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MOLECULAR WEIGHT DISTRIBUTIONS IN IDEAL POLYMERIZATION REACTORS. AN INTRODUCTORY REVIEW

G.R. MEIRA† and H.M. OLIVA‡

† INTEC (Univ. Nac. del Litoral and CONICET), Santa Fe (3000), Argentina. [email protected] ‡ Escuela de Ingeniería Química, Univ. del Zulia, Maracaibo, Venezuela. [email protected]

Abstract The ultimate aim of polymerization million tons by 2015. In volume, the annual production reaction engineering is the production of of polymers exceeds that of the 2 most important met- with tailor-made properties. An introductory review als: iron and aluminum. The raw materials for the pro- into this field is presented, with emphasis on the ef- duction of around 95% of all synthetic polymers are fects on the molar mass distribution (MMD), of the non-renewable sources (fossil oil, gas, and coal). sought combination of polymerization mechanism, Polymerization Reaction Engineering deals with reactor type, and reactor control. Three ideal poly- problems involving the measurement, mathematical merization mechanisms are analyzed: free-radical, modeling, optimization, and control of industrial poly- “living” anionic, and step-growth. “Living” anionic merization processes. It aims at improving both the and step-growth polymerizations are similar in that productivity of the polymerization process and the qual- their growing chains remain reactive while inside the ity of the produced . Some general references reactor; and for these systems the narrowest MMDs on this area are: Ray (1972), Reichert and Moritz are produced in reactors with narrow residence time (1989), Hamielec and Tobita (1992), Kiparissides distributions (RDT); i.e.: batch or continuous tubu- (1996), Ray et al. (2004), Yoon et al. (2004), Meyer and lar reactors. In contrast, in conventional free-radical Keurentjes (2005), Villa (2007) and Asua (2007). polymerizations, the polymer molecules grow in a Polymers are high molar mass substances characte- fraction of a second and thereafter remain inactive rized by the repetition (neglecting ends, branch junc- while inside the reactor. In this case, the RTD does tions, and other minor irregularities) of one or more not affect the MMD, and the homogeneous conti- types of monomeric repeating units. While homopoly- nuous stirred-tank reactors provide the narrowest mers contain a single type of chemical repeating unit, MMDs. Representative mathematical models of po- contain 2 or more. Polymers may be syn- lymerization reactors are useful for: a) quantifying thetic or natural (such as proteins, carbohydrates, etc.). the interrelationships between their numerous inputs In spite of their highly sophisticated structures, natural and outputs; and b) developing open- and closed- macromolecules are synthesized at ambient temperature loop strategies for increasing reactor productivity and in mild aqueous media, with the aid of specialized and product quality. catalysts or enzymes (themselves also polymers). In Keywords Molecular Weight Distribution, contrast, synthetic polymers are considerably simpler in Polymerization, Reactor. their chemical and structural characteristics, are mostly I. INTRODUCTION soluble in organic solvents, and their syntheses typically Synthetic polymers are important materials that find in- require stringent conditions of pressures, temperatures, numerate applications as plastics, composites, rubbers, and solvents. fibers, adhesives, and coatings. Unlike low molar mass The total number of repeating units in a chain is the substances where quality is mainly determined by puri- chain length or degree of polymerization. Most synthet- ty, synthetic polymers are mixtures of a large variety of ic polymers are linear molecules made up of repeating molecular species and morphologies, and therefore are units of functionality 2. Due to their high molar masses difficult to characterize. The physical properties of po- and chain entanglements, polymers are solids at room lymers (both in the solid and in the melt) depend on temperature, but may become viscous liquids between complex interrelationships with: a) the molecular struc- 100 and 300 ºC. Their average molar masses are typical- ture (described by the distributions of molecular ly between 20,000 and 300,000 g/mol. These values are weights, of isomers, of the chemical composition in co- a compromise between mechanical properties (such as polymers, of the molecular topology in long-branched elastic modulus, and tensile strength that all increase polymers, etc.); and b) the supramolecular morphology with the molar mass), and ease of processability in the (degree of crystallinity, particle size in heterogeneous molten state, favored by a low melt viscosity (or a low solids, etc.). “Commodity” thermoplastics and fibers molar mass). In contrast, if the polymer is crosslinked or such as polyethylene, polypropilene, PVC, and polysty- cured, then the material is essentially a single molecule rene are synthesized in large continuous processes that that unless degraded, it will not flow upon increasing were mostly developed in the mid-20th Century. In the temperature. “Reactors” for producing crosslinked 2007, the World production of synthetic polymers was articles are not stirred, and their shapes provide the around 260 million tons, and it is expected to reach 350 shape of the final article (e.g.: a mould for producing a

389 Latin American Applied Research 41: 389-401(2011)

rubber tire by vulcanization of a styrene-butadiene pre- mers (free-radicals are unaffected by water). In contrast, polymer). aqueous media are incompatible with anionic polymeri- The two main polymerization mechanisms are: chain zations. Anionic coordination catalysts are mostly sup- (or monomer-growth) and step (or polymer-growth). In ported on magnesium chloride or silica particles, but chain polymerizations, the linear molecule grows by may also be used in liquid form. Anionic coordination reaction between a monomer and a reactive site on the polymerizations are carried out in dispersions or in ho- growing chain end, with the reactive site being regene- mogeneous organic media. In coordination polymeriza- rated after each propagation step. According to the na- tions, the monomer in contact with the catalyst can be ture of the reactive site, chain polymerizations are clas- either a gas (in the fluidized-bed gas phase process), a sified into free-radical, anionic, and cationic. Many im- pure liquid (in the liquid solution process), or dissolved portant polymers such as low-density polyethylene, in a diluent (in the slurry process). Other heterogeneous poly(vinyl chloride) and polystyrenes are produced via polymerizations are the interfacial processes for the free-radical polymerizations. However, from the point production of nylons and polycarbonates. of total production, the most important synthetic poly- For the random nature of polymerization reactions, mers are obtained via catalyzed chain coordination po- all synthetic polymers exhibit a molecular weight distri- lymerizations. Examples of these are high-density po- bution, or better: a molar mass distribution (MMD). lyethylene (HDPE), linear low-density polyethylene MMDs totally characterize the molecular macrostruc- (LLDPE), isotactic polypropylene, isotactic poly(1- ture of linear homopolymers. In long-branched homopo- butene), various ethylene–propylene co- and terpoly- lymers and in linear copolymers, the macrostructures re- mers, cis-1,4-polybutadiene, and cis-1,4-polyisoprene. spectively include distributions of the number of In step polymerizations, all the molecules exhibit branches per molecule and of the chemical composition. reactive chain ends, and the chains grow by reaction be- Apart from the macrostructure, the microstructure of a tween any two molecules (including the monomers). homopolymer examines the orientation of the different Most step polymerizations are also polycondensations, geometrical or optical isomers along the chain (e.g.: the when a low-molar-mass by-product is generated at each trans content in a dienic monomer or the tacticity of a propagation step. Two important industrial polyconden- mono-substituted vinyl monomer). A homopolymer is sations are the syntheses of Nylon 6,6 (by reaction be- atactic if there is no systematic or regular configuration tween hexamethylenediamine and adipic acid), and of the repeating units along the chain. Atactic polymers poly(ethylene terephtalate) or PET (by reaction between are amorphous materials that soften around the glass terephtalic acid and ethylene glycol). transition temperature (Tg). In contrast, polymers with Most polymerizations are highly exothermic, to chain regularity such as iso- or syndiotactic polypropy- compensate for the reduction in entropy produced when lene are semi-crystalline when cooled slowly from the transforming many disordered monomer molecules into melt. Semi-crystalline materials exhibit a (lower) sof- a reduced number of ordered polymer structures. Thus, tening temperature at Tg, and a (higher) softening tem- most polymerization reactors require an efficient heat perature at the melting point (Tm) associated with the extraction system. The heat extraction capacity limit the crystals fusion. Compared with amorphous polymers, rate of polymerization of many industrial stirred-tank semi-crystalline polymers generally present improved reactors, due to the reduction in the heat interchange mechanical properties, but are non-transparent. area per unit volume when increasing reaction volume. Copolymers widen the range of properties (such as Most polymerization processes require the monomers to Tg and Tm) with respect to the base homopolymers; and be in a liquid phase. However, some industrial polyme- their microstructure also includes the sequence distribu- rizations also employ gaseous or solid monomers. In tions for each of the comonomers. According to their bulk polymerizations, the monomer is in liquid state, topology and sequence distributions, copolymers are and the polymer may or may not be soluble in its mo- classified into: a) statistical, when each comonomer ex- nomer. Bulk polymerizations can be homogeneous or hibits a sequence distribution of known statistics; b) al- heterogeneous according to polymer solubility. In addi- ternate, when the 2 comonomer types are added into the tion, bulk polymerizations can be heterogeneous by chain in an alternative manner; c) linear block, when thermodynamic incompatibility between long chains of long sequences of one comonomer type are followed by different polymers (e.g: a bulk polymerization of sty- long sequences of the other; and d) branched graft, rene in the presence of polybutadiene to produce high- when one of the comonomers constitute the main back- impact polystyrene). In a bulk process, the viscosity of bone onto which long-chained branches of the other the reaction mixture increases drammatically with con- comonomer are bound. version; and for this reason final conversions are often The processability and end-use properties of uncured limited to ensure an adequate mixing and product ex- polymers are mainly determined at the polymerization traction. The problems of heat extraction and viscosity stage. This is because it is generally impossible (or increase can be simultaneously solved by carrying out technically unviable) to modify the base polymer prop- the polymerizations in a dispersed aqueous medium. erties via post-polymerization reactions or unit opera- Suspension and emulsion processes are often employed tions such as fractionation according to molar mass. for the free- of nonpolar mono- The synthesis of complex macromolecules poses

390 G.R. MEIRA, H.M. OLIVA

major challenges and opportunities, with the expectation a) that such materials will exhibit distinctive properties 0.04 xr() and functions (Hawker and Wooley, 2005; Matyjas- zewski, 2005). This work is a basic introduction into that field, with emphasis on the effects on the MMDs of the obtained polymers of the different reaction mechan- 0.02 isms, reactor types, and reactor control. II. MOLAR MASS DISTRIBUTIONS AND wr() AVERAGES 0 Strictly speaking, MMDs are discrete in the molar 0 400 800 masses. In spite of this, MMDs of high polymers are r generally represented by continuous curves due to the b) 0.04 large number of molar mass types involved, and to the difficulty (or impossibility) of independently determin- 0.03 wr() ing the exact amount at each molar mass type. In the xr() case of homopolymers, molar masses are restricted to multiples of the repeating-unit molar mass. At each mo- 0.02 lar mass class M, the ordinates of the MMD can either represent (or be proportional to) the molar fraction (x) 0.01 or the mass fraction (w). In the former case, the distribu- 0 tion is the number MMD (NMMD) x(M), and its arith- 60 80 100 120 140 metic mean is the number-average molar mass (M ). r n Figure 1. Comparison between a number- and a weight-chain-length

In the latter case, the distribution is the weight- or mass- distributions of number-average chain length rn = 100 for: a) a MMD (WMMD) w(M), and its arithmetic mean is the Schulz-Flory distribution; and b) a Poisson distribution. All the distri- weight-average molar mass (M ). The transformation butions are discrete, with values at integers of the chain length r. The w ordinates are either the molar fraction x and the weight fraction w. from a NMMD into a WMMD involves multiplying the W M N M 2 ordinates of the NMMD by its corresponding abscissas.  i i  i i M w  wiM i   (2)  W N M For this reason, WMMDs are more skewed toward the  i  i i higher molar masses than NMMDs, and M w  M n . In The k-th moment of the NMMD is defined by: homopolymers, the chain length r (= 1, 2, ...) is propor- k k  Ni Mi , with k = 0, 1, 2, 3, ... (3) tional to the molar mass, and therefore any MMD may  be directly transformed into its corresponding Number- Equations (1-3) yield: or Mass- Chain Length Distribution (NCLD and 1 2 WCLD, respectively). However, such transformation is M n  ; and M w  (4) impossible for copolymers, because at a given chain 0 1 length there can be a whole distribution of the chemical Note that 0 and 1 respectively represent the total num- composition, and therefore of the molar mass. The ber of polymer moles and the total number of polyme- arithmetic means of the NCLD and WCLDs are the rized monomeric units in a sample. By extension of Eqs number- and weight-average chain lengths (rn and rw , (4), the z-average molar mass is defined by: respectively). W M 2 3  i i The difference in shapes between a number- and a M z   (5)  W M weight-based MMD is more noticeable when the sample 2  i i contains a high fraction of low molar mass. Thus, a Finally, the viscosity-average molar mass M v is de- large difference is observed between x(M) and w(M) in fined by: a Schulz-Flory (or “most probable”) distribution (Fig. 1 1 a a a); while the mentioned difference becomes negligible M v  wi Mi  with 0.5 < a < 1, (6) in a high molar-mass Poisson distribution (Fig. 1 b). where a is the Mark-Houwink-Sakurada exponent, that At each molar mass Mi, call xi, Ni, Wi, and wi, the depends on the solvent nature and on the temperature of corresponding molar fraction, number of moles, mass, the viscosity measurement. The following inequalities and mass fraction, respectively. The following expres- are verified: M  M  M  M , with the equal signs sions can be written: n v w z  N M W indicating a uniform or “monodisperse” distribution. M   x M  i i  i  (1) Several analytical techniques have been developed n i i N N  i  i for measuring molar masses. Absolute measurements of total mass Wi 1 are obtained by membrane osmometry, vapor pres-   M n total moles W w  i  i sure osmometry, or end-group analysis. Absolute mea- M i M i surements of M w are obtained by light scattering pho- tometry. Capillary viscometry is a relative technique for 391 Latin American Applied Research 41: 389-401(2011)

measuring M . Size exclusion chromatography (SEC) is Table 1: Basic Polymerization Mechanisms for the Synthesis of Li- v near Homopolymers. the most important technique for measuring the a) Standard Free-Radical Polymerization WMMD (Meira et al., 2005; Berek, 2010). These mea- k  Initiation I 1 2 R (8) surements may be either an absolute or relative method, c  k2  (9) according to whether or not an on-line light-scattering Rc  M  R1 Propagation  k p  sensor is included in addition to the main concentration R1  M  R 2 (10)

(or mass) detector.  k p  Rn  M  R n1 (11) The ratio D  M w / M n  1 is called the dispersity, Termination   ktd (12) dispersity index, or polydispersity (with the former term R n  R m  Pn  Pm   kt (13) being preferred by IUPAC). The following relationship R n  R m  Pnm may be proven: Transfer k R  M fm P  R (14) 2 n n 1    k  n  (7)  fs  (15) D    1 R n  S  Pn  S  M n   k ft  R n  T  Pn  T (16) where n is the standard deviation of the NMMD (an  ksm  (17a) absolute measure of the distribution breadth). From Eq. S  M  R1  S  ktm  (7), it follows that (D - 1) is a measure of the ratio be- T  M  R1 (17b) tween the absolute breadth of a NMMD and its arith- b) Living Anionic Polymerization metic mean. Thus, D increases when broadening a Initiation k1  I  M  IP1 (18) NMMD while maintaining a constant M n ; but it re- Propagation  k p  IP1  M  P2 (19) mains constant when both n and M are simultaneous- n k  p  (20) ly increased or decreased in the same proportion. Dis- Pn  M  Pn1 Termination  kt persities between 1.004 and 1.2 are typical of the nar- Pn  K  Pn (21) row MMDs produced by living anionic polymerization c) Step Growth Polymerization (Lee et al., 2000). Dispersities between 1.5 and 3.0 are Propagation * * * Pn  Pm  Pnm  E (22) typical of conventional free-radical polymerizations. Dispersities of 20 or higher are typical of polyolefins reactions with the dead polymer. Also, all the reactions obtained via Ziegler-Natta catalysts. of Table 1 have been assumed simple and bimolecular (except for Eq. 8), and irreversible (except for Eq. 22). III. IDEAL POLYMERIZATION MECHANISMS In reality, many stages of Table 1 involve complex me- IN BATCH REACTORS AND THEIR MOLAR chanisms; e.g.: the propagation steps in a gas-solid MASS DISTRIBUTIONS Ziegler-Natta coordination polymerization for the syn- Polymerization chemistry is a complex and well- thesis of polypropylene; the ring-opening polymeriza- established discipline (Carraher, 2000, Matyjaszewski and Davis, 2002, and Odian, 2004). In this review, we tion of -caprolactam for producing Nylon 6; and the shall limit to the 3 more basic and representative poly- production of primary initiator radicals at low tempera- merization mechanisms leading to linear homopoly- tures via redox initiation systems. mers: conventional free-radical (Table 1a), “living” Consider now more detailed descriptions of the reac- anionic (Table 1b), and step growth (Table 1c). tion mechanisms of Table 1; together with the resulting The Nomenclature is as follows. In Table 1a: M = MMDs and averages when such mechanisms are carried * out in isothermal and Homogeneous Batch Reactors Monomer, I = chemical initiator, R c = primary initiator * (HBRs). Figure 2 presents the typical evolutions of the radical, R 1 = activated monomer or free-radical of unit * * number-average chain length r with conversion; and chain length, R n, R m = free-radical of chain lengths n, n m, Pn = dead polymer of chain length n, S, S* = solvent Figs. 3-6 present the theoretical MMDs. For a compre- and solvent radical, and T, T* = chain transfer agent and hensive description of theoretical MMDs produced in corresponding radical. In Table 1b: M and I are as be- batch polymerizations, see Peebles (1971). * 120 fore, P n = reactive anion of chain length n, and K = * rXn () deactivating (or “killing”) agent. In Table 1c: P n = li- 100 * Free-radical near polymer molecule of chain length n, with P 1 representing the bifunctional monomer as a special case, 80 and E = condensation product (e.g.: water and metha- nol). 60

40 Note that while Tables 1a and 1b represent the basic Living schemes of chain (or monomer-growth) polymeriza- anionic 20 tions, Eq. (22) of Table 1c represents the base reaction Step-growth of a step (or polymer-growth) polymerization. Also, 0 note that the anionic mechanism of Table 1b can be 0 0.2 0.4 0.6 0.8 1 X considered as a subset of the free-radical mechanism of Figure 2. Typical evolutions of the number-average chain-length r Table 1a. Neglected in Table 1, are side reactions and n with conversion X, according to the base polymerization mechanisms. 392 G.R. MEIRA, H.M. OLIVA

-3 a) x 10 generally a small effect on polymerization rate. 7 3) The lifetime of a growing radical is 1 s or less, and r rw 6 n this period is negligible compared to the total reaction wr() 2) 1) 101.3 199 2) 72.8 141.9 time. Chain lengths result from a competition between 5 3) 56.9 110.2 rate of propagation and rates of termination; noting that

4 termination by recombination doubles the chain length of the dead polymer with respect to the growing radi- 3 cals. High molar-mass polymer is generated from the 2 1) start of the polymerization. Also, the average molar masses change moderately along the reaction, and are 1 little related to monomer conversion. When monomer 0 consumptions are faster than initiator consumptions, 0 100 200 300 400 500 600 r then the average molar masses will tend to decrease

-3 with conversion (see Fig. 2). However, such tendency b) x 10 5 may be counter-arrested by: i) formation of long chain 3) r r n w branches and/or crosslinking; and/or ii) an increased dif- wr() 1) 200 300 4 fusion control of macroradicals (the “gel” or 2) 2) 142.9 214.3 3) 111.1 166.7 Trommsdorf effect), that slows the effective rate of re-

3 combination termination with respect to propagation due to increased viscosity. Branching reactions onto the 2 1) accumulated polymer are not included in Table 1, but can be produced by propagation with the accumulated 1 polymer containing terminal double bonds and/or by in- tra- or intermolecular chain transfer to the polymer and

0 subsequent chain growth. For long-branched homopo- 0 100 200 300 400 500 600 r lymers produced by free-radical attack onto the accumu- Figure 3. Theoretical WCLDs of the instantaneously-produced linear lated polymer, several mathematical models have been dead polymer obtained in an ideal, batch, and free-radical polymeriza- developed that estimate the evolution of the distribu- tion by disproportionation or chain transfer (a), and by recombination tions of molar masses and branching; e.g.: Pladis and (b). In Fig. 2, note that conventional free-radical polyme- Kiparissides (1998), Iedema and Hoefsloot (2002) and rization enable to produce high polymers at very low Krallis and Kiparissides (2007). For a bulk free-radical monomer conversions. In contrast, in step-growth po- homopolymerization, the Tromsdorff effect on the lymerizations very high extents of reaction (or conver- evolving MMD was modelled by Verros et al. (2005). sion of the initial reactive groups) are required for ob- In the absence of branching, the instantaneously- taining a high polymer. produced MMD ideally exhibits: i) a Schulz-Flory dis- In conventional free-radical polymerizations (Table tribution with D  2 for the fraction of free-radicals 1a), there is a slow but continuous generation of primary that terminate by disproportionation or chain transfer * (Fig. 3a); and ii) a Schulz-Zimm distribution with D  initiator radicals R c, typically via homolytic cleavage of an initiator molecule such as a peroxide (Eq. 8). Not all 1.5, for the fraction of free-radicals that terminate by re- primary initiator radicals initiate a polymer chain, and combination (Fig. 3b). When both termination steps are for this reason an efficiency factor is normally intro- present, then the dispersity of the instantaneously- duced into the kinetics of Eq. (9). The decomposition produced polymer falls between 1.5 and 2. The MMD rate of the initiator is generally slow, to ensure a perma- of the total accumulated polymer is obtained by integra- nent generation of free-radicals along the reaction. The tion of the instantaneous distributions, with appropriate total concentration of free-radicals is low (in the order weighting factors. Due to the varying average molar of 10-7 M), and it results from a balance between rates masses, the final dispersity of the accumulated MMD is of generation (Eqs 8 and 9) and rates of deactivation typically 3 or higher. In Fig. 3, the curves 1) represent 2 (Eqs 12 and 13). When termination occurs by dispropor- possible initial and instantaneous WCLDs (of rn = 101 tionation (Eq. 12), two dead polymer molecules are in a; and rn = 200 in b). Then, the average molar masses generated, with one of them containing a terminal are assumed to decrease with conversion, yielding the double bond. In contrast, a single dead polymer mole- distributions of curves 2) and 3). Note that the rn values cule is produced by termination recombination (Eq. 13). of Fig. 3a double those of Fig. 3b. Chain transfer reactions can occur to the monomer M A Schulz-Flory WCLD is represented by (Flory, (Eq. 14), to the solvent S (Eq. 15), or to a specially- 1953): added chain transfer agent T (Eq. 16); and the new acti-  1   - r  vated species may or may not reinitiate a new growing 2 r1     wr  1 p r p    r exp  (23) chain. Transfer reactions terminate growing chains but  rn   rn  do not reduce the total concentration of free-radicals. where p is either an extent of reaction or a reaction Their effect is to lower the average molar masses, with probability. In Eq. (23), the first equality indicates the 393 Latin American Applied Research 41: 389-401(2011)

exact solution, and the second equality indicates a limit- molar masses, a Poisson WCLD is described by the ex- ing solution that is accurate for high values of rn (e.g.: pression: greater than 100). Similarly, Schulz-Zimm WCLDs are r r1 w r  n r exp  r  represented by (Schulz, 1939):  n rn 1 r 1 ! ; (25) r r  k  2 !  k1 r 1 r1 wr  1 p p rw 1 k 1 ! r 1 ! k p 1 p  exp- rw 1 rw r  2 ! k1 (24) r f  k 1 k 1 r    with rw = 1 + rn . Figure 4a presents 4 Poisson distribu-    exp  k!  rw   rw  tions, where the curve parameters are the number aver- where k is the degree of coupling (i.e.: the number of age chain lengths ( rn ), that increase with monomer con- independently growing chains required to form a single version. For increasing rn values, note that while the dead chain). With k = 2, D = 1.5 at high degrees of po- absolute breadth of the distributions (represented by the lymerization. With k = 1, the Schulz-Zimm distribution standard deviation n) increases, the dispersity D de- reduces to a Schulz-Flory distribution of D  2. creases. In spite of the industrial importance of conventional a) free-radical polymerizations, these mechanisms do not 0.06 enable an independent control of molecular weights and 50 polymerization rate; and are incapable of producing wr() block copolymers by sequential addition of comono- 100 mers. These limitations are at present being circum- 0.04 vented in the so-called “living” or controlled free- 200 radical polymerizations (Matyjaszewski, 2005). In these 400 novel mechanisms, termination by recombination is al- 0.02 most eliminated via introduction of additional reversible reactions that protect the growing free-radicals from each other. Ideally, controlled free-radical polymeriza- 0 tions behave as ideal “living” anionic polymerizations 0 100 200 300 400 500 in the absence of termination and with fast initiation. r Controlled radical polymerizations are incipiently being b) employed by industry for the production of specialty po- 0.04 lymers with well defined molecular structures. Con- wr() 1 trolled free-radical polymerizations are outside the 0.03 scope of this article. However, a large number of publi- 10 cations have been published on: a) their mathematical modelling (e.g.: Monteiro, 2005; Chaffey-Millar et al., 0.02 2005; Tobita, 2006); and b) on the production of tailor- made MMDs (e.g.: Kaminski-Lenzi et al., 2005 and 100 Göbelt, 2006). 0.01 In living anionic polymerizations (Table 1b), bimo- 1000 lecular termination between living ends is avoided be- 0 0 125250 375 500 675 cause anions repel each other. Typical initiators are al- r kyl lithium compounds. Unfortunately, anionic polyme- c) rizations require high purity conditions to avoid termi- 0.04 nation by impurities such as water and acids (Eq. 21). In 0 addition, anionic polymerizations are restricted to rela- 0.03 tively few vinyl monomers; and the reactions must be 1 carried out in a solution of organic solvents (that must 0.02 Living be recuperated after the synthesis). In the absence of distributions termination and with fast initiation, the total moles of 4 growing anions remain constant and equal to the initial 0.01 moles of initiator. Under these conditions, rn of the ac- cumulated polymer becomes directly proportional to the 0 0 125 250 monomer conversion (see Fig. 2), and its value is given r by the ratio between the moles of reacted monomer and Figure 4. Theoretical WCLDs of linear polymers obtained through the initial moles of initiator. Furthermore, if all the liv- ideal anionic polymerizations carried out in batch reactors. a) Poisson distributions obtained with rapid initiation and no termination. b) Gold ing ends grow simultaneously and at the same rate, then distributions of a living polymer obtained by slow initiation and no the MMDs become the narrowest possible of synthetic termination. c) WCLDs obtained with rapid initiation and termination polymers: the Poisson distributions of Fig. 4 a). At high by the “killing” agent K (Eq. 21).

394 G.R. MEIRA, H.M. OLIVA

along the reaction. In coordination polymerizations involving Ziegler- Natta, Phillips, or metallocene catalysts, the catalyst in- fluences the monomer addition during chain growth, and this affects the rates of propagation, chain transfer, and termination reactions. Ziegler-Natta and metallo- cene catalysts require activation by cocatalysts like al- kyl aluminum or alkyl aluminoxane compounds that control the oxidation state of the transition metal. The mechanism is similar to that of living anionic polymeri- zations in that the growing chains exhibit relatively long lifetimes (typically, between 100 and 106 s). Each dif- ferent catalyst has its own set of kinetic parameters. Po- Figure 5. Weight-chain length distribution of a polyolefin made with a lymers produced using heterogeneous Ziegler-Natta cat- coordination catalyst containing three different active-site types. The alysts exhibit broad MWDs, with dispersities of 10 or total distribution (of D = 16.3) is composed of 3 Schulz-Flory distribu- tions with r = 50, 600, and 3000, of weight fractions 0.3, 0.3, and higher, depending on the catalyst. These large dispersi- n ties are the result of chain transfer reactions combined 0.4, respectively. 0.04 with a multiplicity of catalyst active sites (Kissin, 1993). wr() 0.90 Under constant reaction conditions, each catalyst site produces a polymer with a Schulz-Flory distribution of 0.03 different averages, and the total MMD is a weighted combination of such individual distributions (Kissin, 1985). This situation is illustrated in Fig. 5. Soares 0.02 0.95 (2001) reviewed the mathematical modelling of polyole- fins obtained by coordination polymerization. 0.97 0.01 In its most basic level, step polymerizations are 0.99 represented by a single propagation reaction (Eq. 22 in Table 1c). For linear polymers, bifunctional monomers 0 0 50 100 150 200 250 are required, and intramolecular reactions must be r Figure 6. Schulz-Flory WCLDs of linear polymers obtained in ideal avoided. In Eq. (22), the condensation molecule E may step polymerizations carried out in batch reactors. The curve parame- or may not be generated. In its simplest form, the mo- ter is the extent of reaction (X). nomer molecule contains 2 types of reacting groups With slow initiation with respect to propagation but (e.g.: an aminoacid); and all the growing chains also ex- no killing, then the Poisson distributions turn into the hibit the same reacting groups (an acid and an amine) at Gold distributions of Fig. 4b (Gold, 1958). In Fig. 4b, their chain ends. Alternatively, 50:50 mixtures of 2 the curve parameters are the ratios kp/ki (see Eqs 18-20). comonomer types with identical reacting groups are With kp/ki = 1, the Poisson distribution is obtained. With employed. For example, in a reaction between a diamine very slow initiation with respect to propagation (kp/ki = and a diacid, the reaction mixture will contain 3 types of 1000 and higher), then the WCLD tends to a triangular molecules: aminoacids, diamines, and diacids. In the shape with D  1.33, while the corresponding NCLD case of reversible polycondensations, the equilibrium tends to a rectangular shape. can be displaced toward the high molar masses by ex- Figure 4c presents the case of a rapid initiation with traction of E (see Eq. 22). Unlike the case of chain reac- respect to propagation, but with deactivation of living tions, the monomer is rapidly consumed in step polyme- ends (Eq. 21). In Fig. 4c, all the distributions exhibit a rizations. Step-growth reactions are similar to living common rn = 125, and the curve parameters are the ra- anionic in that all the molecules remain potentially reac- tive (or “living”) while inside the reactor, and in that the tios kt/kp (see Eqs 18-20), for an initial recipe [M]º/ [K]º average molar masses increase monotonically with con- = 500. Without termination (kt/kp = 0), a Poisson distri- bution is obtained. With termination, the total WCLD version, but in a highly nonlinear fashion (Fig. 2). Ideal (in continuous trace) contains 2 fractions: a lower molar step polymerizations of bifunctional monomers produce mass tail of dead polymer (in long traces) and a high linear polymers with Schulz-Flory MMDs. Figure 6 molar mass peak of a living polymer (in short traces). presents several of such distributions at different extents At the limit when all the living ends are deactivated, of reaction. Note that (unlike the case of chain reac- then the dead polymer exhibits a Schulz-Flory distribu- tions), the unreacted monomer remains in the product, tion. Apart from the production of narrow homopoly- and it is always the most abundant species from the mers, living anionic polymerizations also enable the point of view of number (see NCLD of Fig. 1a). synthesis of ‘tailor-made’ structures such as block copo- So far, we have have presented the theoretical lymers, star copolymers, and telechelic polymers. For MMDs produced in ideal, isothermal, and homogeneous example, an ABC triblock can be obtained batch polymerizations. In spite of their industrial impor- by sequential addition of comonomers A, B, and C tance, heterogeneous processes are outside the scope of

395 Latin American Applied Research 41: 389-401(2011)

the present article. In particular, the mathematical mod- Table 2: MMDs of Linear Polymers for Different Combinations of elling of free-radical emulsion processes has been re- Ideal Polymerization Mechanisms and Reactor Types (after Hamielec and Tobita, 1992). viewed on several occasions: MacGregor et al. (1984b), Free-Radical Living Anionic Step Growth Saldivar et al. (1998), Gao and Penlidis (2002) and Batch or a) With increasing d) Poisson distr. g) Schulz- Zhang and Feng (2010). Many other heterogeneous CPFTR conversion, MMD for ki  kp, and Flory distri- processes have also been investigated. For example, Ka- in SS increasingly Gold distr. for ki < bution. broader than the kp. rode et al. (1997) modelled a heterogeneous interfacial Schulz-Zimm dis- polycondensation for the synthesis of Nylon 6,10. tribution. The mathematical modelling of polymerization reac- HCSTR b) Schulz-Zimm e) Schulz-Flory h) Much tors is useful for: a) quantifying the interrelationships in SS distr., with D be- distribution of D = broader than tween 1.5 and 2, 2. Schulz- between their numerous inputs and outputs; and b) de- according to ter- Flory distri- veloping open- and closed-loop control strategies for in- mination type. bution. creasing reactor productivity and product quality. SCSTR in c) With increasing f) Schulz-Flory i) MMD be- For producing prespecified MMDs, several alterna- SS conversion, MMD distr. at 0 conver- tween g) and tives to batch isothermal polymerizations are possible. increasingly sion and Poisson h). broader than a). distr. at 100% In a first level of flexibilization, nonisothermal batch conversion. reactions can be used (see, for example Crowley and Continuous Piston-Flow Tubular Reactors (CPFTRs) Choi, 1998, for a batch free-radical solution polymeriza- exhibit the narrowest RTDs, and in the limit they are tion of methyl methacrylate). In what follows, the use of dynamically equivalent to Homogeneous Batch Reac- semi-batch and continuous polymerization reactors will tors (HBRs), with time replaced by distance along the be considered. tube. In contrast, single Homogeneous Continuous IV. MOLAR MASS DISTRIBUTIONS in SEMI- Stirred-Tank Reactors (HCSTRs) exhibit the widest BATCH POLYMERIZATIONS RTDs. Intermediate RTDs are obtained when a single The semi-batch addition of reagents along a polymeriza- HCSTR is replaced by a series 2 or more HSTRs of the tion considerably increases the flexibility of batch reac- same total volume. tors for producing prespecified MMDs. For a free- Since HBRs are equivalent to SS CPFTRs, then ho- radical polymerization of acrylamide in aqueous solu- mogeneous semi-batch reactors are equivalent to SS tion, Kreft and Reed (2009) developed semi-batch con- CPFTRs with SS addition of reagents along the tube. trol strategies for producing multimodal MMDs. For The articles by Asteasuain and Brandolin (2007), and emulsion polymerizations, many publications have de- Asteasuain et al. (2008) are examples of SS optimiza- veloped semi-batch addition policies of reagents for tions of tubular reactors with intermediate feeds for pro- controlling the MMD and other chemical characteris- ducing tailored MMDs. For polymerizations carried out tics; e.g.: Vieira et al. (2002), Arizmendi and Leiza in tubular reactors that do not verify the ideal piston- (2002) and Srour et al. (2009). For obtaining a broad flow condition, then computational fluid dynamics MMD polyurethane without formation of gel, Zavala et (CFD) methods have been applied for simulating the al. (2005) developed a strategy that involves the addi- radial profiles of flow velocity, temperature, and poly- tions of a diol and a diamine along the reaction. mer molecular weights (Meszena and Johnson, 2001). The ability of living anionic polymerizations for In Homogeneous Batch Reactors (HBRs), the con- producing narrow MMDs with prespecified average mo- centration of reagents and products vary in time but not lar masses, make these mechanisms ideal for controlling in space. In HCSTRs operated in the SS, the concentra- the MMDs of homopolymers and of block copolymers tions remain constant both in time and in space. High with prespecified distributions in each of the blocks. For viscosity systems may cause segregation by inadequate a polystyrene homopolymer, Alassia et al. (1988) pro- mixing at a molecular level (or micromixing). Polymeri- posed a method for obtaining almost any MMD shape, zations may be segregated either due to inadequate mi- by controlled deactivation of a living anionic polymeri- cromixing or because the process itself is heterogeneous zation. The strategy involves the application of 2 simul- (e.g.: an emulsion polymerization). In an ideal Segre- taneous flow profiles: i) a monomer feed into the reac- gated Continuous Stirred-Tank Reactor (SCSTR), the tor; and ii) a reactor outlet flow into a reception vessel fluid phase is regarded as subdivided into many small where instantaneous deactivation takes place. At the end isolated compartments. Each compartment contains a of the semi-batch operation, the reactor is empty and the large number of molecules that are permanently con- reception vessel contains the required MMD (Alassia et fined within its limits. Thus, individual compartments al., 1988). function as miniature batch reactors of different resi- V. MOLAR MASS DISTRIBUTIONS IN dence times in the flow reactor. The compartments CONTINUOUS POLYMERIZATIONS themselves are assumed to be ideally mixed, and this Industry employs a large variety of batch, semi-batch, leads to a macromixing, despite total segregation of mo- and continuous polymerization reactors. For continuous lecules in the different compartments. In this case, the reactors operating in the Steady State (SS), then (for RTD for the set of compartments of a SCSTR coincides comparison reasons) it is convenient to classify them with the RTD of a HCSTR. A macroscopic mean taken according to their residence-time distribution (RTD). over all the compartments in the effluent stream and in

396 G.R. MEIRA, H.M. OLIVA

the reactor itself would show constant concentrations lymerizations, the effect of segregation is to broaden the and temperatures both in space and in time. However, a MMD with respect to a HBR of total reaction time . probe capable of microscopic sampling of individual Thus, while HCSTRs produce the narrowest possible compartments would reveal concentrations that varied MMDs (in general, a Schulz-Zimm distribution with k = in a statistical manner from one compartment to anoth- 1, 2, or both), such distributions become considerably er. broader in SCSTRs. In living anionic polymerizations, For the ideal mechanisms of Table 1, the first row of the rate of polymerization is first order with respect to Table 2 summarizes the previously-discussed results for the monomer, and therefore both the HCSTR and HBRs, or equivalently for CPFTRs operating in the SS. SCSTR exhibit the same average polymerization rates Such results are compared with the MMDs obtained in and conversions. Segregation inhibits total molecular HCSTRs and SCSTRs (second and third rows of Table mixing, whereas in a HCSTR all the molecules are dis- 2). Consider first the case of HCSTRs. According to tributed in time according to Eq. (23). In SCSTRs, Eq. Denbigh (1965), two opposing factors influence the (23) is only true with respect to the compartments, but MMDs obtained in a HCSTR. On the one hand, the con- each compartment has a large number of molecules with stant concentrations of reagents and products will tend equal residence times. Thus, the MMDs obtained in to narrow the distribution with respect to the batch. On SCSTRs with living anionic mechanisms are subject to the other hand, the broad RTD will lead to broaden the less broadening than in HCSTRs. At very low conver- MMD. In a free-radical polymerization, a growing radi- sions, the monomer concentration remains essentially cal produces a dead polymer molecule in a fraction of a constant, and the MMDs are almost identical in the 3 second, and thereafter such molecule remains inert until reactor types. At increased conversions, the effect of its reactor exit. Thus, the growing period is negligible RTD diminishes. At 100% conversion, the lifetimes of with respect to the average residence time of an indus- the active species are shorter than the mean residence trial HCSTR, the constant composition factor domi- time, and therefore the MMD tends to the distribution of nates, and a relatively narrow MMD is produced. This a HBR. At intermediate conversions, the MMDs ob- distribution coincides with the MMD instantaneously- tained in SCSTRs with ideal living anionic mechanisms produced in a HBR for the same concentrations of rea- are intermediate between Schulz-Flory and Poisson. gents and products. If however branching reactions with This intermediate distribution is similar to that obtained the accumulated polymer were admitted (not considered in batch anionic polymerizations with termination and in Table 1), then the accumulated polymer would re- rapid initiation (see Fig. 4c). Finally, consider the case main reactive while inside the reactor, and the RTD of step-growth polymerizations carried out in SCSTRs would considerably broaden the MMD with respect to operating in the SS. Segregation reduces the amount of the HBR. When eithe a step-growth or a living anionic polymer with very high or very low molar mass, and polymerization is carried out in a HCSTR, then the therefore the molar mass dispersities obtained in chains continuously grow while inside the reactor, and SCSTRs are between the limiting values obtained in the growth is assumed to stop at the reactor outlet. Thus, CPFTRs/BRs and HCSTRs. the lifetimes of the growing chains are directly affected Random copolymers are generally obtained by by the RTD, and the resulting MMDs are considerably chain-growth copolymerization, with intermediate prop- broader that in HBRs. With ideal anionic polymeriza- erties with respect to their parent homopolymers. Nor- tions, the MMDs vary from Poisson- or Gold- distribu- mally, the aim is to produce narrow Chemical Composi- tions in HBRs, to Schulz-Flory distributions in tion Distributions (CCDs); and to this effect the compo- HCSTRs. In spite of this large increase in the distribu- sition must be maintained constant along the reaction. tion breadth, single HCSTRs are commercially em- Except for the few examples where the reactivity ratios ployed for living anionic polymerizations, due to the of both comonomers are close to unity, batch reactors higher efficiencies of HCSTRs with respect to HBRs, generally produce broad CCDs, due to varying copoly- together with a reduced contamination by impurities in a mer compositions along the reaction. Several strategies more closed and controlled environment. In contrast, have been proposed to solve this problem. For example, single HCSTRs are not employed with step polymeriza- the comonomers mixture can be slowly added along the tions because: i) very high conversions are required for batch reaction to induce a starved semi-batch policy, high polymers, and this would imply unacceptably high with almost complete instantaneous conversion of both viscosities in bulk polymerizations; and ii) extremely comonomers. However, a simpler solution is to carry broad MMDs are produced, and for example for rw  out the copolymerization in a HCSTR. In this case, a 1000, the dispersity is over 40!. constant copolymer composition is ensured by the con- Finally, consider the SS operation of SCSTRs (last stant concentrations of reagents and products. row of Table 2). Each individual compartment works as VI. MONITORING AND CONTROL OF a miniature batch reactor, and the global RTD E(t) coin- POLYMERIZATION REACTORS cides with the RTD of a HCSTR, i.e.: Commercial polymerizations aim at obtaining consistent 1  t polymer properties at increasing productivities, in safe Et  e  (26)  and economical operations. Polymerization processes typically consist of 3 stages: preparation, polymeriza- where  is the mean residence time. In free-radical po- 397 Latin American Applied Research 41: 389-401(2011)

“Chemical” Polymer Quality Variables 1) Free PS molecular weights Polymerization Process Input Variables 2) Morphology: 1) Reaction design (reactor types, recycles, etc.) i) “Salami”, ‘core-shell’, etc. 2) Recipe: ii) Average diameter i) PB or St-Bd block copolymer iii) Occlusions ii) PB microstructure and branching  iv) Grafting efficiency iii) PB weight % 3) Volume fraction and degree of crosslinking iv) Thermal/chemical initiation 4) Weight % of rubber and additives v) Initiator (type, functionality, mean time) vi) Mineral oil, solvent, antioxidant 5) Residual monomer and volatiles. vii) CTA, impurities, colorant  Structure-Property Interrelationships 3) Reaction conditions: i) Temperature profile “Physical” Polymer Quality Variables ii) Stirring rates 1) In the melt: iii) Internal oil recycle i) Melt flow index and viscosity iv) Volatiles recycle 2) In the solid: 4) Devolatilization conditions: i) Tensile strength i) Preheater temperature  ii) Toughness and impact resistance iii) Heat distortion temperature ii) Vacuum iv) Gloss and transparency v) Environmental stress crack resistance

Figure 7. Main process variables of a bulk polymerization of styrene in the presence of polybutadiene for the production of high-impact polystyrene (HIPS). The input variables are in the left column, and the polymer quality variables are in the right column. The “chemical” quality variables (or polymer microstructure) are closely associated with the polymerization stage, while the “physical” quality variables (or macroscopic polymer characteristics) define the processability and end-use properties of the material. The quality variables may be further modified in the final article by addition of additives and loads and through processing operations such as injection molding. (Taken from Meira et al., 2007). tion, and separation. In the preparation stage, the rea- The need of monitoring is obvious in polymerization gents are purified and mixed. The purification of mo- processes; and in particular rapid on-line monitoring is nomer and initiator are vital operations, since small highly desirable for an effective quality control. How- amounts of impurities can importantly affect the reac- ever, most quality measurements such as composition, tion. In the polymerization stage, the heat exchange and particle size, or melt flow index (MFI) are carried out the system viscosity play crucial roles that affect not on- off-line, and in a discontinuous fashion. Furthermore, ly the (mass, heat, and momentum) balances, but also many important variables such as average molar masses the quality of the mixing and the RTD. In the final sepa- and degrees of branching are generally not measured at ration stage, the required polymer purity and state is all, not even off-line. achieved through appropriate thermal and mechanical The problems of reactor productivity and selectivity, operations that include recycling the unreacted mono- process stability and safety, transient control, and start- mer and solvent. Even though the main mechanical, up procedures should be taken into consideration at the physical and chemical properties of a polymer are ac- design stage. Reactor productivity studies aim at in- quired at the reaction stage, further modifications can be creasing the final monomer conversion without affect- introduced during the separation stage and processing. ing quality, and at reducing the off-spec product gener- Several articles have comprehensively reviewed the ated in transitions between steady-states. Reactor selec- field of monitoring and control of polymerization reac- tivity studies aim at improving polymer quality. tors; e.g.: Mac Gregor et al. (1984a), Eliçabe and Meira For an effective reactor design, optimization and (1988), Richards and Congalidis (2006) and Hukkanen control, the results of costly experimentation must be et al. (2007). This last section is a short introduction in- combined with simulation results from representative to such field, with emphasis on the control of molar mathematical models. Mathematical models also help in mass averages and distributions. quantifying the numerous interrelationships between the Polymerization reactors are highly multivariate dy- process inputs and outputs. Mathematical models may namical systems, and the complex interrelationships be- be derived from detailed (mass and energy) balances, or tween their inputs and outputs are in many cases only through empirical input-output (or black-box) tech- scarcely known. For example, Fig. 7 lists the numerous niques. Detailed balances for batch or HCSTRs general- variables involved in the quality control of a bulk poly- ly consist of sets of non-linear, time-invariant, ordinary merization of styrene in the presence of polybutadiene first-order differential equations combined with sets of for the production of high-impact polystyrene (HIPS). nonlinear algebraic equations, such as: The input variables (left-hand side of Fig. 7) are select- dxt  fxt ,u t ,d t (27) able or modifiable by the design or process engineer. dt The output quality variables (right-hand side of Fig. 7) y t  h x t ,u t (28) have been classified into “chemical” and “physical”.        “Chemical” variables are closely related to the polyme- where x(t) is an n-vector of states, u(t ) is an m-vector rization process. “Physical” variables constitute the base of controls or manipulated variables, d(t) is a k-vector material specifications for its processability and end-use of disturbances, and y(t) is a p-vector of measured out- performance. puts. Equations (27) and (28) are known as the state and 398 G.R. MEIRA, H.M. OLIVA

measurement equations, respectively. The state vector producing random copolymers of narrow CCDs. x(t) provides information on the time trajectories of the In living anionic and step polymerizations, the grow- most important reactor variables such as concentrations ing chains remain active while inside the reactor; and of reagents, moments of the MMD, temperature, etc. for this reason HBRs (or SS CPFTRs) yield the narrow- Due to the complex and highly nonlinear nature of est possible MMDs. These distributions are broadened Eqs (27) and (28), the monitoring, optimization, and when the reaction is carried out in a single HCSTR op- control of polymerization reactors present many chal- erating in the SS, due to its broad RTD. For this reason lenging problems. Most industrial control practice is and for the extremely high conversions (and viscosities) centered on batch reactor sequencing, and on the control required, bulk step polymerizations are not carried out of global variables such as temperature and monomer in single HCSTRs. conversion. To this effect, reactor energy balances are MMDs of any prespecified shape can in principle be useful to infer polymer production rates and monomer produced by appropriate addition of narrow MMDs of conversion. In addition, many academic articles have controlled averages. The opposite (i.e.: the narrowing a focused on the quality control of polymerization reac- broad distribution by post-reaction operations) is techni- tors through the development of optimal operating poli- cally unviable for commodity polymers. Thus, living cies for batch, semi-continuous, and continuous reac- anionic polymerizations carried out in semi-batch reac- tors. Since most of such control policies are open-loop, tors present an unsurpassed flexibility for controlling then the real plant performance becomes totally depen- molecular weights, but this advantage is counterarrested dent on the accuracy of the employed mathematical by the experimental difficulties associated with the ex- model. In spite of the important advances in process treme purities required to avoid deactivation of the liv- control (in particular of nonlinear systems), there are ing ends. In the case of polyolefins produced by Ziegler- relatively few successful industrial applications of such Natta catalysis, the flexibility of living anionic polyme- novel techniques. Two illustrative examples of multiva- rizations is lost, due to the multiplicity of catalyst active riable and nonlinear control of free-radical polymeriza- sites that result in very broad MMDs and CCDs. This tions carried out in CSTRs are given in Prasat et al. difficulty is at present partially overcome with the de- (2002) and González and Álvarez (2008). velopment of single-site metallocenic catalysts, where The periodic operation of continuous polymerization MMDs dispersities as low as 2 have been produced. reactors has been investigated in several opportunities Polymerization models are helpful for systematizing as a means of modifying the molecular characteristics of the interrelationships between the numerous inputs and the obtained polymers with respect to those obtained in outputs of an industrial plant. Their ultimate goal is the the SS (Silveston, 1998). For example, free-radical po- a priori calculation of the required recipe, reactor condi- lymerizations carried out in HCSTRs with periodic feed tions, and control procedure for increasing productivity flows of the monomer and the initiator in phase opposi- while simultaneously improving polymer quality. In tion can be used to broaden the MMD with respect to theoretically-developed open-loop strategies, the use of that obtained in the SS (Meira et al., 1979). In contrast, feed-back control loops is helpful for compensating the periodic operation of the initiator and monomer model errors as well as experimental unknowns such as feeds of a living anionic polymerizations enable to pro- the concentration of impurities. duce controlled ’s combined with dispersities both M n ACKNOWLEDGEMENTS above and below the SS value of 2 (Vega et al., 1991). The authors acknowledge the financial support received VII. CONCLUSIONS by CONICET and Univ. Nac. del Litoral (Argentina), The industrial production of synthetic polymers is and by CONDES-LUZ and Univ. del Zulia (Venezuela). among the most complex processes of the chemical in- dustry. In addition, the molecular characterization of the REFERENCES obtained polymers is complex, due to the various distri- Alassia, L.M., D.A. Couso and G.R. 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Received: October 16, 2010 Accepted: February 11, 2011 Recommended by subject editor: Pedro Alcântara-Pessôa

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