R a t e s

o f

P o l y m e r i z a t i o n

A v e r a g e

M o l e c u l a r

W e i g h t

a n d

D e p o l y m e r i z a t i o n ,

W e i g h t s ,

D i s t r i b u t i o n s

o f

a n d

M o l e c u l a r

P o l y m e r s

L. H . Peebles, Jr. Chemistry Division, Naval Research Laboratory, Washington, DC, USA

A. Introduction 11-339 B. Reference Tables for the Calculation of Rates of Polymerization, Average Molecular Weights, and Molecular Weight Distributions of Polymers for Various Types of Polymerization 11-340 Table 1. Addition Polymerization with Termination 11-341 Table 2. Addition Polymerization - "Living" Polymers with Partial Deactivation II-344 Table 3. Linear Condensation Polymerization without Ring Formation II-346 Table 4. Equilibrium Polymerization II-347 Table 5. Nonlinear Polymerization Systems II-348 Table 6. Degradation of Polymers - May be Accompanied by Crosslinking II-350 Table 7. Influence of Reactor Conditions and Design on the Molecular Weight Distribution II-352 C. Some Distribution Functions and Their Properties II-352 1. Normal Distribution Function (Gaussian Distribution) II-353 2. Logarithmic Normal Distribution Function II-353 3. Generalized Exponential Distribution II-354 4. Poisson Distribution II-354 D. Molecular Weight Distribution in Condensation Polymers: The Stockmayer Distribution Function II-354 E. References II-356

A.

INTRODUCTION

An attempt is made to present a systematic guide to the literature dealing with rates of polymerization, average molecular weights, and molecular weight distributions of polymers for various types of polymerization. This chapter is based on a review of molecular weight distributions (1) in which many of the equations are given in detail along with

graphs showing the interrelationship among various distributions; here, we present only references to the literature. In addition, sections have been added on the effects of degradation and reactor design on the reaction rates and the molecular weight distributions. Literature references beyond (312) are those that have been added since the third edition of Polymer Handbook. The theoretical description of the molecular weight distribution of a polymer and its rate of polymerization is dependent on the assumed mechanism of polymerization and on the mathematical simplifications used to obtain analytical expressions. As the number of distinct reactions is increased, such as the various transfer reactions, the mathematical expressions can become quite complex and unwieldy. In general, the equations for the rate of polymerization are the most difficult to describe, the distribution equations are somewhat easier, and the average molecular weights the simplest. In condensation polymerization, many of the distribution formulas are derived by considering the statistics or the probability of a given reaction instead of the kinetics of the reactions. Depending on which assumptions are made, quite different average molecular weights are derived, despite the rigor of the derivation. The emphasis in this section is, therefore, on the distribution functions and their averages; the rates of polymerization are given only if they have been explicitly derived. This chapter is divided into several tables and sections, each treating various types of polymerization. The Stockmayer distribution function for condensation polymers is given in detail because of its general applicability and usefulness. Some general distribution functions are given in Section C. For all the other expressions, the reader must refer to the original literature. Many of the simpler functions are adequately described in textbooks of polymer chemistry. Flory (2), Bamford et al. (3), Odian (4), Billmeyer (5), and Kuechler (6) give extended descriptions of many systems. Bagdasarian (7) gives an extended discussion of methods of determining absolute values of propagation and termination constants, the influence of cage effects on the rate of initiation, and the influence

of retardation, inhibition, and diffusion-controlled termination on the rate of polymerization. A review of the various ways of deriving molecular weight distributions and the moments of a distribution is given by Chappelear and Simon (8). Section B presents a series of tables describing the main assumption or conditions imposed on the theoretical models and references to the articles where the corresponding equations may be found. Tables 1 and 2 present rate equations and the distribution formulas for addition polymerization by a variety of mechanisms. No distinction is made among free radical, cationic, anionic, or coordinationtype polymerization. While Table 1 treats those cases where termination reactions predominate and where steady-state assumptions are usually made, Table 2 treats those cases where termination reactions either do not exist, or may be considered as side reactions, having a minor to major control over the molecular weight distribution. The sequence length distributions for addition-type copolymers are omitted. However, see Kuechler (6) for an extended discussion of copolymerization distributions. Table 3 contains distribution formulas for linear condensation polymers in which the polymer is assumed to be perfectly linear and to contain no rings. Table 4 treats equilibrium polymerization. Table 5 describes nonlinear systems. Table 6 treats those cases where polymers are degraded (or altered) by the application of heat, light, or ionizing radiation. In the latter case, the polymer may undergo scission, crosslinking, or both reactions simultaneously. Several references on crosslinking are included here but not in Table 5. Finally, Table 7 is concerned with the influence of reactor design on molecular weight distribution; the kinetic equations for addition polymerization (with and without termination) and condensation polymerization are considered. Section C lists a number of distribution functions and their properties. Among them is the generalized exponential function which is a good approximation to many real systems (Eq. C29). Section D presents the Stockmayer distribution function for condensation polymerization wherein molecules of various types of kind A react with molecules of various types of kind B. B. REFERENCE TABLES FOR THE CALCULATION OF RATES OF POLYMERIZATION, AVERAGE MOLECULAR WEIGHTS, AND MOLECULAR WEIGHT DISTRIBUTIONS OF POLYMERS FOR VARIOUS TYPES OF POLYMERIZATION

The following symbols are used in this chapter. Rv: rate of polymerization; R^: rate of depolymerization; R\: active, growing polymer containing one monomer unit; R^ and Q*: active, growing polymer chains containing n monomer units; Pr: molecular weight distribution; U1: rate constant for initiation; kv\ rate constant for propagation; /: initiator concentration; M: monomer concentration; Mn and Mw: number-average and weight-average molecular weights,

respectively; 1° and 2° represent first and second order, respectively. No distinction is made among free radical, cationic, anionic, or coordination-type polymerizations. The rate of initiation may be held constant (const) throughout the polymerization, or it may depend on some function of the catalyst and monomer concentrations, or it may be instantaneous (instant), in which case only the total number of initiating species need be known. The rate of propagation is normally only the consumption of monomer; in some cases, the rate of propagation through terminal or pendant double bonds is also considered. Transfer reactions may occur to initiator, momomer, solvent, or polymer. Termination of active species may occur by a first-order deactivation, by second-order combination (comb) or disproportionation (disprop), or not at all ("living" polymers). Confusion exists over the meaning of the transfer-tocatalyst reaction. In free radical systems, it means transfer of the active species to the initiator by a second-order mechanism. In ionic polymerization, it means the expulsion of an active fragment from a growing chain by a first-order mechanism to form dead polymer and an active initiator fragment. The first-order mechanism is called here the "catalyst expulsion reaction" (cat ex). The nomenclature of distribution functions can be quite confusing. In this work, the Flory distribution (Eq. C41) is also known as the Schulz-Flory distribution, the "most probable" distribution, and the exponential distribution. The Schulz distribution (Eq. C36) is also known as the Schulz-Zimm distribution or the generalized Poisson distribution; at large values of k it approximates the Poisson distribution (Eq. C48). The Pearson Type III distribution is a variation of the Schulz distribution. If an addition polymer is made at constant monomer concentration, no transfer reactions occur, termination is only by second-order combination, and the distribution of the polymer is described by the Schulz distribution with k — 2. This distribution is sometimes called the self-convolution distribution or the convoluted exponential distribution. In a uniform distribution, all molcules have the same size - it is monodisperse. A rectangular or box distribution has no molecules below ra, an equal number (or weight) of molecules between r a and Tb, and no molecules whose size is above r\>. In Table 5, systems are treated where branching reactions, ring formation, or gel formation may occur. See also Table 6 for crosslinking reactions during degradation. The symbol RA/ means a monomer containing/reactive A units. The problem of calculating the species distribution of polyfunctional condensation polymers where branched, cyclic, and crosslinked species can be formed is exceedingly complex. Most treatments apply the restriction that ring formation does not occur prior to the gel point, which obviously is incorrect. The restriction is invoked because of the transition from the pre-gel condition, where all unreacted functional groups can react without steric limitations to a condition containing rings in which some of the unreacted groups are sterically unable to react with all of the remaining unreacted groups. The problem is

further compounded because each different reacting monomer will have various degrees of steric hindrance. Therefore, a general treatment must ignore this aspect. An examination of the Stockmayer distribution function in Section D shows that in-depth calculations are required even for simple oligomer species. A number of attempts have been made to provide simpler expressions for the number or weight of individual species and the average

molecular weights before and after the gel point. These include the theory of stochastic processes (271), stochastic graph theory (272), the theory of cascade processes which is based on probability generating functions (151), the use of link distribution functions (273), the recursive nature of branching processes and elementary probability laws (274), Monte Carlo methods (275), graph theory (276), and a kinetic approach (277).

TABLE 1. ADDITION POLYMERIZATION WITH TERMINATION References Set

Initiation

Monomer

Transfer

Termination

Rp

Pr

Mn,M^

1.1. INVARIANT MONOMER CONCENTRATION 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5

Const Const Const Const Const

None Monomer, solvent Monomer, solvent Activator None

2° Disprop or comb 2° Disprop 2° Disprop and comb 2° Comb 2° With catalyst; redox system

1.1.6

Const Const Const Const, redox Const, initiation by activator kxM2

2-4 2,3,10-12 3 13 14

1-4 1-3 1,3 13 -

1-4 1-3 1,3 13 14

Const

2° Term

15

-

15

1.1.7

Instant

Const

Dimer, Monomer Initiator None

2° Term; 1° or 2° reactivation

16

-

16

1.2. VARYING MONOMER CONCENTRATION, NO TRANSFER-TO-MONOMER REACTION 1.2.1 1.2.2 1.2.3 1.2.4

Const Const Photosensitized Const

Varies Varies Varies Varies

None Solvent None None

2° Comb or disprop 2° Comb and disprop 2° Disprop 2° Disprop and comb pseudo 1° with scavenger

3 3 39 17 (rate of scavenger

1,3 1,3 1,3 1,3 39 disappearance)

1.3. VARYING MONOMER CONCENTRATION, TRANSFER-TO-MONOMER REACTION OCCURS 1.3.1 1.3.2 1.3.3 1.3.4 .3.5

Const Const k{M2 kxMl Instant

Varies Varies Varies Varies Varies

Monomer, solvent Monomer, solvent Monomer Monomer, initiator Monomer

2° Disprop or comb 2° Disprop and comb 2° Comb and disprop 2° Disprop; degradative chain transfer Non-steady state conditions, term by comb or disprop

3,18 3,4 20 313

1,3,18 1,3,4 313

1 19 1,3,4 20 313

1.4. 1° TERMINATION OR DEACTIVATION, STEADY-STATE KINETICS 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6

Const kiMI k-xM2 kiMI k-M1 kiMI

Const Const Const Varies Varies Const

Monomer Monomer, solvent Monomer Solvent None None

1° Deactivation 1° Deactivation 1° Deactivation 1° Plus solvent term 1° Deactivation Deactivation by init. expulsion

4 1,4 1,4 4 1.4,21,22 1,4,21,22 4 1,4 1,4 4,23 1,4 1,4 4,23 1,4 1,4 21 1,21 1,21

1.5. TERMINATION BY 2° REACTION WITH MONOMER, STEADY-STATE KINETICS 1.5.1 1.5.2 1.5.3 1.6. 1.6.1 1.6.2 1.6.3

Const kiMI Const

Varies Varies Const

None Monomer Monomer

2° With monomer 2° With monomer 2° With monomer

None Monomer Monomer

2° Disprop 2° Disprop 2° Comb; two active chains couple to form a chain with two active ends

4,23 23 4

1,4 1 1,4

1,4 1 1,4

3 3

1,3 18 1,3

1,3 18 1,3

TWO ACTIVE ENDS PER CHAIN Const Const Const

Const Const Const

1.7. SLOW EXHAUSTION OF INITIATOR, NONSTEADY-STATE KINETICS 1.7.1 1.7.2

kj kj

Const Varies

None None

2° Disprop* or comb 2° Comb

25*,26 27

-

1,25*,26 27

*Data belong together.

References page II - 356

TABLE 1. cont'd References Set

Initiation

Monomer

Transfer

Termination

Rp

Pr

Afn, Mw

1.8. DEAD-END POLYMERIZATION, RAPID DECAY OF INITIATOR, MONOMER CONCENTRATION INVARIANT 1.8.1 1.8.2

kj kj2

Const Const

Monomer, solvent None

2° Disprop or comb 2° Disprop or comb

28 28

1,28 1,28

1,28 1,28

30 30 31

-

1,19* 1 -

40 41

-

-

1,2,3,4,10 32,33 239

34

1,35

239

239

315 -

316

316

37*

1,36

27 42 240 241

240 241

242

242

242

243

243

243

317

-

317

-

1,38

1.9. DEAD-END POLYMERIZATION, SLOW DECAY OF INITIATOR, MONOMER CONCENTRATION VARIES 1.9.1 1.9.2 1.9.3

kj kj kJM

Varies Varies Varies

Monomer, solvent Monomer, solvent None

1.9.4 1.9.5

Instant Redox

Varies Varies

Monomer None

2° Disprop * or comb 2° Comb 1° Term, bimolecular monomer addition. /* and R) do not terminate 1° Term, or 2° with monomer 2° Term

1.10. COPOLYMERIZATION: TWO DIFFERENT MONOMERS PRESENT 1.10.1

Const

Const

Monomer

2° Disprop or comb

1.10.2

Const

Varies

None

1.10.3

Const

Const

None

1.10.4 1.10.5

Const Varies

Const Varies

None Agent

Diffusion controlled and inversely proportional to viscosity Rate const for term is known as fn(conc). Comparison of cross term parameter ^ Alternating copolymerization Various; Monte Carlo calculations; initiation and term influences composition

314

1.11. DIFFUSION-CONTROLLED TERMINATION (see also 1.10.2 and 5.1.4) 1.11.1

Const

Varies

None or solvent*

1.11.2 1.11.3 1.11.4 1.11.5

kj Const kj kj

Varies Varies Varies Varies

None None Monomer None

1.11.6

k[

Varies

None

1.11.7

k{

Varies

Monomer, solvent

1.11.8

kj or none

Varies

Monomer, solvent

1.11.9

Const

Const

Solvent

2° Disprop or comb* and diffusion controlled 2° Comb, Rt = ktMn,n > 1 2° Process 2° Disprop and diffusion controlled 2° Disprop and comb, diffusion controlled 2° Disprop, term rate for long chains depends on entanglement density 2° Disprop, term rate for long chains depends on entanglement density 2° Comb, and disprop term depends on free volume or free volume plus entanglement, CaIc. of gel point kt^m) = ko(nm)~a. Term by comb and disprop.

27

318

1.12. PRIMARY RADICAL TERMINATION 1.12.1

Const

Varies

Monomer

1.12.2

Const

Const

None or init. and monomer*

2° Comb and disprop and primary radicals 2° Term and primary radicals

38 33,43-45

- 44,45,15*

1.13. MIXED SPECIES PROPAGATION 1.13.1

Const

Varies

Monomer

1.13.2

Const

Const

None

1.13.3

Const

Varies

None

*Data belong together.

Propagation, transfer and termination rates depend on species type, i.e. free radical and cationic occurring simultaneously Zwitter-ion polymerization; distance between ions varies as r 3/2 , equilibrium between free and solvated ions; 1° term Bifunctional initiator, term by comb

46 244

46 244

244

47

-

47

319

-

319

TABLE 1. cont'd References Set

Initiation

Monomer

Transfer

Termination

Rv

Pr

Mn,Mw

1.14. EMULSION POLYMERIZATION (see also Tables 2 and 7) 1.14.1

Const

Const within particles

None

1.14.2

Const

None

1.14.3

Const

1.14.4

Const

Const within particles Const within particles Const within particles

1.14.5

Const

1.14.6

Slow and const

1.14.7

Const

1.14.8

None Monomer

Const within Monomer particles varies outside Const None None

Const

Const within particles Const

1.14.9

Varies

Varies

Minimize

1.14.10

Const

Const within particles

Monomer, agent

1.14.11

Const

Monomer, agent

1.14.12

Varies

Const within particles Varies

1.14.13

Const

Const

None

1.14.14

Const

Const

None

None

Monomer

General theory; particles act as independent units; 2° term within particles; number of particles remain constant; number of radicals per particle General theory; Slow-term rate within particles Inst. term within particles; number of particles varies Normal 2° term within particles; rapid interchange between phases of small-sized radicals; number of radicals per particle Rapid exchange between phases of small-sized radicals; term in aq phase and in particles Slow 2° comb; calcn. of number of radicals per particle Const number of particles; term by 2° comb Inst term on entering a particle; const number of particles Adjust initiation and term rates while minimizing transfer to obtain "monodisperse" polymer Instant 2° term when a free radical enters a particle containing two growing chains and reacts with one of them. No term by disprop or comb within particles Same as case 1.14.10 but plus term by disprop or particle by comb Varying rate of entry, desorption of oligometic radicals, term by comb and disprop, Monte Carlo simulation model Any number of chains per particle, 1° term, 2° term by disprop or by comb. Use of Markov chains See 1.14.13. Copolymerization, chain composition distribution

48-54

-

53

55

-

55

56

-

-

-

59

59

60

-

60

-

-

61

72

72

72

245

245

245

245

245

245

-

320

-

-

321

-

322

62

62

62

63

-

63

-

-

68

-

68

69

-

69

57

58

1.15. HETEROGENEOUS POLYMERIZATION 1.15.1

k[MI, I varies

Varies

Monomer

1.15.2

Instant

Varies

None

1.15.3

Const

Const

None

1.15.4

Const

Const

None

Polymerization in monomer rich and monomer poor phases; 2° disprop Term by precipitation onto growing solid particle 2° Comb, 1° occlusion onto particle surfaces, and primary radical term 2° Term in liquid phase, 1° radical precipitation, propagation and 2° term at solid-liquid interface

64 65

1.16. INHIBITION AND RETARDATION 1.16.1

Const

Varies

None

1.16.2

Const

Const

Inhibitor

1.16.3

Const

Const

Retarder

2° Term, 2° addition to inhibitor 2° Term, inhibitor term, inhibitor coupling 2° Term, retarder reinitiation and term

3,66,67,73

References page II - 356

TABLE 1. cont'd References Set

Initiation

Monomer

Transfer

1.16.4

Const

Const

Retarder

1.16.5

Const

Const

Retarder

1.16.6 1.16.7 1.16.8 1.16.9

Const Const Const kj

Const Varies Const Const

Retarder None Inhibitor Inhibitor

1.17.

Termination 2° Term, retarder reinitiation, term and coupling 2° Term, rate of transfer equals rate of reinitiation 2° Term, copolymerization of retarder Pseudo 1° with scavenger 2° Disprop, 2° reaction with inhibitor 2° with inhibitor or with monomer to assess the efficiency of initiation

^p

Pr

Mn, Mw

3,12,70 71,74 10

-

-

-

-

11 17 75 246

-

11 75 -

-

-

247

-

323

-

324

324

324

-

325

-

POLYFUNCTIONAL INITIATOR WITH VARIOUS THERMAL STABILITIES

1.17.1

k\Ml On raising the temp., other peroxide groups can initiate

1.18.

Const

None

2° disproportionate

PERIODIC MODULATION OF TERMINATION OR INITIATION

1.18.1

Const

Varies

None

1.18.2

Varies

Varies

None

1.18.3

Varies

Varies

None

Periodic modulation of term by disprop by addition of an inhibitor or by magnetic or electric fields Periodic modulation of initiation, term by comb and/or disprop, computer calculation Periodic modulation of initiation, term by comb. Calcn. of MWD by generating functions

TABLE 2. ADDITION POLYMERIZATION - "LIVING" POLYMERS WITH PARTIAL DEACTIVATION References Set 2.1.

Initiation

Monomer

Transfer

Termination

kpMI

Varies

None

None

2.1.2

kpMIt

Varies

None

None; initiator added at a constant rate

None

None

2.2.1 2.3. 2.3.1 2.3.2 2.3.3

2.3.4 2.3.5 2.3.6

2A. 2.4.1 2.4.2

Pr

Mn^Mw

103

1,2,101, 102 -

1,2,101, 102 103

102, 104

1,102

1,102

THE POISSON DISTRIBUTION: Jc1 = kp

2.1.1

2.2.

Rp

2,101,102

THE GOLD DISTRIBUTION: Zt1 + kp kiMI

Varies

PARTIAL DEACTIVATION BYA 1° PROCESS OR A 2° PROCESS WITH AN IMPURITY Instant Instant Instant initiator has two active sites Instant Instant Instant

Varies Varies Varies

None None None

1° or 2° Rate of term//?p = const. Rate of term//?p = const.

Varies Varies Const

None None None

Rate of term independent of Rp 1° at infinite time Probability that a chain will terminate rather than propagate is kt/kvM

105 1,106 1,106 - 1,106,107 1,106,107 1,107 1,107

1,106 108,109 -

-

1,106 108,109 248

MULTIPLE PROPAGATING SPECIES: R*n CAN TRANSFORM INTO Ql, ETC. Instant kiMI

Const Varies

None None

None, two propagating species None, two propagating species

1, 77-79

76 1,77,78 80

76 1,77-80

TABLE 2. cont'd References Set

Initiation

Monomer

Transfer

2.4.3 2.4.4

Instant Activated monomer addition

Varies Varies; volume also varies

None None

Termination None, multiple propagating species None; two prop constants kp can increase

Rp

Pr

Mn, M ^

249 -

249 326 327

249 326 327

82,83 84

1,81 81

1,81 83

2.5. SIMULTANEOUS POLYMERIZATION AND DEPOLYMERIZATION 2.5.1 2.5.2 2.5.3

kiMI kiMI JcpM2

Const Varies Varies

None None None

None None None

2.6. THE kp VARIES WITH CHAIN LENGTH (see also 2.4.4, 3.3, and 3.4) 2.6.1

2.6.2 2.6.3 2.6.4 2.6.5

kiMI Varies None None (a) all propagation constants (kT) are different 1,85,86 (b) ki : ki : k2 : k3 :~-kn=m : (m - 1) : (m - 2) : (m - 3) : • • • 1,85 (C) * i ^ * 2 - - - ^ m = W i = ••• = *» 1.85 1,85 (d)*i^*i^*2=*m 1,85 Instant, kx = k2 • • • = km,km+l, etc.= 0 86 86 86 Instant, kp is a linear decreasing function of r 86 86 86 Const Varies None None; kv for monomer, dimer, and 328 328 trimer different from remaining molecules Rate constants can vary with extent of conversion; determination of rate constants from Pr and the use of generating functions; termination by monomolecular decay, disprop and/or comb. 329 -

2.7. DEACTIVATION BY TRANSFER TO MONOMER 2.7.1 2.7.2 2.7.3

kxMI Instant Instant

Varies Varies Varies

Monomer Monomer Monomer

None None None, two active ends per initiator

1,87 1,74,90 1,91

1,87 1,74,87,88 1,89,90 1,74,90 1,91,92 1,91

2.8. DEACTIVATION BY SLOW 1° TERMINATION 2.8.1 2.8.2

Instant Instant

Varies Varies

None Monomer

Slow 1° Slow 1°, at infinite time

1,74 1,74

-

1,74 1,74

None 1° term None

67 250

250

1,93 67 250

95

2.9. DEACTIVATION BY INITIATOR EXPULSION REACTION 2.9.1 2.9.2 2.9.3

Instant kiMI Instant

Varies Varies Varies

None Monomer Monomer

2.10. DEACTIVATION BY DEGRADATIVE CHAIN TRANSFER 2.10.1 2.11. 2.11.1

kiMI

Varies

Degradative transfer to polymer

None

94

-

Varies

None

None

-

96

None; diffusion of monomer through solid polymer 2° Term with monomer; diffusion of monomer through solid polymer Sorption and desorption of chains from the surface; slow 1° term which depends on chain length

97

-

97

98

-

98

-

99

99

100

-

100

COPOLYMERIZATION Instant

2.12. HETEROGENEOUS POLYMERIZATION 2.12.1

Instant

Varies

None

2.12.2

Instant

Varies

None

2.12.3

Const

Const

None

2.13. SPONTANEOUS POLYMERIZATION 2.13.1

Const

Const

None

Vinyl compound and activator form monomer; monomer both initiates and propagates; no term

References page II - 356

TABLE 2. cont'd References Set 2.14.

Initiation

Rev 2° with monomer

k[MI

2.15.2

kM

Const

Monomer

No termination; dead species in equilibrium with living species, irreversible propagation

251

252

Numerical method for calc. of MWD with mono- or polyfunctional transfer agent. Latter leads to branching.

-

330

3-State mechanism consisting of two successive equilibria Equilibrium between dormant aggregated polymer and "living" polymer

-

-

331

332

-

-

-

-

334

-

-

335

SLOW EQUILIBRIA

Varies

Varies

None

POLYMER MICROSTRUCTURE

2.17.1

Varies

Varies

None

2.17.2

NA

NA

NA

TABLE 3.

LINEAR CONDENSATION POLYMERIZATION WITHOUT RING FORMATION

3.7

251

-

2.16.2

3.6

251

-

None

3.5

Mn,Mw

No termination. Transfer creates dead polymer and active initiator

Varies

3.1 3.2 3.3 3.4

Pr

Agent const varies Agent

Varies

Set

Rp

Const or varies Varies

2.16.1

2.17.

Termination

DEACTIVATION BY TRANSFER TO AGENT

2.15.1

2.16.

Transfer

REVERSIBLE INITIATION AND REACTIVATION

2.14.1

2.15.

Monomer

None; concentration of head-to-head and tail-to-tail, sequence length distributions, various dyad and triad fractions Block copolymers

Conditions Condensation of bifunctional monomer AB; the Flory distribution. See Eq. (C41) Bifunctional monomer AA reacting with bifunctional monomer BB; the nylon case of hexamethylene diamine and adipic acid Deviations from the principle of equal reactivity; the "substitution effect" Rate of condensation varies 3.4.1 Rate of condensation proportional to chain size 3.4.2 Condensation requires rotation into colinear orientation prior to reaction 3.4.3 The order of reaction varies with conversion, or a catalytic influence of unreacted A or B groups, or both effects occurring simultaneously Other simple linear condensation cases 3.5.1 AA reacting with BC. BC is an anhydride; within a given molecule, B must react before C 3.5.2 AA reacting with BC. BC is an unsymmetrical acid or glycol; B reacts only with A at a different rate from that of C reacting with A 3.5.3 AB reacting with C and itself. B and C react only with A; C is a terminator or capping material 3.5.4 AA reacting with BB and C; the nylon case again with acetic acid as terminator 3.5.5 AA reacting with BC; A and B react with C 3.5.6 AB reacts with CC or DD kinetics 3.5.7 AA and A reacting with BB and B Further polymerization of polymers with an initial geometric distribution 3.6.1 Further polymerization of AB when the initial distribution is geometric 3.6.2 Further polymerization of AB when the initial distribution is a superposition of two geometric distributions 3.6.3 Further polymerization of AA with BB when the initial distribution of both is geometric Copolymerization of condensation polymers 3.7.1 AB reacting with CD; AB and CD can be hydroxy acids or similar materials 3.7.2 AA reacting with BB and CC. A reacts with B and C only and vice versa; BB and CC can be adipic and sebacic acids 3.7.3 AA and BB reacting with CC and DD; A and B react only with C and D and vice versa 3.7.4 AA reacting with BC and DD; A reacts only with B, C, and D 3.7.5 AA and DD reacting with BC; A and B react only with C and D and vice versa 3.7.6 AA reacting with BC-BC, the latter can be a dianhydride; B must react before C

References 1,2,110 1,24,111 1,112,253,254 1,113,114,134 255 256 1,111 1,111 1,111 1,111 1,111 115 336 1,116 1,116 1,116 1,111 111,257 111 111 111 258,259

TABLE 3. cont'd Set 3.8

3.9 3.10 3.11

Conditions Coupled polymers 3.8.1 AB polymerized to extent of conversion a, then coupled with CC 3.8.2 AB polymerized to extent of conversion a, then coupled with CD. A and B can react with C or D 3.8.3 AA and BB polymerized to extent of conversion a, then coupled with an excess of CC. A and B to react completely on coupling 3.8.4 Poisson-distribution polymer of AA coupled with BC 3.8.5 Monomer AB polymerized to extent of conversion a, then coupled with excess CC to extent of conversion 7, then recoupled with excess DD 3.8.6 Particularly narrow distributions via coupling reaction I. AA and BB (great excess)—^BBAABB, then remove excess BB. CC and BBAABB (great excess)—> BBAABBCCBBAABB, then remove excess BBAABB, and continue in like manner II. AA and 2BC^CBAABC then CBAABC and 2DE^EDCBAABCDE, etc III. AB and CD^ABCD then ABCD and EF^ABCDEF, etc 3.8.7 Blocks of polymers of known distribution are coupled together I. A series of Poisson-type-polymers coupled together II. Poisson-type-polymers coupled to "most probable"-type polymers III. A series of "most probable"-type polymers coupled together AB reacts with CC or CD; rate of reaction of A dependent upon whether or not B has reacted Segmented block copolymers; distribution of block sizes Reacted sequences in homopolymers

TABLE 4. Set 4.1

References

1,117 1,117 1,117 119 119 119

120,118 115 260-262 263, 264

EQUILIBRIUM POLYMERIZATION Conditions

References

The "most probable" distribution of Flory has been derived for condensation polymerization when all reactions are assumed to have the same probability, regardless of chain length, and whether or not exchange reactions occur: P r + P5 = P r + s - i + P t ,

4.2

1,117,118 1,117

Eq. C41

i