Robin A. Hutchinson
Free-radical polymerization (FRP) is one of the most important commercial pro-cesses for preparing high molecular weight polymers. It can be applied to almost all vinyl monomers under mild reaction conditions over a wide temperature range and, although requiring the absence of oxygen, is tolerant of water. Multiple mono-mers can be easily copolymerized via FRP, leading to the preparation of an endless range of copolymers with properties dependent on the proportion of the incorpo-rated comonomers. This chapter will provide an overview of the kinetics and mech-anisms, and the techniques used to construct mathematical representations of bulk and solution FRP. The description will also serve as a good base for the sus-pension and emulsion FRP chapters that follow.
4.1
FRP Properties and Applications
Polymers produced via free-radical chemistry include the following major families:
Low-density polyethylene (LDPE) and copolymers, used primarily in films and packaging applications. LDPE has density of <0.94 g cm3, and is produced via high-pressure free-radical polymerization; polyethylenes of higher density (and polypropylene) are produced via transition metal catalysis, as described else-where (see Chapter 8).
Poly(vinyl chloride) and copolymers, used primarily to produce pipe and fittings, flooring material, and films and sheet.
Polystyrene and its co- and terpolymers with acrylonitrile and butadiene. Homo-polymer is used for packaging and containers, while the acrylonitrile-containing polymers are used for various molded products in the appliance, electronics, and
Handbook of Polymer Reaction Engineering. Edited by T. Meyer, J. Keurentjes Copyright 8 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-31014-2
1) The symbols used in this chapter are listed at the end of the text, under ‘‘Notation’’.
153
automotive industries. Styrene–butadiene is the most widely used synthetic rubber.
Acrylic- and methacrylic-based polymers. Poly(methyl methacrylate) (PMMA), due to its transparency and weatherability, is used extensively in signs, lighting fixtures, and windows. Polyacrylates and copolymers are used extensively in the adhesives and coatings markets, and are also combined with acrylonitrile to make acrylic fibers.
Poly(vinyl acetate) and copolymers, used extensively in adhesives, coatings, and paper and textile treatment.
Fluoropolymers including polytetrafluoroethylene and copolymers, used widely in the wire and cable industry. They also have many specialty applications as coatings due to their inertness and low-surface tension.
In addition to these major product families, there exist many other smaller-volume (but often high-value) polymeric products synthesized via free-radical chemistry.
These products are manufactured via heterogeneous (emulsion, suspension) or homogeneous (bulk, solution) polymerization in a wide range of reactor configura-tions ranging from tubular to well-mixed tanks (and everything in between) in pro-cesses that may be continuous, batch, or semi-batch. FRP kinetics together with re-actor design and operating conditions controls the composition and architecture of the polymer produced. As with other chemistries, the final product consists of a mixture of polymer chains with varying length, composition, and structural ties such as branch points and branch lengths. The processing and end-use proper-ties of the polymer depend upon the distributions of these characteristics, not just the average values. Thus it is necessary to develop methods to relate the fundamen-tal kinetic mechanisms of free-radical polymerization to these distributed charac-teristics.
4.2
Chain Initiation
Free-radical polymerization, like other chain growth mechanisms, involves the se-quential addition of vinyl monomers to an active center. The defining characteristic of FRP is that the active centers are free radicals. Each growing polymeric radical increases in size rapidly; a typical chain is initiated, grows to high molecular weight, and is terminated in the time scale of, at most, a few seconds. When the macromolecule stops growing it cannot generally react further (barring side reac-tions), and is considered ‘‘dead’’. These dead chains have a residence time of mi-nutes or hours in the polymerization reactor, and the final polymer product is an intimate mixture of chains formed under time and/or spatially varying conditions.
The free radicals that initiate polymerization are in most cases generated by ther-mal or photochemical homolytic cleavage of covalent bonds. Commercial initiators include azo and peroxy compounds. The driving force for the dissociation of azo 154 4 Free-radical Polymerization: Homogeneous
initiators is the formation of the stable nitrogen molecule and resonance stabilized tertiary radicals, as shown for 2,20-azobisisobutyronitrile (AIBN) in Scheme 4.1.
Many types of peroxides (R-O-O-R0) are also utilized, including diacyl peroxides, peroxydicarbonates, peroxyesters, dialkyl peroxides, and inorganic peroxides such as persulfate, the latter being used mainly in water-based systems. The rate of per-oxide decomposition as well as the subsequent reaction pathway is greatly affected by the nature of the peroxide chemical structure, as illustrated for tert-butyl perox-yesters in Scheme 4.2. Pathway (a), the formation of an acyloxy and an alkoxy rad-ical via single bond scission, is favored for structures in which the carbon atom in the a-position to the carbonyl group is primary (for example, tert-butyl peroxyace-tate, R ¼ CH3). Pathway (b), concerted two-bond scission, occurs for secondary and tertiary peroxyesters (for example, tert-butyl peroxypivalate, R ¼ C(CH3)3) [1, 2]. The tert-butoxy radical formed in both pathways may decompose to acetone and a methyl radical, or abstract a hydrogen atom to form tert-butanol.
The exact nature of the decomposition pathway is important, as it plays a role in the efficiency of the primary radicals in initiating new polymer chains. When an initiator decomposes, the primary radicals are nearest neighbors surrounded by a
‘‘cage’’ of other molecules through which they must diffuse to escape from each other before they recombine. Once one radical leaves the cage it is extremely un-likely that the pair will encounter each other again. In-cage reactions for pathway (a) in Scheme 4.2 will lead to the re-formation of the original initiator molecule, while the in-cage reactions for pathway (b) lead to the formation of an ether which is not capable of forming free radicals by another dissociation step.
In general, peroxide decomposition can yield both carbon- and oxygen-centered primary radicals that add to the carbon–carbon double monomer bond to form a new propagating chain, abstract hydrogen atoms from other molecules (including
N N CH3
Scheme 4.1. Decomposition of AIBN.
O
Scheme 4.2. Decomposition oftert-butyl peroxyesters. The preferred pathway depends on the nature of the R substituent.
4.2 Chain Initiation 155
polymer) in the system, or recombine to form inactive compounds. The relative rates of these processes are dependent on both the nature of the primary radicals and the monomer system. The mechanistic pathway followed will influence end-group structures of the polymeric products, affecting final properties such as ther-mal stability. Further details on initiator decomposition kinetics and mechanistic pathways can be found in the excellent monograph by Moad and Solomon [3].
The above discussion highlights the fact that the simple initiation process of most polymer texts is the exception rather than the rule, with the fraction of pri-mary radicals that initiate a new polymer chain a complex function of the reaction system. Nonetheless, the kinetic treatment is usually simplified by the introduction of a fractional initiator efficiency ( f ), formally defined by Eq. (1), where n is the number of moles of primary radicals generated per mole of initiator; n ¼ 2 for most common initiators.
f ¼Initiation Rate of Propagating Chains
nðRate of Initiator DisappearanceÞ ð1Þ
The initiator efficiency is normally in the range 0.4–0.9, with a low value indicating inefficient usage of the initiator and potentially a high formation rate of undesired by-products.
The kinetic descriptions in this chapter are developed for thermal unimolecular scission of a compound to yield two radicals, as this is the most common means of generating radicals in industrial systems. Thermal initiation of monomers is an ad-ditional mechanism capable of forming primary radicals at higher temperatures, as discussed for styrene (see Section 4.3.1.3). Other initiation systems are also avail-able, and bear a brief mention at this point. Initiators with multiple peroxide link-ages ðn > 2Þ have been the subject of recent academic study [4]. Photoinitiators that produce radicals by ultraviolet irradiation are commonly used to initiate cross-linking and curing reactions in polymeric systems, as the rate of initiation can be controlled through the intensity and location of the light source. And finally, a re-dox (reduction–oxidation) process is often used to initiate chains in emulsion poly-merization (see Chapter 6).
4.3
Polymerization Mechanisms and Kinetics
It is important to achieve an understanding of how the basic FRP mechanisms control polymerization rate and average polymer chain length. This section starts with the derivation of appropriate kinetic expressions for a single monomer system. Complicating (but industrially important) secondary reactions are then introduced, followed by the extension to multi-monomer systems. Dispersed throughout are up-to-date estimates for important free-radical polymerization rate coefficients, and descriptions of how they are obtained experimentally.
156 4 Free-radical Polymerization: Homogeneous
4.3.1
Homopolymerization
Many commercial polymers, including polystyrene, PMMA, and LDPE, are synthe-sized via homogeneous free-radical polymerization of a single monomer. Homo-polymer properties are controlled by average chain length and chain-length distri-bution as well as, in some cases, structural characteristics such as branching level.
4.3.1.1 Basic Mechanisms
The basic set of FRP mechanisms includes initiation, propagation, termination, and transfer to monomer and solvent or transfer agent, as shown in Scheme 4.3.
The subscript n denotes the number of monomeric units in growing polymer radicals (Pn) and dead polymer chains (Dn). Each reaction has an associated kinetic rate law expression and a specific rate coefficient. The free-radical initiator (I) un-imolecularly decomposes (with rate coefficient kd) to form two primary radicals (I) with efficiency f. Chain initiation occurs when the primary radical adds to mono-mer M, and chain growth continues via successive addition of monomono-mer units to the radical center (chain propagation, with rate coefficient kp). Bimolecular cou-pling of two growing chains results in the loss of two radicals from the system and the formation of either one (termination by combination, ktc) or two (termina-tion by dispropor(termina-tiona(termina-tion, ktd) dead polymer chains. Chain stoppage may also oc-cur via a transfer mechanism, where the growing radical abstracts a weakly bonded Initiator Decomposition I→2f I∗
Chain Initiation I∗+M→ P1 To Solvent or Agent
*
Scheme 4.3. Basic free-radical homopolymerization mechanism.
4.3 Polymerization Mechanisms and Kinetics 157
atom (usually hydrogen) from monomer or other molecules (solvent or chain-transfer agent, denoted by S) in the system to generate a dead polymer chain as well as a new radical that initiates another polymer chain.
A key assumption implicit in the formulation of Scheme 4.3 is that the rates of propagation, transfer, and termination reactions are independent of n, the length(s) of the radical(s) involved. It is known that propagation and likely transfer reactions involving very short chains (n ¼ 1; 2; 3) are faster by a factor of 10 than addition to long-chain radicals [5], but this effect diminishes rapidly with chain length and has a negligible effect on the overall kinetics of the system. Chain ter-mination, the coupling of two polymeric radicals, is a very fast chemical process that is controlled by the rate at which the two radicals find each other in the reac-tion system. The nature of this diffusion control makes terminareac-tion the most com-plex reaction in the polymerization process since the apparent rate coefficient can vary greatly with system conditions such as monomer conversion and solution vis-cosity (see Section 4.3.3). Although termination may also exhibit some chain-length dependence, most engineering treatments of FRP neglect this complex de-pendence. For further discussion of the individual mechanisms of Scheme 4.3 and their rate coefficients, see Section 4.3.1.2.
The set of rate laws that can be written from Scheme 4.3 is given by Eqs. (2)–(6).
Initiator Decomposition Rd¼ kd½I ð2Þ
Chain Initiation Rinit¼ 2f kd½I ð3Þ
Chain Propagation Rp¼ kp½M½Ptot ð4Þ
Chain Termination Rterm¼ ðktcþ ktdÞ½Ptot2¼ kt½Ptot2 ð5Þ Chain Transfer Rtr¼ ðktrmon½M þ ktrsol½SÞ½Ptot ð6Þ Here Ptot represents the concentration of all polymer radicals in the system [Eq.
(7)].
½Ptot ¼Xy
n¼1
½Pn ð7Þ
In some literature the right-hand side of the termination rate expression [Eq. (5)] is written as 2kt½Ptot2. The mode of termination – combination or disproportionation – has no effect on the overall termination rate, and thus the two events can also be expressed by the nomenclature of Eq. (8), where d is the fraction of the termination events that occur by disproportionation.
kt¼ ktcþ ktd; d¼ ktd
ktcþ ktd
ð8Þ
The following assumptions are widely accepted and usually valid in FRP systems:
158 4 Free-radical Polymerization: Homogeneous
The small radical species I;M, and Sare not consumed by side reactions and do not accumulate in the system, but are converted to polymeric radicals with 100% efficiency. Thus, the total rate of polymer radical formation is given by (Rinitþ RtrÞ. The net formation of polymeric radicals is Rinit, since transfer events both consume and create a polymeric radical species.
With a continuous source of new radicals in the system, an equilibrium is achieved instantaneously between radical generation and consumption, such that Rinit¼ Rterm. This characteristic, proven to be true for almost all FRP condi-tions [6], is a result of the fast dynamics of radical reaccondi-tions compared to that of the overall polymerization system. Often referred to as radical stationarity or the quasi-steady-state assumption (QSSA), it leads to the well-known analytical expres-sion for total radical concentration [Eq. (9)].
½Ptot ¼ Rinit
kt
1=2
¼ 2f kd½I
kt
1=2
ð9Þ
The consumption of monomer by chain-initiation or transfer events is negligible compared to that by propagation. This result, called the long-chain hypothesis (LCH), must be true if high molecular weight polymer is being produced. Thus the rate of polymerization (disappearance of monomer) can be taken as equal to the rate of propagation (Rpol¼ Rp) with the rate of heat generation proportional to the rate of this exothermic reaction.
Under these (generally valid) assumptions, the classic expressions for rate of poly-merization (Rpol), kinetic chain length (u, the average number of monomer units on a living chain), and instantaneous degree of polymerization (DPninst, the average number of monomer units on a dead polymer chain formed at any instant) are given in Eqs. (10)–(12), respectively.
Rpol¼ kp½M½Ptot ¼ kp½M 2f kd½I
kt
1=2
ð10Þ
u¼ Rp
Rtermþ Rtr
¼ kp½M
kt½Ptot þ ktrmon½M þ ktrsol½S ð11Þ
DPninst¼ kp½M
ðktdþ 0:5ktcÞ½Ptot þ ktrmon½M þ ktrsol½S ð12Þ
The difference between Eqs. (11) and (12) arises because termination by combina-tion yields a single polymer chain such that the chain length of dead polymer formed (DPninst) is greater than the chain length of polymer radicals (u) in the sys-tem at the same instant.
Table 4.1 lists the range of concentration and rate coefficient values typically en-countered in homogeneous free-radical polymerization systems at low conversion.
These can be combined with Eqs. (9)–(12) to illustrate the tradeoffs involved be-4.3 Polymerization Mechanisms and Kinetics 159
tween the desire for high throughput (Rpol) and the need to produce high MW (DPn) polymer.
The denominator of Eq. (12), the rate of dead chain formation, must be of the order 105–108 chains L1 s1 in order to produce polymer with a DPn of 102–104. Individual polymer radicals exist on average only for a fraction of a sec-ond, as calculated by the expression u=ðkp½M). Thus after the first few seconds of polymerization, the concentration of dead polymer chains is higher than that of polymeric radicals, and by the end of a typical polymerization the concentration of dead chains is orders of magnitude higher than [Ptot]. Final polymer MW and MWD (molecular weight distribution) are controlled by how the concentrations and kinetic coefficients in Eq. (12) vary with polymer conversion.
The theoretical MW limit for a system is controlled by transfer events, and is cal-culated by setting [Ptot] to zero in Eq. (12). For bulk FRP with no solvent, limiting values of DPn are 104–106. However, this theoretical limit can only be ap-proached in homogeneous FRP by reducing rates of polymerization to extremely low levels. For most systems both termination and transfer events play an impor-tant role in controlling polymer MW.
To produce high MW polymer (DPnof 102–104) it is necessary to keep total rad-ical concentration low, so that [Ptot] is of the order 108–106 mol L1. This dic-tates the choice of initiator such that Rinit (the product of kd and [I]) is also of order 108–106 mol L1s1.
Transfer can occur to monomer, solvent or any other species in the system. In some cases, chain-transfer agents are added deliberately to limit and control poly-mer DPn. These agents are generally chosen such that the rate of abstraction is much higher than that which occurs with monomer or solvent (ktr=kp¼ 103– 100) and thus can be added in trace quantities (f 1 mol L1). The use of transfer agents allows for independent manipulation and control of Rpol and DPn, but is only possible if the desired MW is less than that achieved for the corresponding transfer-free reaction.
Tab. 4.1. Typical values of coefficients and concentrations in low-conversion homogeneous FRP systems.
Coefficient/Concentration Typical range
kd[s1] 106–104
f 0.4–0.9
kp[L mol1s1] 102–104
kt[L mol1s1][a] 106–108
ktrmon=kp 106–104
ktrsol=kp 106–103
[I] [mol L1] 104–102
[M] [mol L1] 1–10
[S] [mol L1] 1–10
[a]At low conversion.
160 4 Free-radical Polymerization: Homogeneous
Initial rates of polymerization (monomer consumption rates) at low conversion are of order 104–102 mol L1 s1. Approximately 103–105 s are required to take a batch system to complete conversion. Faster rates can be achieved by in-creasing Rinit, but at the expense of decreased polymer MW. Achievable values of Rpol are also often limited by the heat removal capabilities of the reactor sys-tem, as the heat released by monomer addition is of the order 50–100 kJ mol1. It should be cautioned that these statements are generalities for a typical FRP sys-tem. Rate coefficients vary with monomer, initiator, and solvent choice (see Section 4.3.1.2) as well as polymerization conditions, and the kinetic treatment is compli-cated by the occurrence of side reactions (Section 4.3.1.3) and the variation of kt
with conversion and other system conditions (Section 4.3.3). These factors necessi-tate the use of more-powerful modeling techniques to quantitatively describe FRP systems (Section 4.4). Nonetheless, Eqs. (9)–(12) provide an idea of the factors con-trolling rate and MW, and are very useful for a qualitative examination of FRP systems.
4.3.1.2 Kinetic Coefficients
The coupling of polymer MW and polymerization rate is further illustrated via re-arrangement of Eq. (12) to give Eq. (13).
1
DPninst¼0:5ktc½Ptot
kp½M þktd½Ptot kp½M þktrmon
kp þktrsol½S
kp½M
¼0:5ktcRpol
kp2½M2 þktdRpol
kp2½M2þktrmon kp
þktrsol½S
kp½M ð13Þ
Rpol [Eq. (10)] and DPnare both dependent on k2p=kt, with DPnalso a function of mode of termination (disproportionation versus combination) and chain transfer.
Although Rpoland DPnare easily measured experimentally, it is not possible to re-solve the quantities into estimates for individual rate coefficients. Even the estima-tion of the ratio k2p=ktfrom Rpolrequires independent knowledge of initiator char-acteristics f and kd, and the assumption that radicals are not being consumed or retarded by adventitious impurities in the system. These factors have led to consid-erable scatter in rate coefficients reported in the literature (for example, Ref. 7), es-pecially for individual rate coefficients [8, 9]. Yet individual values, and knowledge of how they vary with temperature, are required for model development and an ac-curate representation of multi-monomer systems. The emergence of specialized experimental techniques since 1988 has greatly improved this situation and led to an improved understanding of free-radical polymerization kinetics. The following discussion highlights some of these advances, as well as summarizing key FRP rate coefficients as expressed by the Arrhenius law [Eq. (14)].
ki¼ AiexpððEiþ 0:1DViPÞ=RTÞ ð14Þ
4.3 Polymerization Mechanisms and Kinetics 161
Activation energies (Ei) and volumes (DVi) are reported with units of kJ mol1 and cm3mol1respectively, with T in K and P in bar. All second-order rate coefficients
Activation energies (Ei) and volumes (DVi) are reported with units of kJ mol1 and cm3mol1respectively, with T in K and P in bar. All second-order rate coefficients