Stoichiometric network chain

Figure 3. Dependence of the structure factors A, Ae, and As on the stoichiometric network chain concentrations.

Note 2 A model network is not necessarily a perfect network. If a non-linear polymerization is used to prepare the network, non-stoichiometric amounts of reactants or incomplete reaction can lead to network containing loose ends. If the crosslinking of existing polymer chains is used to prepare the network, then two loose ends per existing polymer chain result. In the absence of chain entanglements, loose ends can never be elastically active network chains. 

Fig. 15. Calculated dependence of the sol fraction, w., and the number of elastically active network chains per monomer unit, N, on the extent of transesterification, Stoichiometric mixture of dicarboxylic acid (M = 188) and diepoxide (M = 340). The extent of addition esterification = Op (1.0, 0.99, 0.95) is indicated...

Fig. 16. Time dependence of the gel fraction, w, and concentration of elastically active network chains, v, in the stoichiometric mixture of azelaic acid and DGEBA...

For a network generated from stoichiometric quantities of a difunctional polymer and a tetrafunctional cross-linker where cross-linking occurs only at the chain ends the network chain average molecular weight should approximate the prepolymer 1. ... 

Calculations. The presence of sol in a network indicates that the curing reaction was not complete or the ingredients were not present in stoichiometric amounts, either of which give elastically inactive chains, i.e., chains attached to the gel at one end only. (Also, the monohydroxy PPO in the present formulations will always give sol.)... 

Networks formed from stoichiometric, end-linking polymerisation are often assumed to be perfect networks 1-4). However, such an assumption means that intramolecular reaction within gel molecules, which must occur for a network to be formed, never leads to inelastic chains. The assumption is unlikely to be true. The smallest loops which can occur must be elastically ineffective(5-9) and from chain... 

The first step involves preparation of a bifunctional "living" precursor, of known molecular weight and low polydispersity. Crosslinking can be achieved either by the addition of stoichiometric amounts of a multifunctional electrophilic deactivator, or by adding small a small amount of a bifunctional monomer (such as DVB or ethylene glycol dimethacrylate), the polymerization of which will be initiated by the carbanionic sites of the precursor. In either case, the precursor chains become the elastically effective chains of the networks. The experimental conditions... 

A large number of metal borides have been prepared and characterized. Several hundred binary metal borides M Bj, are known. With increasing boron content, the number of B-B bonds increases. In this manner, isolated B atoms, B-B pairs, fragments of boron chains, single chains, double chains, branched chains, and hexagonal networks are formed, as illustrated in Fig. 13.3.1. Table 13.3.1 summarizes the stoichiometric formulas and structures of metal borides. 

The choice of polyol, especially its size (moleeular weight), flexibility of its molecular structure, and functionality, has significant effect on the properties of the resultant polyurethanes. Varying isoeyanates also have major influenee on the properties of polyurethanes, sinee the reaetion of di- or polyfunctional isocyanates with polyols forms the polyurethanes. When there is excessive isocyanate with respect to diol, many secondary reactions may occur to create chemical cross-links between chains and network strueture in the polyurethanes. Thus pad properties can be eontrolled and fine-tuned through the control of the stoichiometric ratio of isocyanate to diol. 

Fig. 11 a,b Schematic representation for the formation of PEO-PEI-dexy-CD networks, a A supramolecular network is formed via the double-strand complex between y-CD and double strands of the PEO-PEI chains. The double-strand complexes are either of the parallel or antiparallel type, b a-CD and y-CD include single and double strands of PEI, respectively. Stoichiometric ratios of a-CD or y-CD to the repeating unit of PEI are 1 2 and 1 4, respectively [84]... 

Chemical reactions may involve large numbers of steps and participants and thus many simultaneous rate equations, all with their temperature-dependent coefficients. The full set of rate equations is easily compiled as shown in Section 2.4, and to obtain solutions by numerical computation poses no serious problems. With a large number of equations, however, it may become too much of a task to verify the proposed network and obtain values for all its coefficients. Therefore, every available tool must be brought to bear to reduce the bulk of mathematics, and that without unacceptable sacrifice in accuracy. The present chapter critically reviews the principal tools for such a purpose stoichiometric constraints and the concepts of a rate-controlling step, quasi-equilibrium steps, and quasi-stationary states. Other tools useful in catalysis, chain reactions, and polymerization will be discussed in the context of those reactions (see Sections 8.5.1, 9.3, 10.3, and 11.4.1). 

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