Lecture 5

Question 1

What are the kinetics of Step polymerization?

Answer 1

Two cases:

Case one: ignoring the elimination of product

Case two: without ignoring the condensation product

Check written notes pt.1

Analysis:

Equations 1 and 2 have been derived assuming that the reverse reaction (i.e. depolymerisation) is negligible. This is satisfactory for many polyadditions, but for reversible polycondensation, it requires the elimination product to be removed continuously as it is formed. The equations have been verified experimentally using step polymerizations that satisfy this requirement, as is shown by the polyesterification data plotted in Figure 3.2 (shown in digital notes). These results further substantiate the validity of the principle of equal reactivity of functional groups.

Question 2

Ring formation

Answer 2

A complication not yet considered is the intramolecular reaction of terminal functional groups on the same molecule. This results in the formation of cyclic molecules (i.e. rings), e.g. in the preparation of a polyester.

Question 3

What does ring formation depend on

Answer 3

The ease of ring formation depends strongly upon the number of atoms linked together in the ring. For example, 5-, 6- and, to a lesser extent, 7-membered rings are stable and often form in preference to linear polymer. For the self-condensation of ω-hydroxy carboxylic acids HO—(CH2)i—CO2H when i=3 only the monomeric lactone is produced. When i=4, some polymer is produced in addition to the corresponding monomeric lactone, and
when i=5, the product is a mixture of polymer with some of the monomeric lactone.

Normally, 3- and 4-membered rings and 8- to 11-membered rings are unstable due to bond-angle strain and steric repulsions between atoms crowded into the centre of the ring, respectively, and usually are not formed. Whilst 12-membered and larger rings are more stable and can form, their probability of formation decreases as the ring size increases. This is because the probability of the two ends of a single
chain meeting decreases as their separation (i.e. the chain length) increases. Thus large rings rarely form.

Question 4

What is the problem of ring formation and molar mass distribution?

Answer 4

Ring formation disturbs the form of the molar mass distribution and reduces the ultimate molar mass. However, since linear polymerization is a bimolecular process and ring formation is a unimolecular process, it is possible to greatly promote the former process relative to the latter by using high monomer concentrations. This is why many step polymerizations are performed in bulk (i.e. using only monomer(s) plus catalysts in the absence of a solvent).

Question 5

What are the limitations that arise when using solvents in step polymerisations

Answer 5

Although step polymerizations can be carried out in a solvent that dissolves the monomers and the polymer to be produced, finding suitable solvents can be difficult because the polymers often are
semi-crystalline and of low solubility. The isolation of the polymer from the solvent also can prove difficult. Hence, most step polymerizations are performed by reacting liquid monomers together in the absence of a solvent.

Question 6

Linear step polymerization process

Answer 6

The preceding Flash cards highlight the many constraints upon the formation of high molar mass polymers by linear step polymerization.

Special polymerization systems often have to be developed to overcome these constraints and are exemplified below by systems developed for the preparation of polyesters and polyamides.

Question 7

The process of ester esterification

Answer 7

Ester interchange (or transesterification) reactions commonly are employed in the production of polyesters, the most important example being the preparation of poly(ethylene terephthalate). The
direct polyesterification reaction of terephthalic acid with ethylene glycol indicated is complicated by the high melting point of terephthalic acid (in fact it sublimes at 300 °C before melting) and its low solubility. Thus poly(ethylene terephthalate) is prepared in a two-stage process.

The first stage involves the formation of bis(2-hydroxyethyl)terephthalate either by

i) the reaction of dimethylterephthalate with an excess of ethylene glycol (i.e. via ester interchange): Shown in digital notes

ii) direct esterification of terephthalic acid with an excess of ethylene glycol (more common nowadays): Shown in digital notes.

The methanol or water produced during these first-stage reactions is removed as it is formed.

On completion of the first stage, the reaction temperature is raised to about 277 °C so that the excess ethylene glycol and the ethylene glycol produced by further ester interchange reactions can be removed, and so that the polymer is formed above its melting temperature (265 °C): Shown in written notes

Question 8

The process of preparing aliphatic polyamides from diamines and diacids?

Answer 8

The preferred method for preparing aliphatic polyamides from diamines and diacids is melt polymerization of the corresponding nylon salt. For example, in the preparation of nylon 6.6, hexamethylene diamine and adipic acid are first reacted together at low temperature to form hexamethylene diammonium adipate (nylon 6.6 salt) which then is purified by recrystallization. The salt is heated gradually up to about 277 °C to effect melt polymerization and maintained at this temperature whilst removing the water produced as steam.

This is shown in the digital notes!

A major advantage of melt polymerization by salt dehydration is that the use of pure salt guarantees exact 1:1 stoichiometry.

Question 9

The process for preparation of polyesters and polyamides?

Answer 9

A convenient method for preparation of polyesters and polyamides in the laboratory is the reaction of diacid chlorides with diols and diamines, respectively (i.e. Schotten–Baumann reactions).

These reactions proceed rapidly at low temperatures and often are performed as interfacial polymerizations in which the two reactants are dissolved separately in immiscible solvents which are then
brought into contact.

The best-known example of this is the ‘nylon rope trick’ where a continuous film of nylon is drawn from the interface as illustrated in Figure 3.3 (shown in digital notes). For example, the preparation of nylon 6.10 would proceed by the following reaction (Shown in digital notes).

The reaction takes place at the organic solvent side of the interface and, because it usually is diffusion-controlled, there is no need for strict control of stoichiometry

Question 10

The other process

Answer 10

The schematics he showed in the lecture slides for the processes already described are shown below.

Question 11

What is gel point? (network polymers)

Answer 11

The inclusion of a monomer with a functionality greater than two has a dramatic effect on the structure and molar mass of the polymer formed. In the early stages of such reactions, the polymer has a branched structure and, consequently, increases in molar mass much more rapidly with the extent of reaction than for a linear step polymerization. As the reaction proceeds, further branching
reactions lead to hyper-branching which lead ultimately to the formation of complex network structures which have properties. that are quite different from those of the corresponding linear polymer.

The point at which the first network molecule is formed is known as the gel point because it is manifested by gelation, that is, an abrupt change of the reacting mixture from a viscous liquid to a solid gel which shows no tendency to flow.

Question 12

Network polymerization

Answer 12

Network polymers produced by step polymerizations were amongst the first types of synthetic polymers to be commercialized and often are termed resins. The polymers are completely intractable and so at the stage when the network chains are generated, the polymerizations must be carried out
within a mould to produce the required artefact.

Question 13

What are formaldeyde-based resins?

Answer 13

Formaldehyde-based resins were the first network polymers prepared by step polymerization to be commercialized. They are prepared in two stages. The first involves the formation of a prepolymer of low molar mass which may either be a liquid or a solid. In the second stage,
the prepolymer is forced to flow under pressure to fill a heated mould in which further reaction takes place to yield a highly crosslinked, rigid polymer in the shape of the mould. Since formaldehyde is difunctional, in order to form a network polymer the co-reactants must have a
functionality f greater than two; those most commonly employed are phenol (f = 3) to form phenol-formaldehyde, urea (f = 4) to form urea-formaldehyde and melamine (f = 6) to form melamine-formaldehyde

Question 14

Phenol-formaldehyde?

Answer 14

The hydroxyl group in phenol activates the benzene ring towards substitution in the 2-, 4- and 6-positions. Upon reaction of phenol with formaldehyde, methylol substituent groups are formed (this is shwon in digital notes).

Further reaction leads principally to the formation of methylene bridges but also to dimethylene ether links (this is shown digtal notes)

Question 15

What are two types of phenol-formaldehyde?

Answer 15

1. resoles
2. Novolaks

Question 16

What are resoles?

Answer 16

Those prepared using an excess of formaldehyde with base catalysis. The resole prepolymers possess many unreacted methylol groups that upon further heating react to produce the network structure

Question 17

What are novolaks?

Answer 17

prepared using an excess of phenol and acid catalysis, which promotes condensation reactions of the methylol groups. Thus the prepolymers produced contain no methylol groups and are unable to crosslink (this is shown in notes).

Normally, they are dried and ground to a powder, then compounded (i.e. mixed) with fillers (e.g. mica, glass fibres, sawdust), colourants and hardeners. Hexamethylenetetramine, with magnesium or calcium oxide as a catalyst, usually is employed as the hardener to activate curing (i.e. crosslinking) when the compound is converted into an artefact by heating in a mould. Most of the
crosslinks formed are methylene bridges, though some dimethylene amine (–CH2–NH–CH2–) links are formed. The fillers are added to reduce the cost and to improve the electrical or mechanical properties of the resin

Question 18

Urea-formaldehyde and melamine-formaldehyde?

Answer 18

The chemistry of urea–formaldehyde and melamine–formaldehyde resins involves the formation and condensation reactions of N-methylol groups (This is shown in notes).

The reactions usually are arrested at the prepolymer stage by adjusting the pH of the reacting mixture to slightly alkaline. After blending (e.g. with fillers, pigments, hardeners, etc.) the prepolymers are cured by heating in a mould. The hardeners are compounds (e.g. ammonium sulphamate)
which decompose at mould temperatures to give acids that catalyse further condensation reactions.

Question 19

Epoxy Resins

Answer 19

Epoxy resins are low molar mass prepolymers containing epoxide end-groups. The most important are the diglycidyl ether prepolymers prepared by the reaction of excess epichlorohydrin with
bisphenol-A in the presence of a base (Shown in notes)

These prepolymers are either viscous liquids or solids depending upon the number of monomers. Usually,
they are cured by the use of multifunctional amines which undergo a polyaddition reaction with the terminal epoxide groups in the manner showned in notes.

Together, the amine R group and epoxy resin chain length control the mechanical properties of the fully-cured resin. Some examples of polyfunctional amines used to cure epoxy resins are shown in notes

Epoxy resins are characterized by low shrinkage on curing and find use as adhesives, electrical insulators, surface coatings and matrix materials for fibre-reinforced composites.

Question 20

Network Polyurethanes

Answer 20

Polyurethane networks find a wide variety of uses (e.g. elastomers, flexible foams and rigid foams) and usually are prepared by the reaction of diisocyanates with polyols, which are branched polyether (or, less commonly, polyester) prepolymers that have hydroxyl end-groups.

Commercial poly(propylene oxide) (structure is shown in notesO polylols often have terminal ethylene oxide units (i.e. –O–CH2–CH2–OH) (see Section 7.3.1) to increase reactivity (i.e. primary –CH2OH groups are more reactive than the secondary –CH(CH3)OH groups).

The molar mass and functionality of the prepolymer determine the crosslink density and hence the flexibility of the network formed. Typically, polyether polyols have a functionality of 3–6 and those with Mn of up to about 1 kg mol^−1 are used to prepare rigid polyurethanes, whereas flexible polyurethanes are prepared from those with Mn of about 2–8 kg mol^−1.

Question 21

How are polyurethanes foams made?

Answer 21

Polyurethane foams can be formed by inclusion of a small amount of water, which reacts rapidly with the isocyanate groups to give an unstable carbamic acid that instantly decomposes to produce
an amine end-group and carbon dioxide gas, which causes foaming of the polyurethane as it is formed. The amine end-group is extremely reactive towards isocyanate groups, so reacts immediately to
form a urea link. (Both reactions are depicted in notes)

Polyurethane foams can also be produced by inclusion of compounds that vaporize due to the heat released by the exothermic reaction of isocyanates groups with hydroxyl groups.

Question 22

Geletation theory

Answer 22

Three-dimensionally crosslinked polymers are incapable of macroscopic viscous flow because, at the molecular level, the crosslinks prevent the network chains from flowing past one another. When the first network molecule forms in a non-linear polymerization, it encompasses the whole reactant mixture which instantly becomes immobilized; this corresponds to the gel point, which clearly is a very important stage in a network-forming polymerization. Much effort has been devoted to prediction of the extent of reaction at the gel point.

Here, we introduce two simple theories for the gel point in non-linear step polymerizations:

i) Carothers Theory of Gelation

ii) Statistical Theory of Gelation

Question 23

Carothers Theory of Gelation

Answer 23

Check written notes pt 2

Final note:

It is possible to extend the theory to prediction of pc when there is an imbalance of stoichiometry. However, this simple method of analysis will not be pursued further here because it is rather inelegant and always yields overestimates of pc.

The approach is fundamentally flawed because it is based upon x¯n, an average quantity, tending to infinity. Molecules with degrees of polymerization both larger and smaller than x¯n are present, and it is the largest molecules that undergo gelation first.

Answer 24

The basic statistical theory of gelation was first derived by Flory who considered the reaction of an f-functional monomer RAf
(f >2) with the difunctional monomers RA2 and RB2. It is necessary to
define a parameter called the branching coefficient, α, which is the probability that an f-functional
unit is connected via a chain of difunctional units to another f-functional unit.

In other words α is the probability that the general sequence of linkages shown in the written notes

In order to derive an expression for α from statistical considerations it is necessary to introduce another term, γ, which is defined as the initial ratio of A groups from RAf
molecules to the total number of A groups. Using γ, it is possible to calculate the probabilities for the existence of each of
the linkages in the general sequence given in the written notes. The probabilites are shown in notes.

Network molecules can form when n chains are expected to lead to more than n chains through branching of some of them. The maximum number of chains that can emanate from the end of a single chain, such as that analysed above, is (f−1) and so the probable number of chains emanating
from the chain end is α(f−1). Network molecules can form if this probability is not less than one, i.e. α(f−1) ≥1. Thus the critical branching coefficient αc for the onset of gelation is given by ac = 1/(f-1)

If the reactant ratio r is defined as the initial ratio of A groups to B groups then pB =rpA and:

(Pa)c = [ r+r y (f-2) ] ^-1/2

(Pb)c = r^1/2 [1+ y(f-2)]^-1/2

When RA2 molecules are absent (i.e. in a RAf+RB2 polymerization), γ=1 and (PaPb)c= 1/(f−1), in which case (PaPb)c=αc.

Question 25

The validity of the Cathores and Statistical theories

Answer 25

Figure 3.4 shows the variation of p, x¯n and
viscosity, η, with time for a reaction. In this reaction gelation occurred after about 238 min and was manifested by η becoming infinite. The observed extent of reaction at gelation was 0.894 when x¯n was
only about 25 (i.e. well below the value of infinity assumed in the Carothers theory of gelation), but the statistical theory also is inaccurate and predicts (pApB)c=0.844.

In a similar polymerization carried out using r=1.000 and γ=0.194, the gel point occurred at p=0.939 which may be compared to the prediction of pc=0.968 from the Carothers Equation. which (as expected) is high, whereas Statistical gives a value of 0.915, which again is lower than observed.

The statistical theory always underestimates pc because it does not take into account the effect of intramolecular reactions between end groups. These give rise to loops in the polymer structure and the polymerization must proceed to higher extents of reaction in order to overcome this wastage of functional groups.
When the effects of intramolecular reaction are eliminated the statistical theory gives accurate predictions of the gel point.

The theories of gelation presented here can be applied only when it is clear that the assumption of
equal reactivity of functional groups is satisfactory. In terms of the polymerizations described earlier, the theories generally are applicable to the formation of polyester and polyurethane networks, but not to the formation of formaldehyde-based resins and epoxy resins. Failure of the principle of equal reactivity for the latter systems results from modification of the reactivity of a particular functional group by reaction of another functional group in the same molecule of monomer.