2 Step-Growth Polymerization
2.14 COMPARISON WITH EXPERIMENT
The gel point in a branching system is usually detected by a rapid increase in viscosity η, indicated by the inability of bubbles to rise in the medium. It is also characterized by a rapid increase in x. The values of these quantities for the reaction of diethylene glycol + succinic acid + 1,2,3-propanetricarboxylic acid are shown in Figure 2.5.
The increase in xn is not as dramatic as xw, which can be identified with the η curve.
The divergence of xw and xn is illustrated in Table 2.2 for the preceding system when the reaction mixture has been adjusted hypothetically to provide a ratio of carboxyl to amine groups of 1. This situation can be achieved by assuming that the mixture contains 98.5 mol of diacid A, 100 mol of diol B, and 1 mol of triacid C. From Equation 2.21, it follows that r = 98.5 × 2 + (1 × 3)/(2 × 100) = 1. These reaction conditions lead to the appearance of a gel point at pG= 0.9925, and the ratio (xw/xn) increases sharply as the reaction approaches the critical point. The distribution is readily compared with that for a totally bifunctional system for which (xw/xn) = 1 + p, and the broadening of the molar-mass distribution, characteristic of these branch-ing polymerizations, is well illustrated.
A comparison of experimental and theoretical values of pG has been reported by Flory for a mixture of a tricarboxylic acid with a diol and a diacid; the results are given in Table 2.3.
The statistical equation underestimates pG whereas Equation 2.24 overestimates the experimental value. The Carothers equation leads to a high pG because molecules larger than the observed xn exist in the mixture, and these undergo gelation before the predicted value is attained. This difficulty is overcome in the statistical treatment,
ζG=1/(f−1),
A A A +
A A
B B +
pG= +
[
r rρ(f −2)]
−1 2/ .9813_C002.fm Page 44 Friday, June 15, 2007 10:48 AM
Step-Growth Polymerization 45
but now differences are attributable to intramolecular cyclization in the system, and the loops that are formed are nonproductive in a branching sense. This means that the reaction must proceed further to overcome waste.
FIGURE 2.5 Variation of the viscosity η and the degree of polymerization xn with the extent of network polymer formation in the system diethylene glycol + succinic acid + 1,2,3-propanetricarboxylic acid. (Data from Flory.)
TABLE 2.2
Branching System with pG = 0.9925
P xw xw/xn
0.100 1.2 1.1
0.500 3.0 1.5
0.700 5.8 1.7
0.900 20.4 2.0
0.950 45.6 2.2
0.980 153.8 2.7
0.990 747.2 5.6
0.992 3306.8 18.2
TABLE 2.3
1,2,3-Propanetricarboxylic Acid, Diethylene Glycol, and Adipic Acid or Succinic Acid System
pG
R ρ Exponent Equation 2.24 Equation 2.26
0.800 0.375 0.991 1.063 0.955
1.000 0.293 0.911 0.951 0.879
1.002 0.404 0.894 0.933 0.843
0 0.2 0.4 0.6 0.8
50 100 150 200
4 12 20 28 36 p
xn η, xn
p
Gel point
η 9813_C002.fm Page 45 Friday, June 15, 2007 10:48 AM
46 Polymers: Chemistry and Physics of Modern Materials
2.15 POLYURETHANES
An important and versatile family of polymers, whose diverse uses include foams, fibers, elastomers, adhesives, and coatings, is formed by the interaction of diisocy-anates with diols.
This leads to the production of linear polymers, although branched or cross-linked structures can also be prepared by using multifunctional starting materials or, inadvertently, through side reactions. The nature and stiffness of the groups R and R1 will control the type of material formed and its rigidity or flexibility. This, in turn, will control the properties, and ultimately, the use of the polyurethanes formed.
The basic chain-growth reaction is addition without elimination of a small molecule and is a consequence of the highly electrophilic nature of the carbon atom in the isocyanate group.
This makes it susceptible to attack by nucleophilic reagents, such as alcohols, acids, water, amines, and mercaptans. The electrophilicity of the carbon atom can be increased if R is an aromatic ring which can conjugate with the isocyanate group.
Thus, aromatic diisocyanates are more reactive than aliphatic ones.
Isocyanate groups may not all have equal reactivity, for example, in 1-methyl-2,4-diisocyanatobenzene
the isocyanate group nearest the methyl group has a different reactivity from the other; also when one isocyanate group is reacted, the susceptibility of the second to a reaction may be altered.
Although it is expected that difunctional monomers will give a linear polyure-thane, the polymerization reaction is subject to possible side reactions. The formation of allophanate groups can occur, particularly if reaction temperatures exceed 400 K.
Here, an isocyanate group adds onto the secondary amine in the urethane link, and a branched or cross-linked structure is formed.
OCN R NCO HO R1 OH O R1 O C O
N R H
N C H O
+ n
R N C O H O R1
R N C O
H O R1
R N C O R1 H O +
CH3 NCO
NCO 9813_C002.fm Page 46 Friday, June 15, 2007 10:48 AM
Step-Growth Polymerization 47
Polyurethanes are often prepared in two stages: first, the production of a prepolymer and, second, a chain extension reaction. During the first step, diisocyanate is reacted with a dihydroxy-terminated short-chain polyether or polyester, such as poly(ethylene adipate), poly(ε-caprolactone), or poly(tetramethylene glycol) of approximate molar mass 1000–3000. Throughout this stage, the diisocyanate is used in excess to give isocyanate end-capped blocks. These are then chain-extended by subsequent reaction with a short-chain diol (e.g., ethylene glycol or 1,4-butane diol) or a diamine (see Table 2.4). The reaction with the diamine gives a urea linkage and a poly(urethane-co-urea) structure, which can also react with other (NCO) groups leading to biuret formation.
Cross-linked systems can also be obtained by the use of multifunctional mono-mers. In the polyurethanes such as those illustrated in Table 2.4 and Figure 2.6, the isocyanate monomer unit is regarded as the “hard” segment, and the polyol forms the “soft” segment. The structures shown are particularly useful in biomedical research and have been demonstrated to be suitable for cardiovascular applications.
A major use of polyurethanes is in the manufacture of foams, both rigid and flexible.
The chain-extension reactions described previously are normally used when elastomeric-type products are required, but for foams, the chain-extender molecule can be omitted and polyols with an average functionality in excess of three are used. The reaction is base-catalyzed by tertiary amines or organo tin compounds (e.g., stannous octanoate) and must also include a “blowing” agent in the reaction mixture. This can be achieved by adding controlled quantities of water to the system and making use of the reaction:
where water reacts with an isocyanate group to form the unstable carbamic acid, which decomposes to produce an amine with evolution of CO2. The released gas forms spherical bubbles, which increase in size, and eventually impinge on one
R N C O R
9813_C002.fm Page 47 Friday, June 15, 2007 10:48 AM
48 Polymers: Chemistry and Physics of Modern Materials
another to form a polyhedral cell structure in the polymer matrix. A volatile liquid can be used as an alternative “blowing” agent, and Freon (CFCl3) with a boiling point of 294 K can be included in the reaction mixture. As the polymerization is exothermic, liberating about 80 kJ mol−1, the heat is sufficient to vaporize the CFCl3 and create the foam. Use of these chlorofluorocarbon compounds is now discouraged on environmental grounds as they are believed to attack and destroy the ozone layer.
TABLE 2.4
Formation of (a) Aromatic Polyurethane, Pellethane, (b) Aromatic Polyurethane Biomer, and (c) Aliphatic Polyurethane Tecoflex
(a)
Dicyclohexylmethanediisocyanate Poly(tetramethylene glycol) 1,4-Butanediol
H H
+ 9813_C002.fm Page 48 Friday, June 15, 2007 10:48 AM
Step-Growth Polymerization 49
If a flexible foam is required, then longer, more flexible polyols and trifunctional cross-linking monomers are used, whereas higher-cross-link densities and short-chain polyols tend to form more rigid foams.
In the absence of a blowing agent and with conditions favoring the formation of linear chains, thermoplastic polyurethane elastomers can be formed. Materials with different properties can be obtained by altering the ratio of hard to soft blocks, and it is also observed that, in many cases, the hard segments can crystallize. This can give rise to phase-separated structures, shown schematically in Figure 2.6, which behave as thermoplastic elastomers (see also Section 15.6).
2.16 THERMOSETTING POLYMERS
The production of highly branched network polymers is commercially important, but as cross-linking results in a tough and highly intractable material, the fabrication process is usually carried out in two stages.
The first stage is the production of an incompletely reacted prepolymer; this is either solid or liquid and of moderately low-molar mass. The second stage involves conversion of this into the final cross-linked product in situ (i.e., a mold or form of some descrip-tion). The prepolymers are either random or structoset and are discussed separately:
Phenol-formaldehyde: Random prepolymers are prepared by reacting phenol (f = 3 for the ortho and para positions in the ring) with bifunctional formal-dehyde. The base-catalyzed reaction produces a mixture of methylol phenols.
FIGURE 2.6 Schematic representation of a polyurethane, with hard blocks shown as the bold lines and soft blocks as the thin lines, phase separating in the solid state and undergoing disordering on heating. (Adapted from Pearson, R.G., in Speciality Polymers, Dyson, R.W.
(Ed.), Blackie, 1987.)
Heating Cooling
OH HCHO
OH CH2OH
OH
CH2OH CH2
OH CH2
OH
CH2 OH
CH2OH
CH2OH
OH CH2OH
CH2OH HOH2C
+
+ +
9813_C002.fm Page 49 Friday, June 15, 2007 10:48 AM
50 Polymers: Chemistry and Physics of Modern Materials
The composition of the mixture can be varied by altering the phenol to formaldehyde ratio. At this stage, the methylol intermediates are dried and ground, and in some cases, a filler such as mica, glass fiber, or sawdust may be added. A cross-linking agent such as hexamine is mixed with the prepolymer together with CaO as a catalyst. When further heating takes place during molding, the hexamine decomposes to form HCHO and ammo-nia, which acts as a catalyst in the final cross-linking process by the HCHO.
Amino resins: A related family of polymers is made from random prepolymers prepared by reacting either urea or melamine (shown below) with HCHO.
The products are known as aminoplasts.
Epoxides: Structoset prepolymers are designed to have controlled and defined structures with functional groups located either at the chain-ends (structo-terminal) or located along the chain (structopendant). Epoxy resins make use of the epoxy group for the former, and hydroxyl groups for the latter.
One of the major resin prepolymers formed by the reaction of bisphenol A and epichlorohydrin can be treated as either.
These prepolymers can subsequently react with a cross-linking (or curing) agent to turn them into strong intractable network structures. The most commonly used group of low-cost, room-temperature, cross-linking agents is the aliphatic amines, e.g., diethylene triamine (H2NCH2CH2NHCH2CH2NH2) and triethylene tetramine
These react with the epoxy groups.
Anhydrides are also used as curing agents and have the advantage that they do not irritate the skin as do some of the amines. The reaction usually proceeds best in the presence of a catalyst such as a Lewis base (or acid).
C
9813_C002.fm Page 50 Friday, June 15, 2007 10:48 AM
Step-Growth Polymerization 51
One proposed mechanism is that of a two-step reaction with ring opening at stage one and addition of the epoxy at stage two. After this, the anion reacts with another molecule of anhydride.
In the uncatalyzed reaction, the anhydride ring is opened by reaction with a hydroxyl group, but the reaction is much slower. The hydroxyl group also reacts with the epoxy group.
Other structures can be generated, and an important group consists of the epoxy novolac resins, which find use as molding compounds.
The high-cross-link densities that can be achieved in these systems make the resulting materials mechanically stable and resistant to high temperatures.
Flame-retardant resins can be made using tetrabromobisphenol A as part of the prepolymer. When degraded at high temperatures, this compound releases halogen compounds, which trap the free radicals formed, thereby helping to quench the flame.
Epoxy resins are used in tool making, as adhesives, insulators, tough surface coatings and, importantly, in composites in combination with reinforcing fibers. They have also found extensive use in the encapsulation of electronic devices.
O 9813_C002.fm Page 51 Friday, June 15, 2007 10:48 AM
52 Polymers: Chemistry and Physics of Modern Materials
PROBLEMS
1. A list of monomers capable of undergoing condensation reactions is given in the following text. For each, indicate the functionality. Using different combinations, write as many polymeric structures as possible. Indicate whether a linear chain or a network is formed.
2. The condensation reaction between maleic anhydride and propylene glycol leads to a polyester. Draw the structure of the polymer that is formed.
What is the architecture of the polymer produced after addition and poly-merization of styrene? What change do you expect if maleic anhydride were to be replaced by sebacic acid?
3. Draw the structure of the polymers obtained from the monomer or mono-mers listed in the following text, and classify the nature of the linkage between monomer units.
a. Ethylenediamine and terephthalic acid b. Sebacic acid and 1,6-hexanediol
c. Hexamethylene diisocyanate and 2-methyl-1,3-propanediol d. Glycine
4. Draw the repeat units of the two polymers obtained by the polymerization of the following two monomers:
Which of the two would you expect to exhibit the higher melting point and why?
5. A nylon-6 sample prepared by ring-opening polymerization of caprolac-tam was analyzed to determine its molar mass. The acid- and amine-group concentrations were obtained by end-group analysis (i.e., titration of the acid
(CH2)2 9813_C002.fm Page 52 Friday, June 15, 2007 10:48 AM
Step-Growth Polymerization 53
groups with KOH/ benzyl alcohol to neutral point and potentiometric titration of the amine groups) (Oshinski et al., 1996). Draw the structure of the polymer, and calculate the number average molar mass, given that [COOH]
= 60.8 µeq g–1 and [NH2] = 59.0 µeq g–1. Do the same for a different nylon 6 sample with [COOH] = 50.7 µeq g–1 and [NH2] = 35.8 µeq g–1. Comment on the difference between these two samples and suggest reasons for this.
6. Titration of polymers containing acidic groups with alcoholic (water or methanol) KOH to a phenolphthalein end point gives the acid value AV.
The equivalent weight is then
Determine the acid value and Mn of the polyester prepared from 124 g (I), 104 g of (II), and 460 g of (III).
7. The following data were obtained for the uncatalyzed equimolar esterifi-cation (Hamann et al.,1968) of lauryl alcohol (b = 0.200 mol) with lauric acid (a = 0.200 mol) in lauryl laurate at 163°C.
Time (Min) Percentage Reaction 0 9813_C002.fm Page 53 Friday, June 15, 2007 10:48 AM
54 Polymers: Chemistry and Physics of Modern Materials
Determine the order of the reaction, given that for equimolar esterifications and n >1 the general rate formula is
where a is the initial concentration of acid groups, equal to the initial concentration of hydroxyl groups, x is the concentration of ester groups at time t, and k is the rate constant.
8. For the polyesterification reaction between diethylene glycol and adipic acid, calculate the number-average molecular weight of the polyester that is formed when the extent of reaction p is equal to 0.90. Note that, for condensation polymers that are synthesized from two reactants, half the average-molar-mass of the repeat unit is used to calculate the degree of polymerization.
9. Kinetic data for the uncatalyzed equimolar polyesterification (Hamann et al., 1968) of 1,10-decamethylene glycol and adipic acid at 161°C and 190°C are tabulated below. In this experiment, time and percentage of reaction were measured using, as a starting point, an equimolar mixture of the acid and alcohol dissolved in their ester. Thus, the extent of reaction at t = 0 was equal to 82%.
a. By assuming that [COOH]o is equal to 1.25 mol per kg of mixture, determine the rate constants and activation energy of the uncatalyzed reaction.
T = 161°C T = 190°C
Time (min) Percentage Reaction Time (min) Percentage Reaction 0
9813_C002.fm Page 54 Friday, June 15, 2007 10:48 AM
Step-Growth Polymerization 55
b. Compare results for the polyesterification reaction in the preceding text with those obtained in Problem 7 for the uncatalyzed equimolar ester-ification of lauryl alcohol with lauric acid. Which conclusion can you draw on the dependence of reactivity on molecular size to which groups are attached?
c. By comparing the kinetic data reported in the preceding text to those of Figure 2.4(a) for the polyesterification of adipic acid with ethylene glycol, discuss reasons why the preceding reaction was followed start-ing from p = 0.82.
10. The differential rate law for the catalyzed esterification is given by:
Find the integrated rate law when the initial concentrations of A and B groups, [A]o and [B]o, are different, i.e., [A]o ≠ [B]o.
11. The second-order rate constant for the catalyzed polyesterification of 12-hydroxystearic acid at 133.5°C is 9.23 × 10–5 mol–1 L sec–1. Using an initial concentration of ester groups equal to 3.5 mol L–1, determine the time required for p to reach values of 0.5, 0.7, and 0.9. Determine the number- and weight-average molecular weights corresponding to these p values. The activation energy for this reaction is reported to be 47.9 kJ mol–1. Find the reaction constant at 160°C. How would this value change if the concentration of catalyst employed in the reaction (0.0354 mol l–1, in this case) was to double?
12. The graph of Figure 2.5 shows that Nx/N is larger for x = 100 at p = 0.9875 than for a degree of conversion of either 0.9600 or 0.9950. At any given extent of reaction p, there is a distribution of chain sizes. The maximum probability of a given chain-length occurring depends on the extent of reaction. Show that the relationship between the extent of reaction at which the probability of occurrence of x-mers is at a maximum, pmax and x is
13. Consider a mixture of 1 mol of 1,6-hexane diol reacting with 1.0 mol of adipic acid.
a. By neglecting end-group contributions, determine the extent of reaction p that is necessary to achieve Mn = 5700.
b. If a 1% excess of diol is used, what would the Mn value be if the reaction was to be carried out to the same extent of reaction p as in (a)? What is the p value now required to achieve the same Mn as in (a)?
14. Nylon-6,6 is prepared by reacting 1,6-diaminohexane and adipic acid.
Determine the amount of acetic acid that should be added to the reaction
−d A = = −
dt k A B dx
c dt [ ] [ ][ ]
p x
max x
( )
( )
= −
+ 1 1
9813_C002.fm Page 55 Friday, June 15, 2007 10:48 AM
56 Polymers: Chemistry and Physics of Modern Materials
mixture to produce a polymer of number average molar mass equal to 10,000 at 99.5% conversion.
15. Consider the condensation reaction taking place between 1.5 mol of phthalic acid, 0.2 mol of glycerol, and 1.2 mol of ethylene glycol.
a. Use the modified Carothers equation to determine the number-average degree of polymerization at p = 0.950 and compare this value with xn obtained if glycerol were to be replaced by an equivalent amount of ethylene glycol to provide the same number of functional groups.
b. Calculate the extent of reaction at which gelation is expected to occur on the basis of either the modified Carothers equation or the Flory statistical theory.
REFERENCES
Flory, P.J., J. Am. Chem. Soc., 61, 3334, 1939; 62, 2261, 1940; 63, 3083, 1941.
Hamann, S.D., Solomon, D.H., and Swift, J.D., J. Macromol. Sci. — Chem., A2, 153, 1968.
Oshinski, A.J., Keskkula, H., and Paul, D.R., Polymer, 37, 4891, 1996.
Pearson, R.G., in Speciality Polymers, Dyson, R.W. (Ed.), Blackie, 1987.
BIBLIOGRAPHY
Allen, G. and Bevington, J.C., Eds., Comprehensive Polymer Science, Vol. 5, Pergamon Press, 1989.
Flory, P.J., Principles of Polymer Chemistry, Cornell University Press, 1953, chap. 3.
Frazer, A.H., High Temperature Resistant Polymers, Interscience Publishers, 1968.
Lenz, R.W., Organic Chemistry of Synthetic High Polymers, Interscience Publishers, 1967, chap. 3.
Mark, H.F. and Whitby, G.S., The Collected Papers of Wallace Hume Carothers, Interscience Publishers, 1940.
Nielson, P.O., Properties of Epoxy Resins, Hardeners and Modifiers, Adhesives Age, Vol. 42, 1982.
Odian, G., Principles of Polymerization, 4th ed., John Wiley and Sons, 2004, chap. 2.
Oertel, G., Ed., Polyurethane Handbook, 2nd ed., Hanser Gardner Publications, Munich, 1994.
Potter, W.G., Epoxide Resins, Butterworth, 1970.
Rempp, P. and Merrill, E.W., Polymer Synthesis, 2nd ed., Hüthig and Wepf, 1991.
Rogers, M.E. and Long, T.E., Synthetic Methods in Step Growth Polymers, John Wiley and Sons, 2003.
Solomon, D.H., The Chemistry of Organic Film Formers, John Wiley and Sons, 1967.
9813_C002.fm Page 56 Friday, June 15, 2007 10:48 AM
57