Polymerization, kinetics

Since the polymerization kinetics in the above cases are extremely simple, ionic polymerization kinetics can be conveniently classified according to whether the initiators are quantitatively and instantaneously dissociated or not. 

For a kinetic analysis, the process of anionic polymerization is divided in the conventional way into three main steps, viz., initiation, propagation, and termination. Representing the initiator by CA (or C A ) and a terminating agent by X, the reactions can be written (Allcock and Lampe, 1990) as  

The rate constant kp is, in fact, an apparent rate constant or overall rate constant since there will be both undissociated (ion pair) and dissociated (free ions) species in the polymerization system and their propagation rate constants are different (discussed later). Integrating Eq. (8.27) one obtains the time dependence of the monomer concentration as 

In the above cases, the polymerization kinetics are so simple that it is useful to classify ionic polymerization kinetics according to whether the initiators are quantitatively and instantaneously dissociated or not. (It should be noted that the term dissociation does not denote any special kind of charge separation. Probably one has to regard this dissociation as a separation of ion pairs by solvent molecules, but not a separation in the sense of forming single ions which can move independently from the counterion.) 

Problem 8.5 Consider the flow tube for rapid polymerization reactions shown schematically in Fig. 8.1. Let V be the volume of the tube (distance between the mixing jets) and V be the volume of the total liquid flowing through in time t. Denoting the total concentration (constant) of polymer chain ends by Eq. (8.29) and the concentration of monomer units in polymer by [Mjp derive an expression for monomer conversion as a function of t. 

The effective polymerization time is the same as the residence time t given by T = 7 (P8.5.1) 

General features of the polymerization kinetics for polymerizations with deactivation by reversible coupling have already been mentioned. Detailed treatments appear in reviews by Pischer, Fukuda ct and Goto and Fiikuda and will not be repeated here. 

In conventional radical polymerization the rate of polymerization is described by eq. 5 (Section 5.2.1). As long as the rate of initiation remains constant, a plot of ]n([My[M],) ra time should provide a straight line. 

If there is an external source of free radicals e.g. from thermal initiation in S polymerization or from an added conventional initiator) eq. 5 may again apply. The rate of polymerization becomes independent of the concentration of IX and, as long as the number of radicals generated remains small with respect to [IX]o, a high fraction of living chains and low dispersilies is still possible. The validity of these equations has been confimied for NMP and with appropriate modification has also been shown to apply in the case of ATRP.  

In efforts to control polymer synthesis and thus polymer composition, kinetics plays a key role. Building off our development of the essentials of kinetics in Chapter 7, here we develop the basics of polymerization kinetics. A key issue is the difference between step-growth/ condensation polymerization and the chain mechanism. We will see that after a few basic assumptions, the kinetics of polymerization are not too different from those of conventional reactions. 

Much of what we will describe in this section is based on the pioneering work of Flory, who earned the 1974 Nobel Prize in Chemistry for his work in polymer chemistry. Flory was hired by DuPont in 1934, where he was assigned to the labs of Carothers. The brilliant Caro-thers is certainly one of the fathers of pol)nner chemistry, and his DuPont labs first produced neoprene, polyesters, and nylon, among others. Carothers would have certainly earned a Nobel Prize himself, but he committed suicide in 1937 at the age of 41. Beginning in the environment that created modern polymer science and later in an academic career, Flory devel-of ed the foundations of the physical organic chemistry of polymerization. 

Since the reaction is affected by the wavelength of the ligth employed and monomer crystal features such as crystal size or purity, the same apparatus and monomer crystals with the same history are employed for any series of experiments involving mechanistic study. 

The monomer crystals are dispersed in a definite amount of dispersant and stirred with a magnetic stirrer at constant speed. Dispersant is required to provide homogeneous irradiation of the crystal surfaces. 

Kinetic plots have been obtained for the polymerization of several monomers. Time vs. conversion and conversion vs. reduced viscosity curves of p-PDA Et at various temperatures are shown in Figs. 4 and 5. 

The reduced viscosity gradually increases with increasing conversion and rises sharply above 80% conversion. The viscosity also increases with the reaction time and continues to rise on irradiation even after the conversion is completed. 

Additives, e.g. initiator, for any type of chain reaction are not involved in the crystalline state polymerization. An intermittant irradiation has no appreciable effect on kinetic curves as far as the total irradiation time is the same. An induction period has not been reported except in one case (see Sect. IV.b.)28). 

According to experiments with model compounds that do not polymerize, termination can occur through an alkylation  

If termination by the monomer or the polymer occurs, this is known as suicide of the polymer. In the polymerization of propylene by typical cationic initiators (that is, in the absence of a polyinsertion mechanism), a hydride shift, for example, can occur  

The allylic group produced is resonance-stabilized and cannot add on any more propylene. 

A suicide also occurs if the atom carrying the cation in the polymer is more basic than the same atom in the monomer, and in this case it occurs by transfer to polymer. An example of this is the polymerization of thietanes 

The tertiary sulfonium ion produced is too stable to start a thietane polymerization. 

Higher conversions of monomers can be accommodated more readily in suspension processes than in bulk processes because suspensions are more mobile than molten polymers. Therefore, simple rate expressions may not be applicable because the values of some rate coefficients diminish at high polymer concentrations (see Section 5.3.2). 

It is often assumed that the polymerization chemistry which occurs in the dispersed phase is identical to that which occurs in the equivalent bulk process. That assumption may be valid if the monomers and initiator are virtually insoluble in the continuous phase. Then, polymerization rates, molecular weight distributions, and copolymer compositions can be predicted from conventional kinetic schemes. But drop stabilizers may react with species inside the drops (for example, to form graft copolymers). 

When all the monomers in a suspension polymerization are virtually immiscible with the continuous phase, then the instantaneous copolymer composition can be predicted from idealized relationships which apply to homogeneous systems. However, the use of those relationships is not straightforward if one, or more, of the monomers is partially soluble in the continuous phase, because the actual composition of the drops may then be unknown. The effective monomer concentrations. 

Abbreviations AS, p-acetoxystyrene S, styrene AN, acrylonitrile MA, methyl acrylate VC, vinyl chloride VA, vinyl acetate, MMA, methyl methacrylate MAA, methacryhc add. 

Apparent reactivity ratios obtained directly from suspension polymerization experiments may not be identical to those expected from the equivalent bulk processes if some monomer migrates to the continuous phase. Ashady et al. [10] found values for reactivity ratios that were not expected from results observed in bulk or solution copolymerization. Izumi and Kitagawa [11] showed that reactivity ratios for suspension copolymerization, of acrylonitrile and methyl acrylate, were different from those obtained from either solution or emulsion polymerization. Table 5.1 compares reactivity ratios obtained from solution copolymerization with those observed in suspension copolymerization. 

The photodegradation of poly(alkylacrylate)s and poly(methacrylate)s under UV irradiation (248 nm) in solution was studied for the first time by TR EPR by Harbron et Well-resolved spectra of oxo-acyl radicals from the ester side chain and of main-chain polymeric alkyl radicals were used to show the side-chain cleavage via the Norrish I process. The methacrylate spectra are strongly influenced by the stereoregularity of different polymer tacticity, the temperature and the solvent. The relations of these dependences on the conformational motion in the polymer chain are discussed. 

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PHOST is often prepared by polymerization of 4-acetoxystyrene followed by base-catalyzed hydrolysis (Fig. 29). The acetoxystyrene monomer s stabihty and polymerization kinetics allow production of PHOST of higher quaUty than is easily obtained by direct radical polymerization of HOST. The PHOST homopolymer product is then partially or fully derivatized with an acid-cleavable functionaUty to produce the final resist component. 

This monomer polymerizes faster ia 50% water than it does ia bulk (35), an abnormaHty iaconsistent with general polymerization kinetics. This may be due to a complex with water that activates the monomer it may also be related to the impurities ia the monomer (eg, acetaldehyde, 1-methyl pyrroHdone, and 2-pyrroHdone) that are difficult to remove and that would be diluted and partitioned ia a 50% aqueous media (see Vinyl polymers, A/-VINYLAMIDE POLYPffiRS). 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. The theory of multicomponent polymerization kinetics has been treated (35,36). 

In studies of the polymerization kinetics of triaUyl citrate [6299-73-6] the cyclization constant was found to be intermediate between that of diaUyl succinate and DAP (86). Copolymerization reactivity ratios with vinyl monomers have been reported (87). At 60°C with benzoyl peroxide as initiator, triaUyl citrate retards polymerization of styrene, acrylonitrile, vinyl choloride, and vinyl acetate. Properties of polyfunctional aUyl esters are given in Table 7 some of these esters have sharp odors and cause skin irritation. 

Studies of the copolymerization of VDC with methyl acrylate (MA) over a composition range of 0—16 wt % showed that near the intermediate composition (8 wt %), the polymerization rates nearly followed normal solution polymerization kinetics (49). However, at the two extremes (0 and 16 wt % MA), copolymerization showed significant auto acceleration. The observations are important because they show the significant complexities in these copolymerizations. The auto acceleration for the homopolymerization, ie, 0 wt % MA, is probably the result of a surface polymerization phenomenon. On the other hand, the auto acceleration for the 16 wt % MA copolymerization could be the result of Trommsdorff and Norrish-Smith effects. 

Polymerization Kinetics of Mass and Suspension PVC. The polymerization kinetics of mass and suspension PVC are considered together because a droplet of monomer in suspension polymerization can be considered to be a mass polymerization in a very tiny reactor. During polymerization, the polymer precipitates from the monomer when the chain size reaches 10—20 monomer units. The precipitated polymer remains swollen with monomer, but has a reduced radical termination rate. This leads to a higher concentration of radicals in the polymer gel and an increased polymerization rate at higher polymerization conversion. 

The production of hydrocarbons using traditional Fischer-Tropsch catalysts is governed by chain growth or polymerization kinetics. The equation describing the production of hydrocarbons, commonly referred to as the Anderson-Schulz-Flory equation, is ... 

An alternating copolymer of a-methyl styrene and oxygen as an active polymer was recently reported [20]. When a-methyl styrene and AIBN are pressurized with O2, poly-a-methylstyreneperoxide is obtained. Polymerization kinetic studies have shown that the oligoperoxides mentioned above were as reactive as benzoyl peroxide, which is a commercial peroxidic initiator. Table 1 compares the overall rate constants of some oligoperoxides with that of benzoyl peroxide. 

Bamford43,59 63 has proposed a general treatment for solving polymerization kinetics with chain length dependent kt and considered in some detail the ramifications with respect to molecular weight distributions and the kinetics of chain transfer, retardation, etc. 

Knowledge of kui/kii is also important in designing polymer syntheses. For example, in the preparation of block copolymers using polymeric or multifunctional initiators (Section 7.6.1), ABA or AB blocks may be formed depending on whether termination involves combination or disproportionation respectively. The relative importance of combination and disproportionation is also important in the analysts of polymerization kinetics and, in particular, in the derivation of rate parameters. 

It has been proposed that transfer to monomer may not involve the monomer directly but rather the intermediate (110) formed by Diels-Alder dimerization (Scheme 6.28). 70 Since 110 is formed during the course of polymerization, its involvement could be confirmed by analysis of the polymerization kinetics. 

In this chapter, we restrict discussion to approaches based on conventional radical polymerization. Living polymerization processes offer greater scope for controlling polymerization kinetics and the composition and architecture of the resultant polymer. These processes are discussed in Chapter 9. 

Tire simplest model for describing binary copolyinerization of two monomers, Ma and Mr, is the terminal model. The model has been applied to a vast number of systems and, in most cases, appears to give an adequate description of the overall copolymer composition at least for low conversions. The limitations of the terminal model generally only become obvious when attempting to describe the monomer sequence distribution or the polymerization kinetics. Even though the terminal model does not always provide an accurate description of the copolymerization process, it remains useful for making qualitative predictions, as a starting point for parameter estimation and it is simple to apply. 

Fukuda et al.lj were the first to recognize that a further two radical reactivity ratios were required to completely define the polymerization kinetics. 

For many systems, the copolymer composition appears to be adequately described by the terminal model yet the polymerization kinetics demand application of the penultimate model. These systems where rAAB=rliAR and aha bba hut sAfsB are said to show an implicit penultimate effect. The most famous system of this class is MMA-S copolymerization (Section 7.3.1.2.3). 

For less polar monomers, the most extensively studied homopolymerizations are vinyl esters (e.g. VAc), acrylate and methacrylate esters and S. Most of these studies have focused wholly on the polymerization kinetics and only a few have examined the mierostructures of the polymers formed. Most of the early rate data in this area should be treated with caution because of the difficulties associated in separating effects of solvent on p, k and initiation rate and efficiency. 

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

The preparation of polymer brushes by controlled radical polymerization from appropriately functionalized polymer chains, surfaces or particles by a grafting from approach has recently attracted a lot of attention.742 743 The advantages of growing a polymer brush directly on a surface include well-defined grafts, when the polymerization kinetics exhibit living character, and stability due to covalent attachment of the polymer chains to the surface. Most work has used ATRP or NMP, though papers on the use of RAFT polymerization in this context also have begun to appear. 

German, A.L., Ed. Macromol. Symp., Free Radical Polymerization Kinetics and... 

This book will be of major interest to researchers in industry and in academic institutions as a reference source on the factors which control radical polymerization and as an aid in designing polymer syntheses. It is also intended to serve as a text for graduate students in the broad area of polymer chemistry. The book places an emphasis on reaction mechanisms and the organic chemistry of polymerization. It also ties in developments in polymerization kinetics and physical chemistry of the systems to provide a complete picture of this most important subject. 

The Tafel slopes obtained under concentrations of the chemical components that we suspect act on the initiation reaction (monomer, electrolyte, water contaminant, temperature, etc.) and that correspond to the direct discharge of the monomer on the clean electrode, allow us to obtain knowledge of the empirical kinetics of initiation and nucleation.22-36 These empirical kinetics of initiation were usually interpreted as polymerization kinetics. Monomeric oxidation generates radical cations, which by a polycondensation mechanism give the ideal linear chains ... 

Both initiation and polymerization kinetics obtained from Tafel slopes (Fig. 5) are related to the formation of very thin films, which are not useful for most applications of conducting polymers. A similar restriction can be attributed to the combination of electrochemical and gravimet-... 

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