Network formation, kinetics

Curing Agents for Carboxyl-Terminated Polybutadiene Prepolymers. The types of curing agents used to prepare binders for CTPB propellants are the same as those for PBAN or PBAA. The bifunctionality of CTPB, however, requires that part of the curing agents be polyfunctional to provide for the formation of the tridimensional network. Almost without exception, the polyfunctional aziridines and epoxides used with CTPB undergo side reactions in the presence of ammonium perchlorate, which affects the binder network formation. Kinetic studies conducted with model compounds have established the nature and extent of the cure interference by these side reactions. The types and properties of some of the crosslinkers and chain extenders used to prepare solid propellants are summarized in Table IV. 

Brovko 0 0, Fainleib A M, Slinchenko E A, Dubkova V I and Sergeeva L M (2001) Filled semi-interpenetrating polymer networks formation kinetics and properties. Compos Polym Mat 23(2) 85-91. 

This chapter emphasizes the recent mechanistic and kinetic findings on phenolic oligomer syntheses and network formation. The synthesis and characterization of both novolac- and resole-type phenolic resins and dieir resulting networks are described. Three types of networks, novolac-hexamethylenetetramine (HMTA),... 

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. 

Generalization of Flory s Theory for Vinyl/Divinyl Copolvmerization Using the Crosslinkinq Density Distribution. Flory s theory of network formation (1,11) consists of the consideration of the most probable combination of the chains, namely, it assumes an equilibrium system. For kinetically controlled systems such as free radical polymerization, modifications to Flory s theory are necessary in order for it to apply to a real system. Using the crosslinking density distribution as a function of the birth conversion of the primary molecule, it is possible to generalize Flory s theory for free radical polymerization. 

There are yet many problems to be solved to build a more realistic model for network formation, and more experimental information will be necessary in order to clarify these complicated phenomena. We do however believe these kinetic models will provide greater insight into the phenomenon of network formation. 

Kinetic investigations demonstrate that the order of the network formation is nearly unity (see Fig. 1). This result agrees with the polymerization kinetics [3], The formation of the network and the decrease of double bond follow the same kinetic law. 

The effect of hydrogen pressure in the reaction network and kinetics of quinoline hydrodenitrogenation has been matter of debate. Some controversial results and explanation were raised by the proposal of light hydrocarbons formation [78], The lack of observation of these hydrocarbons in previous experiments was explained by the low pressure employed and the deviations observed of the mass balances in these experiments were an evidence for the formation of lights HCs. The controversy is not clear yet and might be the subject for further investigations. 

Several theories of network formation have been developed in the past half century, including statistic [50,64-66,138-144] and kinetic ones [100,145-153], and... 

Figure 5.9 Difference in concepts of statistical (A) and kinetic (B) network formation theories...

In the case of network formation controlled by (irreversible) kinetics programmed polymerization regime (starved feed conditions, etc.). 

Several applications of hyperbranched polymers as precursors for synthesis of crosslinked materials have been reported [91-97] but systematic studies of crosslinking kinetics, gelation, network formation and network properties are still missing. These studies include application of hyperbranched aliphatic polyesters as hydroxy group containing precursors in alkyd resins by which the hardness of alkyd films was improved [94], Several studies involved the modification of hyperbranched polyesters to introduce polymerizable unsaturated C=C double bonds (maleate or acrylic groups). A crosslinked network was formed by free-radical homopolymerization or copolymerization. 

The determination of the kinetic regularities for different systems is important in the first turn for understandina of the process of the networks formation and for the study of sol and gel properties. On the other hand, the solution of the kinetic problem is of the great importance from the viewpoint of the further development of the general theory of macromole-cular 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. 

The branching theories In their present state can treat a number of complex branching reactions of Industrial importance. It is to be stressed, however, that there does not exist any universal approach to all systems. The understanding of the reaction mechanism and kinetics is a necessary prerequisite for adaptation of the proper theory to give relations for structural parameters. Further progress in the network formation theory seems highly desirable particularly in the field of cycllzatlon and diffusion control and in understanding the network structure-properties relations. 

Differences in Network Structure. Network formation depends on the kinetics of the various crosslinking reactions and on the number of functional groups on the polymer and crosslinker (32). Polymers and crosslinkers with low functionality are less efficient at building network structure than those with high functionality. Miller and Macosko (32) have derived a network structure theory which has been adapted to calculate "elastically effective" crosslink densities (4-6.8.9). This parameter has been found to correlate well with physical measures of cure < 6.8). There is a range of crosslink densities for which acceptable physical properties are obtained. The range of bake conditions which yield crosslink densities within this range define a cure window (8. 9). 

The mathematics again must be tailored to specific applications but, as an illustration, we consider the case that chains polymerize while being crosslinked by ABP, the latter forming tetrafunctional junctions (f = 4). We assume that binding of ABP occurs sufficiently fast that network formation is limited only by chain growth kinetics, so that the condition a>a implies (2A/4C) (-l), and (cf. Equation 10)... 

We again consider a network crosslinked by actin binding protein. The number of crosslinks that are formed. A, is given by Equation 10, and a plot of G vs (the total amount of added ABP) is shown, schematically, in Figure 3. Both the slope and the intercept provide information about the kinetic parameters of network formation. Elasticity determinations clearly can be used to assess the amount of crosslinking protein in an assembly if all other conditions are kept constant, G varies linearly with consequently, after appropriate calibration (in principle with only two data points), elasticity measurements could be used for quantitative assessment of the efficacy of biochemical purification procedures. Parenthetically, we note that if conditions can be arranged such that K S 1, gives a direct measure of the number of nuclei iIq. 

Low-molecular-weight model compounds such as phenylglycidyl or other mono-glycidyl ethers as well as primary, secondary and tertiary amines have been used for the study of the kinetics, thermodynamics and mechanism of curing. To reveal the kinetic features of network formation, results of studies of the real epoxy-amine systems have also been considered. Another problem under discussion is the effect of the kinetic peculiarities of formation of the epoxy-amine polymers on their structure and properties. 

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. 

Techniques. Experimentally, several techniques are important tools for the study of photoimaging parameters. Though solution techniques common to photomechanistic studies can be applied in some instances, they must be used with care in photopolymer systems. The kinetic and rate expressions just described are only valid in model systems in which homopolymerization processes are the only ones which occur. Kinetic complications can result if crosslinking processes are important. Network formation is common, and represents a further complication. In practice, conversion must be kept to a low level in order to prevent depletion of initiator or monomer below acceptable levels. 

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. 

The possible inhomogeneous course of network formation should be reflected first of all in the reaction kinetics itself or, what is more relevant here, in the distribution of groups in various reaction states at conversions higher than zero. Specifically, for a... 

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