Kinetics of Network Formation

An impressive number of papers on the polymerization kinetics of thermosets have been published since the 1970s. This kind of sport of reporting kinetic results is possibly based on the simplicity with which they can usually be obtained. All one needs is a differential scanning calorimeter (DSC) and some centigrams of a commercial formulation. The task is even facilitated if the software for kinetic calculations, provided by most commercial DSC devices, is used to fit a phenomenological rate expression. 

After three decades of accumulating experimental results, we should be expected to have an almost complete knowledge of the rate equations that describe the most important thermosetting polymerizations. Unfortunately, the situation seems to be quite different on the one hand, some authors persist in using intrinsically incorrect methodologies to analyze kinetic data on the other hand, even for the most studied systems - e.g., the epoxy-amine reaction no general kinetic schemes are universally accepted. 

The first aim of this chapter is to analyze the significant implications associated with the mere statement of a rate equation. Limitations of phenomenological kinetic equations are discussed and more rigorous analysis based on the reaction pathway, for both stepwise and chainwise polymerizations, is presented. The effect of vitrification on polymerization rate is 

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Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

It is important to note that this statistical calculation is only vaHd as long as the kinetics of network formation is totally controlled by the reactivity between the precursor monomers. With the formation of an infinite network at gelation and corresponding increase in viscosity, the reaction is slowed down considerably. Consequently, Eq. (15) is only valid prior to gelation. 

A key problem in the kinetics of the reactions under study is a relation between the rate constants of the epoxy ring opening under the effect of the primary and secondary amino groups, i.e. manifestation of the substitution effect. This problem has been briefly reviewed by Dusek64>. Knowledge of the relationship between these rate constants is very important for an adequate description of the kinetics of network formation. It should be emphasized that knowledge of such a relation, rather than the absolute values of the rate constants would be sufficient. 

The chemistry described in this chapter is the same for the synthesis of both thermoplastic and thermosetting polymers. The transformations occurring during network formation may have a bearing either on the mechanisms (e.g., variation of the reactivity ratios along polymerization) or on the kinetics of network formation (e.g., decrease of reaction rate at the time of vitrification). These transformations and the effects they produce on the buildup of the polymer network will be discussed in the following chapters. 

Diffusion coefficients are proportional to 1/M, the molecular weight of linear chains [7]. They are not well known and therefore neither is the interdigitated thickness. Hence, it is not possible to say whether the observed behavior has to be related to the interdiffusion depth, or to the number of crosslinks formed in the interfacial region or, most hkely, to both effects. These results given for the elastomer joints crosshnked by a sulfur-based vulcanizing system show that it is very difficult to separate interdiffusion and crosshnking mechanisms because the temperature influences both the chain mobihty and the kinetics of network formation. 

The kinetics of network formation of an amine-terminated linear or three-arm star poly(propylene oxide) and a bifunctional epoxy prepolymer were evaluated by NIR spectroscopy, and the dynamics... 

Thus, the concentration of initiator, radical-liable moieties, and nature of solvent system all have a collective influence over the rate, stability, and kinetics of network formation. These parameters, in turn, reflect on the overall performance of the material in terms of cross-linking density, mechanical properties, and degradation profiles. Distinct differences in the application of systems cross-linked through photo-initiated and redox-initiated mechanisms have been reported in various literatures. For... 

CCS can be introduced into injectable materials by separately modifying soluble polymer chains with a pair of molecules that have specific affinity to each other. When these modified polymeric chains are injected simultaneously to the cross-linking site, they undergo rapid cross-linking to give rise to a covalent cross-linked network. The most commonly used pairs of molecules with specific affinities towards each other are iV-hydr-oxysuccinimide (-NHS) to amine (-NH2), 1,4-addition of a doubly stabilized carbon nucleophile to an a,p-unsaturated carbonyl compound (Michael-type addition reaction), and alkyne to azide (click chemistry). In these types of reactions, the rate, stability, and kinetics of network formation are solely dependent upon the strength of the affinity of one molecule to its counterpart. 

For simultaneous semi-IPNs made from PU and PS, the kinetics of phase separation was studied using optical microscopy completed by image analysis [90]. The development of a nodular structure was observed. A thermodynamic approach has allowed us to establish that the diameter of the phase-separated species was the result of the competition between the kinetics of network formation and the kinetics of phase separation. The mechanism of phase separation was not discussed. 

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