affect chemical cross-linking are the concentration ofthe cross-linking agents and the cross-linking duration. Highconcentration of cross-linking agent induces rapid cross-linking. Like physical cross-linking, high counterion concen-tration require longer exposure times to achieve completecross-linking of the polysaccharides.

Polysaccharides can be chemically cross-linked with eitheraddition or condensation cross-linking mechanism. For addi-tion polymerization, the network properties can be easilytailored by the concentration of the dissolved polysaccharideand the amount of cross-linking agent. These reactions arepreferably carried out in organic solvents because water canalso react with the cross-linking agent.

Polysaccharides can be cross-linked through condensationusing 1,6-hexamethylene diisocyanate or 1,6-hexanedibromideor other reagents. Condensation cross-linking can also be doneby carbodiimide which induces cross-links between carboxylicacid and amine groups without itself being incorporated.The commonly used carbodiimide is a water-soluble




carbodiimide called 1-ethyl-3-(3-dimethyl aminopropyl) car-bodiimide (EDC). EDC cross-linking involves the activation ofthe carboxylic acid groups of aspartic acid (Asp) or glutamicacid (Glu) residues by EDC to give O-acylisourea groups.Besides EDC, another reagent, N-hydroxysuccinimide (NHS)is used in the reaction for the purpose of suppressing sidereactions of O-acylisourea groups such as hydrolysis andthe N-acyl shift. NHS can convert the O-acylisourea groupinto a NHS activated carboxylic acid group, which is veryreactive toward amine groups of hydroxy lysine, yielding a socalled zero length cross-link. In this cross-linking process, nei-ther EDC nor NHS is incorporated in the matrix.

1.121.4.2.3. Cross-linking agentsCross-linkers (CL) are either homo- or hetero-bifunctionalreagents permitting the establishment of inter- as well as intra-molecular cross-linkages. Homo-bifunctional reagents, specifi-cally reacting with primary amine groups (i.e., e-amino groupsof lysine residues) have been used extensively as they aresoluble in aqueous solvents and can form stable inter- andintrasubunit covalent bonds.

Genipin is a naturally occurring cross-linking agent thathas significantly low toxicity. It can form stable cross-linkedproducts with resistance against enzymatic degradation that iscomparable to that of glutaraldehyde-fixed tissue. Genipinreacts in a similar manner to glutaraldehyde, but can onlybind to one other genipin molecule.

Even though the definite cross-linking mechanism ofgenipin is not known some mechanisms are proposed as pre-sented in Figure 13(a) and 13(b). In scheme (a) NH2 groupof the protein binds to the ester group (outside the ring

structure) which then reorganizes by releasing a methanolgroup and achieves the binding. Then two protein-bound gen-ipins interact to create the cross-linkage. In scheme (b), thereaction begins with an initial nucleophilic attack of a primaryamine group of the protein on the C3 carbon atom of genipinto form an intermediate aldehyde group. Opening of thedihydropyran ring is then followed by an attack on the result-ing aldehyde group by the secondary amine formed in thefirst step of the reaction.

The predominant chemical agent that has been investigatedfor the treatment of collageneous tissues is glutaraldehyde,which yields a high degree of cross-linking when comparedto formaldehyde, epoxy compounds, cyanamide, and the acy-lazide method. Glutaraldehyde, a popular reagent, has beenused in a variety of applications where maintenance of struc-tural rigidity of protein is important. It covalently bindsto amino groups, but can also bind to other glutaraldehydemolecules.

The glutaraldehyde cross-linking reactions have been exten-sively studied (Figure 14). In general, it is believed that alde-hydes react with the amine groups of proteins, yielding aSchiff base. However, the exact cross-linking structure is stillnot clear because a mixture of free aldehyde and mono- anddehydrated glutaraldehyde and monomeric and polymerichemiacetals is always present in a glutaraldehyde aqueoussolution. However, depolymerization of polymeric glutar-aldehyde cross-links has been reported. This depolymeri-zation leads to the release monomeric glutaraldehyde andsubsequent toxicity.

Calcium ions may also be used as a cross-linker for alginateswhich are water soluble polymers. When a sodium alginate

COOH +

R

N

C

N

R

(EDC)

C

O

OO C

NH

R!

N

R

N

O

O

HO

(NHS)

N

O

O

OC

O

p

pH2N

pHNC

O

+ pN

O

O

HO + NHC

O

RNHR

p p

R = H2C CH2 CH3

R! = H2C CH2 CH2 CH2 NH2+

CH3

CH3Cl–

Figure 12 Mechanism of protein cross-linking using carbodiimide (EDC).

368 Polymers



solution is dipped into a solution containing calcium ions,each calcium ion replaces two sodium ions. The alginate mol-ecule contains plenty of hydroxyl groups that can be coordi-nated to cations (Figure 15).3,11

1.121.5. Conclusion

In brief, polymers are very complexmolecules owing to the largevariety of initiators, catalysts, monomers, and mechanisms

OCH3OCH3

OCH3OCH3

OCH3 OCH3

OCH3

CH3OH

CH2OHCH2OHCH2OHCH2OH

CH2OHCH2OH CH2OH CH2OH

O

OO

O

O O

OCH

O O

O O O

OO

OHOHOH

pp

OH

OH

p: protein

(a)

(b)

+

C

CC C C

OH

p pN N

C C

HN p

C

H2N

H2N HN

H2NNH

p

p p–

+

–

CH2OH

p

2

HN NH

NH

CH3

CH3

p

p

C C

C

O O

O

O

O

OH

OH

CH

O

OH

OCH3 H3COCH3

CH3

OCH3

CH2OH

O O

ONN

2

pp

pp: protein

C

CH

N+

Figure 13 Mechanism of protein cross-linking using Genipin. a) Protein binding to ester group (outside the ring structre) of genipin andcrosslinking, b) Protein binding to ring structure of genipin and crosslinking.

RNH2 + HOC-CH2-CH2-CH2-CHO

2RNH2 + HOC-CH2-CH2-CH2-CHO

Glutaraldehyde(a)

(b)

Glutaraldehyde

RNH2 : Chitosan

R-N=CH-CH2-CH2-CH2-CHO

R-N=CH-CH2-CH2-CH2-CH=N-RNH2

Figure 14 Cross-linking mechanism with glutaraldehyde. (a) Glutaraldehyde activated chitosan and (b) Glutaraldehyde cross-linked chitosan.




available. This enables us to produce very large numbers ofdifferent polymers with very diverse properties and this isprecisely why polymers play a very important role as a sourcefor materials needed to satisfy human needs. They can be madeflame retardant, conductive, bio- or hemocompatible, inert orreactive, stable or degradable at a controlled rate, very toughor soft as gelly. The biomedical field benefits from this diver-sity immensely since the physical and chemical propertiesof polymers resemble that of the tissues of the human bodymore than any other material type such as metals or ceramics.With the developments in biotechnology, nanotechnology,and nanomedicine polymers will keep getting better andmore useful for human well-being.

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Figure 15 Cross-linking of alginic acid with calcium ions.

370 Polymers



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