Lecture No.01 Polymer Engineering

8/4/2019 Lecture No.01 Polymer Engineering

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POLYMER ENGINEERING (MM 538)

Dr. Kausar Ali Syed

Lecture No 1 J

une 30, 2010

Review of polymerization, structure, and properties of polymeric materials

Although many people probably do not realise it, everyone is familiar with polymers. They

are all around us in everyday use, in rubber, in plastics, in resins and in adhesives and

adhesive tapes. They are an extraordinarily versatile class of materials, with properties of a

given type often having enormously different values for different polymers and even

sometimes for the same polymer in different physical states. We are here concerned

primarily with synthetic polymers, i.e. materials produced by the chemical industry, rather

than with biopolymers, which are polymers produced by living systems and are often used

with little or no modification. Many textile fibers in common use, such as silk, wool and

linen, are examples of materials that consist largely of biopolymers. Wood is a rather morecomplicated example, whereas natural rubber is a biopolymer of a simpler type.

Since most polymers are organic in origin, we briefly review some of the basic conceptsrelating to the structure of their molecules. The major bonds that hold atoms together are

covalent, where electrons are shared by adjacent atoms, ionic, where electrostatic attraction

occurs when electrons are donated or accepted to provide complete electron shells, and

metallic, where the atoms donate their valence electrons to form a sea of electronssurrounding the atoms. The valence electrons move freely within the electron sea and become

associated with several atom cores. The positively charged ion cores are held together by

mutual attraction to the electrons, thus producing a strong metallic bond. There are also

secondary bonds that are relatively weak by comparison. These are seldom mentioned whenstudying metals and ceramics because they are not important. In polymer materials, covalent

bonds provide strong, rigid bonding of atoms within a long chain molecule while the

secondary bonds provide the attraction forces between long chain molecules and thus held

them together. Secondary bonds play an equally important role in the properties of polymers.

Now, many organic materials are hydrocarbons; that is, they are composed of hydrogen and

carbon. Furthermore, the intramolecular bonds are covalent. Each carbon atom has four

electrons that may participate in covalent bonding, whereas every hydrogen atom has only

one bonding electron. A single covalent bond exists when each of the two bonding atoms

contribute one electron. A bond between two carbon atoms may involve the sharing of two

pairs of electron; this is termed a double bond. For example in ethylene, which has thechemical formula C2H4, the two carbon atoms are doubly bonded together, and each is also

singly bonded to two hydrogen atoms.

H H

C C H H

Where and denote single and double covalent bonds. Molecules that have double and

triple covalent bonds are termed unsaturated; that is each carbon atom is not bonded to themaximum four atoms.


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Polymer molecules The molecules in polymers are gigantic in comparison to the

hydrocarbon molecules. For most polymers, these molecules are in the form of long and

flexible chains, the backbone of which is a string of carbon atoms:

C C C C C C C C

These long molecules, called polymers are formed by linking together a large number of

identical units, or mers. These polymers offer a variety of useful properties. Although all

polymers contain covalent bonds within the molecules, they may have either primary or

secondary bonds bridging the macromolecules.

The term polymer is used to mean a particular class of macromolecules consisting, at least to

a first approximation, of a set of regularly repeated chemical units of the same type, or

possibly of a very limited number of different types (usually only two), joined end to end, or

sometimes in more complicated ways, to form a chain molecule. If there is only one type ofchemical unit the corresponding polymer is a homopolymer; if there is more than one type it

is a copolymer. Here we will deal briefly with some of the main types of chemical structural

repeat units present in the more widely used synthetic polymers and with the polymerization

methods used to produce them.

It should be noted that the term monomer or monomer unit is often used to mean either the

chemical repeat unit or the small molecule which polymerizes to give the polymer. These are

not always the same in atomic composition, as will be clear from what follows, and the

chemical bonding must of course be different even when they are. The simplest polymers are

chain-like molecules of the type

AAAAAAAAAAAAA

where A is a small group of covalently bonded atoms and the groups are covalently linked.

The simplest useful polymer is polyethylene

CH2CH2CH2CH2CH2CH2CH2CH2 or[CH2] n

wherein a typical length of chain, corresponding to n ~ 20 000 (where ~ means of the orderof), would be about 3 mm. A piece of string typically has a diameter of about 2 mm, whereasthe diameter of the polyethylene chain is about 1 nm, so that a piece of string with the same

ratio of length to diameter as the polymer chain would be about 1.5 m long. It is the

combination of length and flexibility of the chains that gives polyethylene its importantproperties. The phrase typical length of chain was used above because, unlike those of otherchemical compounds, the molecules of polymers are not all identical. There is a distribution

of relative molecular masses (Mr) (often called molecular weights) and the corresponding

molar masses, M.

The value of Mr for the chain considered in the previous paragraph would be 280000,

corresponding to M = 280000 g mol-1

. Commercial polymers often have average values of M

between about 100 000 and 1 000 000 g mol-1

, although lower values are not infrequent.

The flexibility of polyethylene chains is due to the fact that the covalent bonds linking the

units together, the so-called backbone bonds, are non-collinear single bonds, each of whichmakes an angle of about 112 with the next, and that very little energy is required to rotate


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one part of the molecule with respect to another around one or more of these bonds. The

chains of other polymers may be much less flexible, because the backbone bonds need not be

single and may be collinear. A simple example is polyparaphenylene, for which all the

backbone bonds are collinear and also have a partial double-bond character, which makes

rotation more difficult.

Such chains are therefore rather stiff. It is these differences in stiffness, among other factors,

that give different types of polymer their different physical properties. The chemical

structures of the repeat units of some common polymers are shown in fig. 1.1, where for

simplicity of drawing the backbone bonds are shown as if they were collinear. The real

shapes of polymer molecules are considered elsewhere. Many polymers do not consist of

simple linear chains of the type so far considered; more complicated structures are introduced

in the following section.

Fig. 1.1 Structures of the repeating units of some common polymers.


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The classification of polymers

Polymers are classified in several ways: by how the molecules are synthesized, by their

molecular structure, by their chemical family, by their crystal structure, or by their

application.

Two other useful classifications are the following.

(i) Classifications based on structure: linear, branched or networkpolymers. A linearpolymer consists of spaghetti-like molecular chains. In a branched polymer, there

are primary polymer chains and secondary offshoots of smaller chains that stem

from these main chains. Note that even though we say linear, the chains areactually not in the form of straight lines. Figure 1.3 shows these types of polymer

schematically. It should be noted that the real structures are three-dimensional,

which is particularly important for networks. In recent years interest in more

complicated structures than those shown in fig. 1.2 has increased.

Fig. 1.2 Schematic representations of (a) a linear polymer, (b) a branched polymer and (c)

a network polymer. The symbol represents a cross-link point, i.e. a place where two chains

are chemically bonded together.

(ii) Classifications based on properties: A better method to describe polymers is in termsof their mechanical and thermal behavior e.g., (thermo) plastics, rubbers (elastomers)

or thermosets.

These two sets of classifications are, of course, closely related, since structure and properties

are intimately linked. A brief description of the types of polymer according to classification

(ii) will now be given.

The three major polymer catagories are; (1) Thermoplastics, (2) Thermosetting polymers,

and (3) Elastomers.

Thermoplastics

Distinction between two major subclasses of polymers is based on the type of bond between

adjacent polymer chains. It may be noted that in contrast to the monomer, the PE polymer

chain is saturated, so that there are no additional sites for primary bond formation. Thus, the

only mechanism that remains for bond formation between PE chains is secondary bond

formation.


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H H H H H H H H

C C C C C C C C

H H H H H H H H

Secondary bondsH H H H H H H H

C C C C C C C C

H H H H H H H H

Linear or branched polymers that form melts upon upon heating such as PE, are called

thermoplastic polymers. Thermoplasts soften when heated (and eventually liquefy) andharden when cooledprocesses that are totally reversible and may be repeated. In the moltenstate they consist of a tangled mass of molecules. On cooling they may form a glass (a sort of

frozen liquid) below a temperature called the glass transition temperature, Tg, or they maycrystallise. The glass transition will be considered later on. If they crystallize they do so only

partially, the rest remaining in a liquid-like state which is usually called amorphous, but

should preferably be called non-crystalline. These materials are normally fabricated by the

simultaneous application of heat and pressure. On a molecular level, as the temperature is

raised, secondary bonding forces are diminished (by increased molecular motion) so that the

relative movement of adjacent chains is facilitated when a stress is applied. Irreversible

degradation results when the temperature of a molten thermoplastic material is raised to the

point at which molecular vibration become violent enough to break the primary covalent

bonds. In addition, thermoplastics are relatively soft and ductile. Most linear polymers and

those having some branched structures with flexible chains are thermoplastic.

Thermosetting polymers

Thermosets are network polymers that are heavily cross-linked to give a dense three-

dimensional network.Thermosetting polymers become permanently hard when heat is applied

and do not soften upon subsequent heating. During the initial heat treatment, covalent

crosslinks are formed between adjacent molecular chain; these bonds anchor the chains

together to resist the vibrational and rotational chain motions at high temperatures.Crosslinkling is usually extensive, in that 10 to 50 % of the chain mer units are crosslinked.

Only heating to excessive temperature will cause severance of these crosslink bonds and

polymer degradation. In other words, thermosetting plastics formed into a permanent shape

and cured or set by a chemical reaction cannot be remelted and reformed into another shape.Thermosets polymers are generally harder, stronger, and more brittle, than thermoplastics,

and have better dimensional stability. The name thermoset arises because it was necessary to

first heat the polymers of this type in order for the cross-linking, or curing, to take place. The

term is now used to describe this type of material even when heat is not required for the

cross-linking to take place. Examples of thermosets are the epoxy resins, such as Araldites,

and the phenol- or urea-formaldehyde resins.


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Elastomers

Rubbers, or elastomers, are network polymers that are lightly crosslinked and they are

reversibly stretchable to high extensions (>200%). When unstretched they have fairly tightly

randomly coiled molecules that are stretched out reversibly by applying a force. This causes

the chains to be less random, so that the material has a lower entropy, and the retractive forceobserved is due to this lowering of the entropy. The cross-links prevent the molecules from

flowing past each other when the material is stretched. On cooling, rubbers become glassy or

crystallise (partially). On heating, they cannot melt in the conventional sense, i.e. they cannot

flow, because of the cross-links.

Classical polymerization processes

The chemistry of polymer moleculesThe structurally simplest polymers are synthetic, or man-made. As an example, consider the

linear polymer polyethylene, or PE, for which the monomer is C2H4 molecule that has the

following structure:

H H

C C H H

PE polymer chain is formed by opening the double bond between the C atoms in an

individual monomer and linking a series of monomers together to form the linear molecule.

An examination of bond energies associated with single and double covalent bonds between

carbon atoms shows that the breaking of one double bond and the formation of one single

bond (per monomer) result in a decrease in the free energy of the system. Thus, the formation

of a PE polymer chain from a collection of identical monomers is a thermodynamically

favored reaction.

Functionality of a monomer In order for a monomer to polymerize, it must have at

least two active chemical bonds. When a monomer has two active bonds, it can react with

two other monomers, and by repetition of the bonding, other monomers of the same type canform a long-chain or linear polymer. When a monomer has more than two active bonds,

polymerization can take place in more than two directions, and thus three dimensional

network molecules can be built up.

The number of active bonds a monomer has is called the functionality of the monomer. A

monomer which utilizes two active bonds for the polymerization of long chains is called

bifunctional. Thus ethylene is an example of a bifunctional monomer. A monomer which

utilizes three active bonds to form a network polymeric material is called trifunctional.

Phenol, C2H5OH, is an example of a trifunctional monomer and is used in the polymerization

of phenol and formaldehyde.


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Polymer Synthesis

In polymerisation, monomer units react to give polymer molecules. In the simplest examples

the chemical repeat unit contains the same group of atoms as the monomer (but differently

bonded),

e.g. ethylene polyethylene

n(CH2 CH2) (CH2CH2)n

More generally the repeat unit is not the same as the monomer or monomers but, as already

indicated, it is nevertheless sometimes called the monomer. Some of the simpler, classicalprocesses by which many of the bulk commercial polymers are made are described below.

These fall into two main types, addition polymerisation and step-growth polymerisation.

Addition Polymerization or Chain Growth Polymerization

The sequential addition of monomer units to a growing chain is a process that is easy tovisualize and is the mechanism for the production of an important class of polymers. For the

most common forms of this process to occur, the monomer must contain a double (or triple)

bond.

In chain-growth polymerization, the only chain-extension reaction is that of attachment of a

monomer to an active chain. The active end may be a free radical or an ionic site (i.e.,anion or cation).

Chain Polymerization Steps

It can be divided into three steps: (1) initiation, (2) propagation, and (3) termination.

Initiation In the initiation step an activated species, such as a free radical from an

initiator added to the system, attacks and opens the double bond of a molecule of the

monomer, producing a new activated species. Initiators are the source of free radicals. A free

radical can be defined as a group of atoms having an unpaired electron (free electron) which

can covalently bond to an unpaired electron of another molecule and usually denoted in its

chemical formula by a dot. Usually organic peroxides are used as free radical formers.

For example hydrogen peroxide, H2O2, can decompose into two free radicals, as shown

below

H O O H 2H O

Benzoyl peroxide is an another organic peroxide which is used to initiate some chain

polymerization reactions and decomposes into free radicals as illustrated below:

When the ethylene gas (monomer) is subjected catalytically to appropriate conditions of

temperature and pressure, one of the free radicals created by the decomposition of the organicperoxide can react with ethylene molecule to form a new longer-chain free radical (an active


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mer is formed by the reaction between an initiator or catalyst species (R) and the ethylene

mer unit). The double bond between the two carbon atoms is opened up, the doublecovalent bond is replaced by a single covalent bond as shown below

H H H H Free electron

R O

+ C C R O C C

H H H H

Free radical Ethylene Free radical

The organic free radical in this way acts as an initiator catalyst for the polymerization of

ethylene.

Propagation The process of extending the polymer chain by the successive addition

of monomer units is calledpropagation. The double bond at the end of the ethylene monomer

unit can be opened up by the extended free radical and be covalently bonded to it. Thus, thepolymer chain is further extended by the reaction

R CH2 CH2 + CH2CH2 R CH2 CH2 CH2 CH2The polymer chains in chain polymerization keep growing spontaneously because the energy

of the chemical system is lowered by the chain polymerization process. Although this process

may continue until thousands of monomer units have been added sequentially, it always

terminates when the chain is still of finite length.

Termination Termination can occur by the addition of a terminator free radical or

when two chains combine. Another possibility is that trace amounts of impurities may

terminate the polymer chain. Termination by coupling of two chains can be represented by

the reaction

R (CH2 CH2)m + R' (CH2 CH2)n R (CH2 CH2)m (CH2 CH2)nR'

The simplest type of addition reaction is the formation of polyethylene from ethylene

monomer:

(CH2)nCH2CH2* + CH2 CH2 (CH2) n+2CH2CH2*

There are basically three kinds of polyethylene produced commercially. The first to be

produced, low-density polyethylene, is made by a high pressure, high-temperature

uncatalysed reaction involving free radicals and has about 2030 branches per thousandcarbon atoms. A variety of branches can occur, including ethyl, CH2CH3, butyl, (CH2)3CH3, pentyl, (CH2)4CH3, hexyl, (CH2)5CH3 and longer units. High-density,polymers are made by the homopolymerization of ethylene or the copolymerization of

ethylene with a small amount of higher a-olefin. Two processes, the Phillips process and the

ZieglerNatta process, which differ according to the catalyst used, are of particularimportance. The emergence of a new generation of catalysts led to the appearance of linear

low-density polyethylenes. These have a higher level of co-monomer incorporation and have

a higher level of branching, up to that of low-density material, but the branches in any given

polymer are of one type only, which may be ethyl, butyl, isobutyl or hexyl. 1.3 The chemical


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nature of polymers 13 Polyethylene is a special example of a generic class that includes many

of the industrially important macromolecules, the vinyl and vinylidene polymers. The

chemical repeat unit of a vinylidene polymer is (CH2CXY), where X and Y representsingle atoms or chemical groups. For a vinyl polymer Y is H and for polyethylene both X and

Y are H. If X isCH3, Cl,CN,C6H5 orO(C O)CH3, whereC6H5 represents the

monosubstituted benzene ring, or phenyl group, and Y is H, the well-known materialspolypropylene, poly(vinyl chloride) (PVC), polyacrylonitrile, polystyrene and poly(vinyl

acetate), respectively, are obtained. When Y is not H, X and Y may be the same type of atom

or group, as with poly(vinylidene chloride) (X and Y are Cl), or they may differ, as in poly-

(methyl methacrylate) (X is CH3, Y is COOCH3) and poly(-methyl styrene) (X isCH3, Y is C6H5. When the substituents are small, polymerization of a tetra-substitutedmonomer is possible, to produce a polymer such as polytetrafluoroethylene (PTFE), with the

repeat unit(CF2CF2), but if large substituents are present on both carbon atoms of thedouble bond there is usually steric hindrance to polymerisation, i.e. the substituents would

overlap each other if polymerisation took place. Polydienes are a second important group

within the class of addition polymers. The monomers have two double bonds and one of these

is retained in the polymeric structure, to give one double bond per chemical repeat unit of thechain. This bond may be in the backbone of the chain or in a side group. If it is always in a

side group the polymer is of the vinyl or vinylidene type. The two most important examples

of polydienes are polybutadiene, containing 1,4 - linked units of type

(CH2CH CHCH2)or 1,2-linked vinyl units of type(CH2CH(CH CH2) ), and polyisoprene, containing corresponding units of type (CH2C)CH3)CHCH2)or (CH2C(CH3)(CHCH2) )Polymers containing both 1,2 and 1,4 types of unit arenot uncommon, but special conditions may lead to polymers consisting largely of one type.

Acetylene, CH CH, polymerises by an analogous reaction in which the triple bond isconverted into a double bond to give the chemical repeat unit(CH CH).

Ring-opening polymerisations, such as those in which cyclic ethers polymerise to give

polyethers, may also be considered to be addition polymerisations:

nCH2(CH2)m-1O (CH2)mO)n

The simplest type of polyether, polyoxymethylene, is obtained by the similar polymerisation

of formaldehyde in the presence of water:

nCH2 O (CH2O)n

Step Growth Polymerization

Consider the following simple organic molecules:

ROH RNH2 RCOH

O

Alcohol Amine Acid

R is used to indicate an organic root (eg, CH3, C2H5 etc.). OH,NH2 & COOH arefunctional groups. These functional groups can react with each other forming water and a

linkage. The formation of an amide and an ester is shown below. Note that water is a by-

product of both reactions. These types of reactions are called condensation reactions.


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Fig. 1.4 Fig. 1.5

However these reactions would not form polymers because in these reactions each reactant

has only one functional group. If each reactant has two functional groups, then it is possible

to form a polymer.

In stepwise polymerization, monomers chemically react with each other to produce linear

polymers. The reactivity of the functional groups at the end of a monomer in stepwise

polymerization is usually assumed to be about the same for a polymer of any size. Thus

monomer units can react with each other or with produced polymers of any size. In manystepwise polymerization reactions a small molecule is produced as a byproduct, so these

types of reactions are sometimes called condensation polymerization reaction.An example of stepwise polymerization reaction is the reaction of hexamethylene diamine

with adipic acid to produce nylon 6,6 and water as a by-product, as shown in the figure

below:

Fig.1.6 Two reactants that could form a polyamide

Fig. 1.7 The reaction of a difunctional alcohol and a difunctional amine


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Fig. 1.8 Formation of a poloyamide

This reaction is very similar to the one shown in Fig. 1.4 & 1.5. The amine functional group

(NH2) and the acid functional group (COOH) will react and form an amide linkage NHCOand water. The reaction will not cease in this case. There is no possibility that oneand only one HOOC(CH2)6COOH molecule reacted with one and only one

H2N(CH2)NH2 molecule. Therefore, more than one of the product molecules formed. The

product molecule has an amine functional group (NH2) and an acid group (COOH). These

can react to form an amide linkageNHCOand water. The reaction will continue, and amolecule of n units enclosed in [ ] is called a mer, and because the molecule has manymers, it is called a polymer.

In the labeling of these nylons the first number is the number of carbon atoms in the amineresidue and the second the number of carbon atoms in the acid residue. Two nylons of

somewhat simpler structure, nylon-6 and nylon-11, are obtained, respectively, from the ring-

opening polymerisation of the cyclic compound e-caprolactam: nOC(CH2)5NH (OC(CH2)5NH)n and from the self-condensation of -amino-undecanoic acid:nHOOC(CH2)10NH2 (OC(CH2)10NH)n + nH2O

The most important polyester is poly(ethylene terephthalate), ( (CH2)2OOC C6H5COO)n, which is made by the condensation of ethylene glycol, HO(CH2)2OH, andterephthalic acid, HOOC C6H5COOH, or dimethyl terephthalate, CH3OOCC6H5COOCH3, where C6H5 represents the para-disubstituted benzene ring, or pphenylenegroup. There is also a large group of unsaturated polyesters that are structurally very complex

because they are made by multicomponent condensation reactions, e.g. a mixture of ethylene


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glycol and propylene glycol, CH3CH(OH)CH2OH, with maleic and phthalic anhydrides (see

fig. 1.9).

Fig. 1.9 The chemical formulae of (a) maleic anhydride and (b) phthalic anhydride.

An important example of a reaction employed in step-growth polymerization that does not

involve the elimination of a small molecule is the reaction of an isocyanate and an alcohol

which produces the urethane linkage

RNCO) HOR ! RNHCOOR0

One of the most complex types of step-growth reaction is that between a di-glycol, HOROH,

and a di-isocyanate, OCNRNCO, to produce a polyurethane, which contains thestructural unitORO(CO)(NH)R(NH)(C O).

Several subsidiary reactions can also take place and, although all of the possible reaction

products are unlikely to be present simultaneously, polyurethanes usually have complex

structures. Thermoplastic polyurethanes are copolymers that usually incorporate sequences of

polyester or polyether segments.

Formaldehyde, H2CO, provides a very reactive building block for step-growth reactions.

For example in polycondensation reactions with phenol,OH, or its homologues with morethan one OH group, it yields the phenolic resins, whereas with urea, O C(NH2)2, ormelamine [see fig. 1.6 (a)] it yields the amino resins. The products of such condensation

reactions depend on the conditions employed but they are usually highly cross-linked. Acid

conditions lead to the formation of methylene bridged polymers of the type shown in figs.

1.6(b) and (c), whereas alkaline conditions give structures containing the methylol group,CH2OH, which may condense further to give structures containing ether bridges, of the form

ROR (fig. 1.6(d)).

Fig. 1.6 The chemical formulae of (a) Melamine; and (b), (c), and (d) various

bridging structures in phenolic resins


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Newer polymers and polymerisation processes

The polymerisation processes described in the previous section are the classical processes

used for producing the bulk commercial polymers. Newer processes have been and are being

developed with a variety of aims in mind. These involve the production of novel polymer

topologies

(see box); precise control over chain length and over monomer sequences.

Degree of polymerization The general reaction for the chain polymerization of ethylene

monomer into polyethylene may be written as

The repeating subunit in polymer chain is called a mer. The mer for polyethylene is

[CH2 CH2]

and is indicated in the above equation. The n in the equation is known as the degree ofpolymerization (DP) of the polymer chain and is equal to the number of subunits or mers in

the polymer molecular chain. The average DP for polyethylene ranges from about 3500 to

25,000, corresponding to average molecular masses ranging from about 100,000 to 70,000

g/mol.

Average Molecular weight for polymers

Let's think about a small molecule, say, hexane. Hexane has a molecular weight of 86. Every

hexane molecule has a molecular weight of 86. Now if we add another carbon to our chain,

and the appropriate amount of hydrogen atoms, we've increased our molecular weight to 100.


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That's fine, but the molecule is no longer hexane. It's heptane! If we have a mixture of some

molecules of hexane and some of heptane, the mixture won't act like pure heptane, nor will it

act like pure hexane. The properties of the mixture, say, its boiling point, vapor pressure, etc.,

will be neither those of pure hexane nor pure heptane.

But polymers are different. Imagine polyethylene. If we have a sample of polyethylene, andsome of the chains have fifty thousand carbon atoms in them, and others have fifty thousand

and two carbon atoms in them, this little difference isn't going to amount to anything. If you

really want to know the truth, one almost never finds a sample of a synthetic polymer in

which all the chains have the same molecular weight. Instead, we usually have a bell curve, a

distribution of molecular weights. Some of the polymer chains will be much larger than all

the others, at the high end of the curve. Some will be much smaller, and at the low end of the

curve. The largest number will usually be clumped around a central point, the highest point

on the curve.

So we have to talk about average molecular weights when we talk about polymers. And we're

not going to stop there. The average can be calculated in different ways, and each way has itsown value. So let's talk about some of these averages, why don't we?

The Number Average Molecular Weight,Mn

The number average molecular weight is not too difficult to understand. It is just the total

weight of all the polymer molecules in a sample, divided by the total number of polymer

molecules in a sample.

_

Mn

= NiM

i/N

i

_

or in terms of mole fraction xi, Mn = xi Mi

where xi is the mole fraction of molecules of molar mass MI and is given by the ratio of Ni to

the total number of molecules.

The Weight Average Molecular Weight,Mw

The weight average is a little more complicated. It's based on the fact that a bigger molecule

contains more of the total mass of the polymer sample than the smaller molecules do.

The weight average molecular weightcan be shown mathematically as:

_

Mw = wi Mi /wi = Ni Mi2

/Ni Mi where wi = Ni Mi

Or in terms of weight fraction fi, the weight average molecular weight of the polymer is

described as the sum of the weight fractions times their mean molecular weight for each

particular range divided by the sum of weight fractions. Thus it is written as:

_Mw = fiMi ( fi = Ni Mi /Ni Mi )


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where _

Mw = average molecular weight for a polymer

Mi = mean molecular weight for each particular molecular weight range

selected

fi = weight fraction of the material having molecular weight of a selectedmolecular

weight range

The average molecular weight can be determined by the measurement of various physical

properties such as viscosity and osmotic pressure. One method commonly used for this

analysis is to determine the weight fractions of molecular weight ranges.

Example Problem

Calculate the degree of polymerization in a sample of nylon 6,6 having a molecular weight of

120,000 g / mol.

H H O

[N(CH2)6NC(CH2)4C]

O

(nylon mer)

Mol. Wt. of repeat unit or 1 mer = 2 x 14 + 22 x 1 + 12 x 12 + 2 x 16 = 226 g / mol

DP = 120,000 / 226 = 531 ( Note that chain contains 531adipic acid and 531 HMDA

molecules).


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Example Problem

Consider a sample of polypropylene, that is composed of only three types of chains. 60 % of

the chains in this sample have a degree of polymerization (n) of 10,000, 30 % of the chains

have n = 15,000, and 10 % of the chains have n = 100,000. Calculate the polydispersity for

this sample.

Solution:First we must calculate the weight of a single PP mer (m), then we calculate the molecular

weight each type of chain (Mi). Next we determine the two measures of average molecular

weight (Mn and Mw), and finally we can determine the polydispersity of the sample.

PP mer is [CH2CH]CH3

m(PP) = [ 3 x 12 + 6 x 1] = 42 g /mol / mer

No. of

chains

( Ni )

DP Mol.wt of

each type of

chain (Mi)= DP x Mmer

NiMi

(wi)

fi

= wi/ NiMi

fi x Mi

60 10,000 420,000 252 x 105

252 x 105

/ 861 x

105

= 0.2926

0.2926 x 420,000

= 122,892

30 15,000 630,000 189 x 105

189 x 105

/ 861 x

105

= 0.2195

0.2195 x 630,000

= 138,285

10 100,000 4,200,000 420 x 105

420 x 105

/ 861 x

105

= 0.4878

0.4878 x

4,200,000 =

2,048,760

Ni

= 100

NiMi

= 861 x

105

2,309,937

Mn = NiMi/ Ni = 861 x 105 / 100 = 861,000 g /mol

Mw = fi Mi = 2,309,937 g/mol & PD. = Mw / Mn = 2309937 / 861000 =2.68

Assignment Problem:

Following data was obtained for a Polyvinyl Chloride (PVC) sample :No. of chains or

polymer molecules

Mol. Weight range (g / mol)

1000 5,00010,0004000 10,00015,0005500 15,00020,0006000 20,00025,0006500 25,00030,0002000 30,00035,000

For this material compute (a) the number average degree of polymerization & (b)polydispersity.

Lecture No.01 Polymer Engineering

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Transcript of Lecture No.01 Polymer Engineering