308 CHAIN POLYMERIZATIONS one. The increase in volume (µ =dV /dt) that results drives the surfactant of the empty micelles toward the external envelope of the particles; micelles thus disap- pear from the medium by becoming particles or by supplying surfactant molecules to the already formed particles. As soon as all the micelles have been used up by one of the mechanisms mentioned above (first period in Figure 8.10)—corresponding to approximately 15% monomer conversion—the number of particles (N p ) can be considered constant until the end of the polymerization. The rate of polymerization during this second period in Figure 8.10 can be expressed by the relation R p = k p [M] part N p 2 Thus it will be constant up to 70–80% conversion. Assuming that free radicals are generated at constant rate (d[RM • ]/dt =ρ =const)) and that all of them serve to create particles, at the time t 1 corresponding to the total disappearance of micelles, N p can be written as N p = ρt 1 At t 1 , a particle created at t 0 will exhibit the volume V(t 1 ,t 0 ) = µ(t 1 −t 0 ) with its volume at t 0 (when it was a micelle) being negligible. The surface of its external envelope can be easily deduced from its volume: a(t 1 ,t 0 ) = (36π) 1/3 [µ(t 1 −t 0 )] 2/3 0 time 1 1 2 3 extent of monomer conversion Figure 8.10. Kinetics of the monomer conversion for an emulsion polymerization in a closed batch reactor. Because the number of particles generated for the period of time dt is ρdt, the total external surface at time t 1 can be written A t 1 =  t 1 0 a(t 1 ,t 0 )ρ dt = (36π) 1/3 0.6ρµ 2/3 t 5/3 1 ANIONIC POLYMERIZATION 309 Because this total surface can be directly related to the concentration [S] of the surfactant and to its molar surface (a s ), A t 1 = a s [S] one obtains the following for the expression of N p : N p = 0.53  ρ µ  0.4  a s [S]  0.6 The Smith–Ewart model describes satisfactorily the polymerization of styrene, isoprene, and methyl methacrylate; for these systems, it can be used to predict the size of the latex particles and the corresponding molar masses. In contrast, it is unsuited for the case of monomers partially water-soluble or polymers insoluble in their monomer—that is, polymerization of vinyl chloride and vinyl acetate. It accounts neither for the fact that styrene can be polymerized in absence of surfactant nor for the fact that free radicals (RM • ) can equally penetrate into a micelle or in an already formed particle during the initial phase. Fitch has thus proposed another model which considers that initiation and the early stages of the propagation occur in the aqueous phase, with the chains precip- itating only when a critical size is reached—that is, for degree of polymerization of a few units to a few tens depending upon the hydrosolubility of the oligomer formed. 8.6. ANIONIC POLYMERIZATION This type of polymerization is a very old one, used at the beginning of the twentieth century in Germany to produce a well-known synthetic rubber named “Buna”. However, it is only in the middle of the 1950s that anionic polymerization took all its importance when Szwarc shed a new light on this field and discovered that it can be carried out in the absence of any transfer and termination. Szwarc called such polymerizations “living” (see Section 8.4), and his discovery triggered an intense research activity that culminated in the synthesis of unprecedented complex macromolecular architectures (block copolymers, stars, etc.). 8.6.1. General Characteristics The anionic polymerization is a chain reaction that can be schematized by ~~~~M n − , Met + + M ~~~~M − n+1 , Met + 310 CHAIN POLYMERIZATIONS where ∼∼∼∼M − n represents a negatively charged or polarized species carried by the growing chain, and Met + is a positive counterion (or a polarized species), generally a metallic cation. Whatever the precise mechanism involved in this type of polymerization, it proceeds via repeated nucleophilic reactions. In the case of vinyl and related monomers, for the propagation to occur by nucleophilic addi- tion, an activation of the monomer double bond is generally required (see, however, “Remark,” page 312). Electron-withdrawing substituents (–CO–OR, –CN, etc.) or those inducing a strongly positive polarization of the β-carbon atom of the double bond, when neared by a nucleophilic active species, N ,,, etc. fulfill this condition. Anionic polymerization also applies to heterocyclic monomers. In this case, it can occur either by nucleophilic substitution or by nucleophilic addition onto a carbonyl group followed by an elimination (mechanism B AC 2), and so on. A negative enthalpy of polymerization is a necessary condition for the monomer to be polymerized, and thus heterocyclic monomers must be strained enough to undergo ring-opening and polymerization. Another constraint of prime importance that affects the polymerizability of monomers—in particular, that of ethylenic ones—is the extreme reactivity of species that propagate the process. In a first approach—and without mistaking between the notions of nucleophilicity and basicity—a carbanionic species can be considered as the conjugate base of a pro- tonic acid whose pK a can be evaluated. Thus, the species formed in the anionic polymerization of styrene ~~~CH 2 (C 6 H 5 )HC − is the conjugated base of the species ~~~~CH 2 (C 6 H 5 )HCH whose pK a is around 41, a high value that mirrors an extremely low acidity. The corresponding conjugated base is thus particularly strong; the comparison of a pK a of 41 with that of water which is the conjugated acid of metal hydroxides gives an idea of the very high reactivity of the conjugate base. This imposes that monomers are free of electrophilic species that could potentially react with nucleophilic growing chains. Depending upon the nature of the substituent A, this nucleophilicity varies to a large extent. Anionic polymerization is utilized only when the “living” character of the chain growth can be ensured. In addition, initiators are selected for their ability to give a complete initiation (f ∼1) and a short period of initiation compared to that of prop- agation, allowing a controlled polymerization to occur. This situation is exploited ANIONIC POLYMERIZATION 311 in macromolecular engineering to synthesize polymeric chains with well-defined structure and narrow molar mass distribution. 8.6.2. Structure of the Propagating Species The “living character” of the growing species formed in carbanionic polymerization offers an opportunity to study comprehensively their structure. The concentration of the reactive centers being always extremely low in the polymerization medium, it is easier to carry out such structural studies on simple organometallic models of the “living” ends. Some of these are used to initiate the polymerization and the knowledge of the parameters that determine their reactivity is interesting by itself. There is a close relationship between the structure of organometallic species (∼∼M − n ,Met + ) and their reactivity. In the case of species responsible for the polymerization of ethylenic monomers, their nucleophilicity and thus their reactivity are strongly determined by the electron density on the carbanionic site A ~~~CH 2 HC d− , Met d+ This electron density depends on the polarization of the C–Met bond and the possible delocalization of the negative charge on the substituent A. So, the param- eters that control the structure of the active centers responsible for the anionic polymerization of ethylenic monomers are: • The nature of the substituent(s) carried by the double bond, • The nature of the counterion associated with the carbanionic species, • The nature of the solvent in which the reaction is carried out and the presence of possible additives. 8.6.2.1. Effect of the Substituent A. If the substituent promotes a delocaliza- tion of the negative charge [as is the case for styrene, vinylpyridines, (meth)acry- lates, etc.], it entails a decrease of the intrinsic reactivity of the carbanionic species. Thus, in the case of acrylates, the active center is an enolate of rather low reactivity: CH 2 CH 3 CH O O − , Met + ~~~~ The intrinsic reactivity of carbanionic active centers is increased by the presence of electron-donating substituents and is conversely decreased by that of electron-with- drawing ones. However, in the case of acrylates, the monomer double bond is more activated by the electron-withdrawing character of its substituent than the reactivity of the corresponding enolate is lowered by the same substituent; this explains the 312 CHAIN POLYMERIZATIONS very high anionic polymerizability of these monomers. Thus, the intrinsic reactivity of the monomer determines the global reactivity of the system—that is, its poly- merizability. For example, methacrylic monomers (methyl methacrylate is shown hereafter) are characterized by a lower polymerizability than that of acrylates, in spite of the electron-donating effect of their methyl group presumed to increase the electron density on the active center and thus its reactivity; as a matter of fact, this –CH 3 group in α-position prevents (by its donor effect) a full polarization of the double bond and thus decreases the monomer reactivity. O O CH 3 CH 3 Methyl methacrylate Styrene and butadiene are the two reference monomers in anionic polymeriza- tion. Their high polymerizability is primarily due to the virtue of their double bonds to undergo a positive polarization and an electron shift toward their substituent when neared by a negatively charged active center. Remark. Ethylene is a monomer with no possibility of activation of its double bond. However, it can be polymerized by nucleophilic addition but its anionic polymerizability is very low, the absence of any stabilizing substituent next to the carbanionic site making the latter particularly reactive. 8.6.2.2. Effect of the Nature of the counterion. Examples of polymeriza- tions that can be carried out with nonmetallic counter-ions (quaternary ammonium, phosphonium ions, etc.) are scarce, the vast majority of them requiring the use of alkali or alkaline-earth cations. Lithium and magnesium cations exhibit a small ionic radius which explains the partial covalent character of their bond with carbon atoms in nonpolar solvents, provided that the carbanion is not too delocalized. With cations of higher ionic radius, the interionic distance favors the separation of charges, and thus the corresponding species can be considered totally ionized. In polar solvating media as well as in the presence of solvating additives, the ionic radius of the counterion affects its capacity to be solvated. Large cations like cesium can by no means be solvated even by solvents known for their strong solvating power. Lithium is by far the most used counterion known; this is primarily due to the practical and synthetic ease that is associated with the utilization of butyllithium as initiator, but also to the virtue of this cation to generate different configurational structures in the polymers formed. Indeed, lithium cations can generate either par- tially covalent or totally ionic species with different regio- and stereospecificity, depending upon the solvent in which it is dispersed. ANIONIC POLYMERIZATION 313 8.6.2.3. Effect of the Nature of the Solvent and that of Potential additives. Because of the very high reactivity of anionic reactive species, the solvents used in anionic polymerization should not exhibit any acidic character; thus basic or neutral solvents are generally chosen. The functions of a solvent are manifold and, depending upon its structure, it can fulfill one, two or three of these functions. The first function is that of a diluent; the simultaneous generation of carbanionic initiating/propagating sites and the monomer consumption by the latter can liberate a considerable heat in the reaction medium that can be better removed if a solvent is present. Solvents used as diluents are always aliphatic or aromatic hydrocarbons; they do not modify or only to a little extent the structure of active centers. Organolithium compounds are aggregated species whose degrees of aggregation vary with the nature of the carbanion and sometimes with the range of concentration. For instance, polystyryllithium ion pairs are aggregated as dimers like shown below: HC − ~~~~PS~~~~CH 2 CH 2 ~~~~ PS~~~~ − CH Li + Li + , , In the latter case, only non-aggregated species—in equilibrium with aggregated ones—are reactive and contribute to the propagation: Active Non active 2 K ag ~~~~PS − , Li + 2 ~~~~PS − , Li + The second potential function of a solvent is that of a solvating agent. Solvents used for that purpose are ethers or tertiary amines whose basic character—according to Lewis definition—entails a coordination to the Lewis acids that are the metal cations associated with the nucleophilic species. This role of solvating agent can also be played by additives (crown-ether, cryptands, tertiary diamines, etc.) used in small amount in a hydrocarbon serving as diluent. Depending upon their geometry or their concentration, such additives can either solvate externally the ion pairs [see hereafter the case of polybutadienyllithium in the presence of tetramethylethylene- diamine (TMEDA)], NN ~~~~CH 2 HC CH CH 2 Li + TMEDA 314 CHAIN POLYMERIZATIONS or cause a stretching of the carbon–metal bond (see hereafter the case of polystyryl- lithium solvated by a crown-ether): ~~~~PS~~~~CH 2 HC − , O O O O Li + Depending upon the size of the cation and the geometry of the solvating agent, such solvation may be more or less effective. Stretching ion pairs increases considerably their reactivity due to the easier insertion of monomer between the anion and the cation. When the dielectric constant (permittivity) of the solvent is sufficiently high, it can play the role of dissociating agent. Such a solvent can then cause the charges to separate more markedly and induce a partial dissociation of ion pairs into free ions, K diss ~~~~~M n − , S x ,Met + ~~~~~M n − + S x ,Met + where S x corresponds to X molecules of solvent coordinating to the metal cation. The relation between the dissociation equilibrium constant (K diss )andtheper- mittivity of the reaction medium (ε) can be written as −ln K diss =−ln K 0 diss + e 2 (r 1 +r 2 )εkT where K 0 diss is the constant of dissociation of ion pairs in a medium of infinite permittivity, r 1 and r 2 are the ionic radius of cation and anion, respectively, and e is the electron charge. This relation shows that by increasing the apparent ionic radius of the cation and that of the interionic distance, the solvating effect favors the dissociation; most of high permittivity solvents exhibit also a strong solvating power. The reactivity of free ions resulting from the dissociation of ion pairs is extremely high and, even at relatively low concentration, they have a major impact on the global kinetics of polymerization. In contrast to the case of free radical polymerization, the same monomer can generate various propagating species depending upon the nature of the initiator and that of the surrounding medium. The various reactive species are ranked hereafter in the increasing order of their reactivity, R–Met < (R d− –Met d+ ) x < R d− –Met d+ < R − ,Met + S y Generally inactive species Highly reactive species < R − ,Met + < R − ,S y Met + < R − + S y Met + where R represents the polymer chain and S represents a solvent molecule. ANIONIC POLYMERIZATION 315 8.6.3. Initiation Step The initiator has to be selected with care so as to ensure a short initiation step (compared to that of propagation) and the absence of side reactions. The preference must go to initiators that are more nucleophilic than the active species resulting from their addition onto a monomer molecule. Two types of reaction can be utilized to generate primary active centers. The first one resorts to an electron transfer from a metal atom (generally an alkali metal) to a molecule whose electron affinity is sufficiently high. The role of the electrophilic entity can be played by the monomer molecule and, in this case, the transfer of ns electrons from the alkali metal results in the formation of a radical-anion based on the monomer molecule: Met + Met + A A , Radical-anion − • The species obtained can be represented by the electron distribution shown hereafter, CH 2 HC − , Met + A and by recombination of the two free radical sites, a bicarbanionic species is formed: HC − A , Met + Met + , − HC A A 2 • CH 2 CH 2 CH 2 HC − , Met + This direct initiation is rarely utilized because the formation of such a radical-anion through the reaction between a solid (metal) and a liquid (monomer) is generally slow. To overcome this limitation, an organic intermediate that cannot polymerize itself but can accommodate electrons by transfer is generally utilized. More often, these intermediates are polycyclic aromatic hydrocarbons; for example, naphthalene is commonly used for this purpose; the reaction between naphthalene (in solution) and sodium (solid) is schematized hereafter: Na +naphthalene −−− −−− • (naphthalene) − , Na + The reaction must be carried out in a sufficiently solvating solvent (tetrahydrofuran, dimethoxyethane, etc.) for the electron transfer to occur, and, after elimination of 316 CHAIN POLYMERIZATIONS the metal in excess, a homogeneous and quasi-instantaneous initiation step can be obtained upon addition of monomer: + CH 2 CH 2 CH −− HC , , , Na + Na + Na + Na + + , CH 2 HC − 2 − • • The bicarbanionic species formed is persistent under conditions of “living” poly- merization. Na + , − CH-CH 2 -CH 2 Na + , − CH-CH 2 -CH-CH 2 -CH 2 -CH-CH 2 -CH − ,Na + -CH − ,Na + + 2 etc. Remark. Since two molecules of initiator lead to the formation of a sin- gle chain, the relationship giving the degree of polymerization as a function of the conversion must be modified. In the case of a monofunctional initia- tion, the relation is X n = [M pol ]/[I], whereas for a difunctional initiation we obtain X n = 2[M pol ]/[I] [M pol ], representing the concentration of monomer polymerized. More usually—and in particular in industry—initiation is obtained by the means of strongly nucleophilic Lewis bases. They are usually monofunctional and monovalent organometallic species; compounds like benzylsodium or phenyliso- propylpotassium (cumylpotassium) may be utilized in research laboratories, but in industry it is exclusively the isomers of butyllithium (n-, sec-, tert-) that are employed. They are strongly aggregated in hydrocarbon media (n-BuLi is hex- americ, tert-BuLi is tetrameric, etc.) and they react only under their “unimeric” (nonaggregate) form, the latter being in equilibrium with aggregates: ANIONIC POLYMERIZATION 317 n-BuLi 6 6 n-BuLi K ag k i + A A n-BuLi − , Li + n-Bu In hydrocarbon solution, the initiation is rarely instantaneous and mixed aggregates can be formed which adds to the complexity of the kinetic expression of the initiation step and that of the first propagation steps. In polar solvents or in the presence of certain additives, such aggregation disappears and very reactive species (free ions, solvated ion pairs, etc.) are generated that may provoke side reactions. The above Lewis bases can also be utilized to initiate the polymerization of heterocyclic monomers. However, the high reactivity of the latter authorizes the use of weaker bases (for example, KOH) than those required for the polymerization of vinyl and related monomers. In this way it is possible to limit side reactions and thus to preserve the “living” character of the polymerization: HO − , K + + O HO O − , K + 8.6.4. Propagation Step With vinyl and related monomers, the mechanism of propagation is the same as that of the initiation by Lewis bases: A + A HC − A ~~~~M n ~~~~CH 2 ~~~~M n+1 ~~~~CH 2 , Met + HC − , Met + In hydrocarbon solvents, active centers have a strong tendency to be aggregated; as previously seen, it is the case for the polymerization of styrene initiated by an organolithium compound, in bulk or in a hydrocarbon solvent: (~~~~~~PS − ,Li + ) 2 2 ~~~~~~PS − ,Li + K ag [...]... (“loose” ion pairs) under the effect of the solvent and these are more reactive (b) Addition of homoionic species in the reaction medium by using soluble and highly dissociated salts causes a retrogradation of the dissociation equilibrium of reactive ion pairs; it entails a deceleration of the propagation step By combining the results of the kinetic study and the value of the added homoionic salt dissociation... possible to calculate the propagation rate constant of free ions (kp− ) The stereochemistry of the propagation step closely depends on the polarity of the solvent and on the nature of the counterion For polymerizations involving free ions, the sp 2 hybridization of carbanionic species prevents any marked stereoregulation of the propagation step and the resulting polymers are atactic In nonpolar solvents, the... carbanions, it is often necessary to activate them in order to bring about sufficiently high rates of polymerization In general, the kinetics is complex because of the aggregation of active centers independently of the reaction media, and the degrees of aggregation vary with their concentration Moreover, the energies of activation of the propagation reaction are appreciably different for ion pairs and free ions;... additional advantage of these systems is the accurate control of the degree of polymerization of the polymers obtained, which merely reflects the high efficiency (f ) of the initiators employed Such a good definition of the molecular dimensions associated with the persistence of the active centers was extensively applied for the purpose of so-called macromolecular engineering, to design and construct precision... consists of replacing Li+ by a bulkier cation (quaternary ammonium, phosphonium, etc.) or by adding in the reaction medium, a solvating agent that increases the apparent radius of the lithium ion; the attack of carbonyl groups by ion pairs can thus be thwarted, the probability of termination reduced, and the control of polymerization improved in this way 8 .6. 6.2 Reaction with Termination Reagents Because of. .. general, one operates by sequential addition of the comonomers in the order of increasing electroaffinity 8 .6. 6 Termination Reactions Being mainly known and utilized for its “living” character, it may appear at first glance misleading to mention the existence of termination reactions in the anionic polymerization of vinyl and related monomers They indeed occur, and the conditions have to be found when necessary... level, the probability of existence of these carbocationic species is indeed very low compared to that of onium ions 3 36 CHAIN POLYMERIZATIONS Table 8.17 Energy (in kJ·mol−1 ) related to the strength of various heterocycles with variable number of links Heterocycle Number of links 3 4 5 6 7 8 9 CH2 O S 115 109 25.5 0.4 25.5 40.5 52.5 117 — 28.0 — — — — 77.8 79.0 4.1 9.2 — — — O N 96. 1 — — — — — — O —... the effects of different structural factors: nature of monomer, nature of solvent, retrogradation of equilibrium between ion pairs and free ions, and nature of counterion Monomers prone to polymerize under “living” conditions are also those whose corresponding carbocations are strongly stabilized: N O-R O-R The polarity of solvents should not be too high in order to prevent the tendency of ion pairs... reactivity of active centers are such that only a very few of them give “statistical” copolymers Among those, the styrene/butadiene system is the best known, being industrially produced (in solution) under the trade name of SBR The existence of active centers under the form of various structures for each comonomer, with each of these structures having its own reactivity, complicates the kinetic treatment of. .. construct precision macromolecular architectures An account of the various possibilities is described in Chapter 9, including those based on other “living” polymerizations 8 .6. 9 Techniques of Anionic Polymerization Due to the generation of the totality of active centers at the onset polymerization and the very high polymerizability of vinyl and related monomers, there is no option 328 CHAIN POLYMERIZATIONS . comparison of a pK a of 41 with that of water which is the conjugated acid of metal hydroxides gives an idea of the very high reactivity of the conjugate base. This imposes that monomers are free of. regio- and stereospecificity, depending upon the solvent in which it is dispersed. ANIONIC POLYMERIZATION 313 8 .6. 2.3. Effect of the Nature of the Solvent and that of Potential additives. Because of. r 1 and r 2 are the ionic radius of cation and anion, respectively, and e is the electron charge. This relation shows that by increasing the apparent ionic radius of the cation and that of the