Thermal Analysis of Polymeric Materials

___________________________________________________________________

Fig. 3.23

reactions that may have no termination is treated in Sect. 3.2.4. Most important is that during a chain reaction polymerization occurs only on the free-radical sites, i.e., most molecules are inactive at any given time, while during the step reaction all molecules remain active at all times. The other points at the bottom of Fig. 3.23 follow directly from the mechanism.

Three typical free radical initiation reactions are summarized in Fig. 3.24. In the free radical initiation the center part of the initiator, azobisisobutyronitrile, can eject a stable nitrogen molecule. This gives the driving force to produce the two active free radicals. Before recombination, the free radicals can accomplish the thousands of propagation steps necessary to produce a macromolecule.

Another type of chain reaction is possible by ionic initiation. Both, positive and negative ions may start polymerization reactions (cationic and anionic polymerization). The existence of ions in solution is illustrated in Fig. 3.24 (B = base, M = metal). The interaction with the solvent plays an important role in the activity of the catalyst. In the covalent combination, no reactivity is expected. As the ions separate, they become increasingly available for reaction. While one of the ions supports the reaction, the other, the counterion, is in the vicinity and may also affect the rate of reaction. Since cationic initiators accept a pair of electrons, one finds these among the Lewis acids. Anionic initiators donate an electron pair, so they are Lewis bases.

A third type of chain reaction is based on coordination catalysts. A most common example of such initiation is given in the Ziegler-Natta catalyst described in Fig. 3.24. A coordination complex may be formed on a crystal surface or in solution. The monomer is inserted into the active site, as is illustrated in the reaction sequence of propylene polymerization on a TiCl3 crystal surface, as described on Figs. 3.26 and 27, below. The geometry of the various ligands of the complex may direct the incoming monomer in such a way that a stereospecific polymerization is possible.

208 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.24

Central to the propagation of the chain reaction is a double bond. A >C=C< double bond is chosen as an example for the following discussion. It is represented by a single sigma bond of type sp2 and a pair of overlapping p-electrons, one donated by each carbon atom at the double bond. Besides the double bond, there are four possible substituents, R1 to R4. The goal of the reaction is to convert the double bond to the backbone of the growing polymer. The double bond is stronger than one single bond, but not as strong as two single bonds. Figure 3.25 shows schematically that by reacting >C=C< with the lone electron of a free radical, R•, the top product molecule has a newly made single bond with electron configuration CR3R4•. The p-electron of the left carbon atom is used for bonding, leaving the p-electron of the right carbon as the new free radical position. The new molecule, extended by one monomer, can attack a further monomer and continue the chain. Only the geometry of R1 to R4 may slow the reaction (on one or both sides of >C=C<) by hindering access to the reaction site and/or enhance/retard reactivity by influencing the stability of the free radical. Starting the chain reaction with an anion A: , both p-electrons of the double bond are moved to the right carbon atom, producing CR3R4: , an anion able to continue the chain reaction. Analogously, a cation can be used in propagation of the chain by moving the electrons of the double bond to the left, producing CR3R4+.

A list of common types of termination reactions is given at the bottom of Fig. 3.25. Any time two radicals meet, they may combine and terminate the reaction. A very low free radical concentration is thus important for producing molecules of high molar mass. The free radical terminations include recombination, disproportionation, transfer, and the reverse of initiation. The ionic chain reactions differ from the free radical reactions by needing a counterion to neutralize the charge on the active chain end. Obviously, the actual reaction configuration is complicated by the presence of the counterion. The main difference between the two ionic types of chain reactions

___________________________________________________________________

Fig. 3.25

is the ease of their termination. Anionic polymerization may be kept virtually free from termination due to the relative stability of the anion, as is discussed in Sect. 3.2.4 on chain reactions without termination. Cationic polymerization, on the other hand, may be terminated by any of a large number of reactions known for the organic cation. Poisoning of the active chain is a common termination reaction for all ionic polymerizations. Stringent conditions exist for all ionic reactions as well as the coordination reactions to keep out poisons such as oxygen and moisture.

Coordination reactions are insertion reactions. They may occur on single sites of a dissolved catalyst such as metallocenes [16,17], used for making stereospecific polypropylene or uniform polyethylene copolymers. Multiple sites are found on heterogeneous reactions, i.e., the reactions take place on surface sites of crystals. Most well-known is the Ziegler-Natta1 polymerization [18], for which a recipe is given in Fig. 3.24. The schematic indicates one of the active sites on an TiCl3 crystal which acts by absorbing triethyl aluminum on one vacancy and the monomer on the other. By insertion of the adsorbed monomer between the Al and the C2H5 on the solid surface, the polymer grows by insertion, as illustrated for propylene in Figs. 3.26 and 3.27. Since the geometries of the reaction intermediates are quite restrictive, it is possible to direct the monomer in such a way to yield pure stereoisomers when using catalysts of proper design (for the description of isomers see Sect. 1.2). The discovery of synthetic routes to stereospecific macromolecules was one of the milestones to modern polymer science, as mentioned in Sect. 3.1. Due to the high regularity of the

1 Karl Ziegler (1898–1973, German chemist, Director of the Max Planck Institute for Coal Research at Mülheim an der Ruhr); Giulio Natta (1903 1979, Italian chemist, Professor at the Milan Polytechnic and Research Director of Industrial Chemistry). Both shared in 1963 the Nobel Prize for their work on polymerization.

212 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Table 3.1. Reaction types for the polymerization of various monomers

___________________________________________________________________

3.2.2 Kinetics

The kinetics of chain-reaction polymerization is illustrated in Fig. 3.28 for a free radical process. Analogous equations, except for termination, can be written for ionic polymerizations. Coordination reactions are more difficult to describe since they may involve solid surfaces, adsorption, and desorption. Even the crystallization of the macromolecule after polymerization may be able to influence the reaction kinetics. The rate expressions, as given in Appendix 7, Fig. A7.1, are easily written under the assumption that the chemical equations represent the actual reaction path. Most important is to derive an equation for the kinetic chain length, , which is equal to the ratio of propagation to termination-reaction rates. This equation permits computation of the molar mass distribution (see also Sect. 1.3). The concentration of the active species is very small and usually not known. First one must, thus, eliminate [M•] from the rate expression, as shown in the figure. The boxed equation is the important equation for .

Figure 3.29 displays a schematic plot of the change in monomer concentration with time d[A]/dt. First there is an increase in reaction rates as more new radicals are produced by initiation. Next, a steady state is achieved as new radicals form as fast

___________________________________________________________________

where A is the reaction-specific, pre-exponential factor, and E represents the activation energies. The approximate connection between the activation energies of polymerization and depolymerization is shown in Fig. 3.30 together with the energetics of the transition state. At equilibrium G = 0, Rp = Rd, and [A] = [A]eq. The left sketch in Fig. 3.30 shows a schematic of the change of the rate constants of the forward and reverse reactions based on the above equations. Because of the larger activation energy of the depolymerization, there must be a point of intersection (at Tc) above which the polymer is not stable for the given [A] and the polymer unzips from the chain ends. Note that this “loss of molecular integrity” was a characteristic of rigid macromolecules on melting and evaporation (see Sect. 1.1). For flexible macromolecules, melting is often possible without decomposition. A notable exception is poly(oxymethylene), where the decomposition must be retarded by blocking the unzipping by protection of the molecule with different end groups or by copolymerization with stable monomers.

3.2.4 Chain Reactions without Termination

A chain reaction without termination produces so-called living polymers. Even if on polymerization the initial monomer is used up, a new monomer can be added in a second step and the polymerization restarted as long as the active sites are not destroyed. The reaction became possible when initiation of vinyl polymerization with anionic mechanism was discovered by Szwarc in 1956 [19]. The process is easy to understand. A fixed number of initiator molecules, Ni is added to the monomer under conditions that eliminate termination (i.e., in the absence of water and oxygen). Figure 3.31 illustrates living polymerization with 10 initiator and 42 monomer molecules. Without termination, the reaction stops when all monomers are used up.

The evaluation of the molecular length distribution is a simple probability problem. For other types of polymerizations the molecular mass distributions are discussed in Sect. 3.4. In the present case, adding No monomer molecules to Ni initiator molecules yields an average (kinetic) chain length of repeating units (plus the initiator residue). The probability that a given x-mer is made, is simply the mole fraction, nx, and expressed by the binomial expression defined in Fig. 3.32 and written in the top boxed equation of Fig. 3.31. Its meaning can be understood by noting that the chance that x bonds are made in a given sequence is (1/Ni)x and the chance that the remaining No x bonds are not made in the given sequence, is [1 (1/Ni)]No x. Since one is satisfied to know how often an x-mer is made regardless of the reaction sequence, the product of these very small chances must be multiplied with the number of all possible ways of arranging the No monomers, namely No!, and divided by the number different ways an x-mer can be made out of No monomers.

The Poisson distribution written in the bottom boxed equation of Fig. 3.31 approaches the binomial molar mass distribution for the case that p is small and the average kinetic chain length = No/Ni is large, a condition approached for most living polymers. It is an equation that can be calculated much more easily than the binomial distribution. Analyzing the Poisson distribution, one finds that polymerizations without termination lead to rather narrow molar mass distributions as discussed in Sect. 3.3 with Figs. 3.39–41.

216 3 Dynamics of Chemical and Phase Changes

___________________________________________________________________

Fig. 3.31

Fig. 3.32

Recently, typical step-reaction polymerizations, as in polyesters, polyethers, and polyamides, have been forced into chain-reaction mechanisms by designing complex chain ends that react fast with the monomer only. Under the proper conditions, the step reaction can be suppressed almost completely. Such chain-growth polycondensation may even yield living polymers with narrow molar-mass distribution. A link to the initial literature is given in the General References for this section.