Network structure terminal chains

A subsequent theory [6] allowed for movement of the crosslink junctions through rearrangement of the chains and also accounted for the presence of terminal chains in the network structure. Terminal chains are those that are bound at one end by a crosslink but the other end is free. These terminal chains will not contribute to the elastic recovery of the network. This phantom network theory describes the shear modulus as... 

The two conditions stated above do not assure the occurrence of gelation. The final and sufficient condition may be expressed in several ways not unrelated to one another. First, let structural elements be defined in an appropriate manner. These elements may consist of primary molecules or of chains as defined above or they may consist of the structural units themselves. The necessary and sufficient condition for infinite network formation may then be stated as follows The expected number of elements united to a given element selected at random must exceed two. Stated alternatively in a manner which recalls the method used in deriving the critical conditions expressed by Eqs. (7) and (11), the expected number of additional connections for an element known to be joined to a previously established sequence of elements must exceed unity. However the condition is stated, the issue is decided by the frequency of occurrence and functionality of branching units (i.e., units which are joined to more than two other units) in the system, on the one hand, as against terminal chain units (joined to only one unit), on the other. 

If chain transfer of the radical center to a previously formed polymer molecule is followed ultimately by termination through coupling with another similarly transferred center, the net result of these two processes is the combination of a pair of previously independent polymer molecules. T. G. Fox (private communication of results as yet unpublished) has suggested this mechanism as one which may give rise to network structures in the polymerization of monovinyl compounds. His preliminary analysis of kinetic data indicates that proliferous polymerization of methyl acrylate may be triggered by networks thus generated. 

Figure 4. Sketch of the effects of having cyclics present during the end-linking of functionally-terminated chains to form a network structure. Cyclics such as a, which are not threaded by such a chain before its end linking will be extractable from the subsequently prepared network. Cyclics which have been threaded, such as b, would be permanently trapped, and thus unextractable [196],...

In the simplest study of this type, Al-ghamdi and Mark [138] studied reinforcement of PDMS by two zeolites of different pore sizes. The zeolites were a zeolite 3A (pore diameter 3 A) and a zeolite 13X (pore diameter 10 A), both with a cubic crystalline structure. They were simply blended into hydroxyl-terminated chains of PDMS which were subsequently end-linked with tetraethoxysilane to form an elastomeric network. These elastomers were studied by equilibrium stress-strain measurements in elongation at 25°C. Both zeolites increased the modulus and related mechanical properties of the elastomer, but the effect was larger for the zeolite with the larger pore size. 

In addition to terminal chains and entanglements, there are other types of network imperfections. Figure 6-2 shows that if a short chain were crosslinked only once, the crosslink is a wasted one because the chain cannot support elastic stress. Also, if a crosslink forms an intrachain loop, it is again an ineffective crosslink. Unfortunately, owing to its very complexity, it is at present impossible to completely characterize the network structure of an elastomer. 

Biodegradable shape-memory polymer networks with single POSS moieties located in the center of the network chains would promote POSS crystallization even within a constraining network structure. Successful synthesis of POSS initiated poly(e-caprolactone) (PCL) telechelic diols, utilizing a POSS diol as initiator, was reported by Lee et al. [116]. The POSS-PCL diols were terminated with acrylate groups and photocured in the presence of a tetrathiol crosslinker. Scheme 1 shows the chemical reaction for the synthesis of POSS-PCL network. 

Model silicone networks, i.e., those prepared by end-linking of functionally terminated polymer chains, have been extensively utilized to explain the influence of molecular structure on mechanical properties. An important number of studies have been focused on the contribution of elastically active chains and trapped entanglements to equilibrium properties [1-7]. In contrast, very little work has been done to explain the influence of network structure on non-equilibrium properties [8], and the contribution of some of the main structural parameters to viscoelastic properties has been poorly explored. A few qualitative studies have shown in the past that pendant chains have a strong influence on relaxation properties, but the type of contribution was not clearly understood [9]. 

Problem 3.20 The structure of a three-dimensional random network may be described quantitatively by two quantities the density of crosslinking designated by the fraction e of the total structural units engaged in crosslinkages and the fraction / of the total units which occurs as terminal units or free chain ends (i.e., which are coimected to the structure by only one bond). Alternative quantities, such as the number (mole) N of primary molecules and the number (mole) v of crosslinked units, in addition to M and Me, de ned above, are also used to characterize a random network structure. Relate N and v to these other quantities. 

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