Network step growth

Sol-gel syntheses are typically carried out in the presence of polar solvents such as alcohol or water media, which facilitate the two primary reactions of hydrolysis and condensation (Eqs. 15 and 16, respectively). During the sol-gel process, the molecular weight of the oxide product continuously increases, eventually forming a highly viscous three-dimensional network (step-growth polymerization - Chapter 5). 

We noted above that the presence of monomer with a functionality greater than 2 results in branched polymer chains. This in turn produces a three-dimensional network of polymer under certain circumstances. The solubility and mechanical behavior of such materials depend critically on whether the extent of polymerization is above or below the threshold for the formation of this network. The threshold is described as the gel point, since the reaction mixture sets up or gels at this point. We have previously introduced the term thermosetting to describe these cross-linked polymeric materials. Because their mechanical properties are largely unaffected by temperature variations-in contrast to thermoplastic materials which become more fluid on heating-step-growth polymers that exceed the gel point are widely used as engineering materials. 

Traditionally, we create thermoset polymers during step growth polymerization by adding sufficient levels of a polyfunctional monomer to the reaction mixture so that an interconnected network can form. An example of a network formed from trifimctional monomers is shown in Fig. 2.12b). Each of the functional groups can react with compatible functional groups on monomers, dimers, trimers, oligomers, and polymers to create a three-dimensional network of polymer chains. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

Some polymer materials, particularly biomedical materials and step-growth polymers, comprise crosslinked networks. The effect of irradiation on networks, compared with linear polymers, will depend on whether scission or crosslinking predominates. Crosslinking will cause embrittlement at lower doses, whereas scission will lead progressively to breakdown of the network and formation of small, linear molecules. The rigidity of the network, i.e. whether in the glassy or rubbery state (networks are not normally crystalline), will affect the ease of crosslinking and scission.. ... 

The first type, termed sequential IPN s, involves the preparation of a crosslinked polymer I, a subsequent swelling of monomer II components and polymerization of the monomer II in situ. The second type of synthesis yields materials known as simultaneous interpenetrating networks (SIN s), involves the mixing of all components in an early stage, followed by the formation of both networks via independent reactions proceeding in the same container (10,11). One network can be formed by a chain growth mechanism and the other by a step growth mechanism. 

For the nonlinear step growth case above, eiTg, the crosslink density must be related to p. A relevant model, based on calculating the probabilities of finite chains being formed, has been published For the reaction of A -1- 2B2 (e.g., tetra-functional amine -b difunctional epoxy), A4 is considered to be an effective cross-linking site if three or more of its arms lead out to the infinite network. The probability of finding an effective crosslink is related to one minus the probability of a randomly chosen A leading to the start of a finite chain, which in turn is related to the extent of reaction. Application of this procedure to the system of Fig. 15 has been presented in detail The more complicated reaction of a tetrafunctional amine with a trifunctional epoxy was also considered. ... 

The formation of crosslinked networks has been the basis for polymer technology since the development of phenol-formaldehyde resins by Baekeland in 1910. The changes to the rheology of the phenolic system, as it develops from a liquid to a rubber and then to a glass, arise from the formation of a three-dimensional network as the step-growth chemical reactions occur. Water is evolved and the end product is a solid infusible mass. 

The formation of networks by addition polymerization of multifunctional monomers as minor components included with the monofunctional vinyl or acrylic monomer is industrially important in applications as diverse as dental composites and UV-cured metal coatings. The chemorheology of these systems is therefore of industrial importance and the differences between these and the step-growth networks such as amine-cured epoxy resins (Section 1.2.2) need to be understood. One of the major differences recognized has been that addition polymerization results in the formation of microgel at very low extents of conversion (<10%) compared with stepwise polymerization of epoxy resins, for which the gel point occurs at a high extent of conversion (e.g. 60%) that is consistent with the... 

Macosko and Miller (1976) and Scranton and Peppas (1990) also developed a recursive statistical theory of network formation whereby polymer structures evolve through the probability of bond formation between monomer units this theory includes substitution effects of adjacent monomer groups. These statistical models have been used successfully in step-growth polymerizations of amine-cured epoxies (Dusek, 1986a) and urethanes (Dusek et al, 1990). This method enables calculation of the molar mass and mechanical properties, but appears to predict heterogeneous and chain-growth polymerization poorly. 

Many thermoset polymers of major commercial importance are synthesized by step-growth polymerization, as the case of unsaturated polyester, polyurethanes, melamines, phenolic and urea formaldehyde resins, epoxy resins, silicons, etc. In these systems, the crosslinking process, which leads to a polymer network formation, is usually referred to as curing. 

The formation of polymer networks by step-growth polymerization has been modeled using statistical theories, such as the Flory-Stockmayer classical theory [61-64], the Macosko-Miller conditional probability model [65-70], and Gordon s cascade theory [71-74]. However, statistical methods have not been successful for modeling of polymer network formation in chain-growth polymerization systems. 

The description of the variety of chemistries that are used to produce thermosetting polymers can be the subject of a whole book and is beyond the scope of this chapter. A description of chemistries involved in the synthesis of several families of thermosets can be found elsewhere [2]. In this section, we focus on some aspects of the chemistry of epoxy polymers because it provides examples of both step-growth and chain-growth polymerizations employed in the synthesis of polymer networks. 

The epoxy group (oxirane ring) can react with both nucleophilic and electrophilic reagents. The most typical example of a step-growth polymerization of epoxy monomers is the reaction with amines, which are the most commonly curing agents/hardeners used to build up epoxy networks. The reactions shown in Scheme 28.1 take place in this case. 

Several epoxy formulations are cured by both step-growth and chain-growth polymerizations occurring sequentially or in parallel. For example, BF3 complexes or tertiary amines may be added as catalysts of an amine-epoxy reaction, leading to different reaction mechanisms taking place whose relative significance depends on the cure temperature (or thermal cycle) and the initial stoichiometry. The structure and properties of the resulting polymer networks depend on the relative contribution of both mechanisms. 

As recalled from our earlier discussion, we stated that if one of the reactants in step-growth polymerization has a functionality greater than 2, then the formation of a branched or a three-dimensional or cross-linked polymer is potentially possible. An example is the reaction between a dibasic acid and glycerol, which has two primary and one secondary hydroxyl groups (functionality of 3). A monomer that possesses such a functionality is referred to as a branch unit. Every reaction of such a molecule introduces a branch point for the development of the three-dimensional network. The portion of a polymer molecule lying between two branch points or a branch point and a chain end is called a chain section or segment. 

Epoxy resins are complex network polyethers usually formed in a two-staged process. The first stage involves a base-catalyzed step-growth reaction of an excess epoxide, typically epichlorohydrin with a dihydroxy compound such as bisphenol A This results in the formation of a low-molecular-weight prepolymer terminated on either side by an epoxide group. 

In any reaction resulting in the formation of a chain or network of high molar mass, the functionality (see Section 1.2) of the monomer is of prime importance. In step-growth polymerization, a linear chain of monomer residues is obtained by the stepwise intermolecular condensation or addition of the reactive groups in bifunctional monomers. These reactions are analogous to simple reactions involving monofunctional units as typified by a polyesterification reaction involving a diol and a diacid. 

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