Randomly cross-linked

Some commercially important cross-linked polymers go virtually without names. These are heavily and randomly cross-linked polymers which are insoluble and infusible and therefore widely used in the manufacture of such molded items as automobile and household appliance parts. These materials are called resins and, at best, are named by specifying the monomers which go into their production. Often even this information is sketchy. Examples of this situation are provided by phenol-formaldehyde and urea-formaldehyde resins, for which typical structures are given by structures [IV] and [V], respectively ... 

Radiation cure of methyl vinyl sihcone mbber results ia a random cross-linking process with no differentiation between methyl and vinyl groups... 

The stmcture of activated carbon is best described as a twisted network of defective carbon layer planes, cross-linked by aHphatic bridging groups (6). X-ray diffraction patterns of activated carbon reveal that it is nongraphitic, remaining amorphous because the randomly cross-linked network inhibits reordering of the stmcture even when heated to 3000°C (7). This property of activated carbon contributes to its most unique feature, namely, the highly developed and accessible internal pore stmcture. The surface area, dimensions, and distribution of the pores depend on the precursor and on the conditions of carbonization and activation. Pore sizes are classified (8) by the International Union of Pure and AppHed Chemistry (lUPAC) as micropores (pore width <2 nm), mesopores (pore width 2—50 nm), and macropores (pore width >50 nm) (see Adsorption). 

At the gel point, (3 —l) = l/p, which with the foregoing expression gives Eq. (14), thus establishing equivalence of the two procedures. The primary molecules in a condensation polymer must almost invariably conform to a most probable distribution (see Chap. VIII). The random cross-linking of primary molecules otherwise distributed in size has no counterpart in polyfunctional condensation, therefore. 

RA4 molecules and random cross-linking of primary moleculeshaving the most probable distribution can be demonstrated also. In this case, however, it is desirable to define jy, in terms of the repeating unit... 

The other case which we consider is that of a most probable primary distribution. The molecular size distribution after random cross-linking must correspond exactly to that which would be obtained by random condensation of a mixture of bifunctional and tetrafunctional units. This follows as an extension of the correspondence between these two cases considered in the discussion of the critical condition given in the preceding section. The equations developed there are applicable to this case. 

Experimental determinations of the contributions above those predicted by the reference phantom network model have been controversial. Experiments of Rennar and Oppermann [45] on end-linked PDMS networks, indicate that contributions from trapped entanglements are significant for low degrees of endlinking but are not important when the network chains are shorter. Experimental results of Erman et al. [46] on randomly cross-linked poly(ethyl acrylate)... 

Figure 3. Threshold tear energy T . Key O, A, , PDMS networks , A. PB networks , PI networks versus molecular weight Mc between cross-links calculated from Ct. O, , , random cross-linking A, A. trifunctional end-linking , tetrafunctional end-linking.

These observations require a detailed explanation. After several unsuccessful attempts a satisfying answer was finally found. A first step was made by the ingenious derivation of the molar mass distributions of randomly branched or randomly cross-linked materials [14]. The equation, that was later rederived by Elory [13], will be given in the next section. Here it suffices to point out that the width of the distribution, or the polydispersity index MJM , increases asymptotically with the weight average degree of polymerization... 

Figure 35 shows the result for the scaled forward scattering from randomly cross linked polyester chains which were prepared by anhydride curing of phe-nylglycidylether in the presence of bisphenol A diglycidylether [173-175]. The data could be fitted with Eq. (91) with values for g and which are collected in Table 5. 

The selectivity of glass for alkah metal ions is connected with the presence of oxides of trivalent metals in the glass structure. Zachariasen [450] states that silicate glass has a random cross-linking, where each silicon atom lies in the centre of a tetrahedron formed of oxygen atoms (see planar scheme (6.5.5)). 

At higher molecular weights, the polymer begins to separate from the solution. This effect is similar in nature to changing the EO/PO ratio as described above — with one important difference. If these cross-links are placed randomly throughout the polymer backbone, the natural chemistry of the polymer is altered. Figure 1.4 depicts random cross-linking. If this principle is applied to the current problem, the ability of the polymer to extract is affected. 

Equation (7.20) is general, although the expression for Te itself depends on the primary distribution, the gel fraction, and the relative rates of random cross-linking and chain scission. 

Randomly cross-linked chains (polydisperse (m = 1) primary chains)... 

If an alkyl- or aryltrichlorosilane is treated, in bulk or in solution, with a considerable excess of water, an amorphous, infusible, insoluble product is usually formed with the approximate empirical composition, (RSi01-5)x or (ArSiOi.g). Insolubility has precluded estimation of the molecular weights of these products, and the amorphous appearance has discouraged crystallographic studies. These amorphous polymers are probably randomly cross-linked. Only in recent years have definable, low polymeric components of this composition been isolated and identified. 

Ladder polymers are double-strand linear polymers. Their permanenee properties are superior even to those of conventional network polymers. The latter are randomly cross-linked, and their molecular weight ean be redueed by random scission events. When a chemical bond is broken in a ladder polymer, however, the second strand maintains the overall integrity of the molecule and the fragments of the broken bond are held in such close proximity that the likelihood of their recombination is enhanced. 

Questions of the origin and composition of marine macromolecular organic matter continue to challenge us. A key point that has emerged, especially from NMR studies, is that the formation of randomly cross-linked macromolecules... 

Ringsdorf showed a nice example of confinement of supramolecular polymers.192 In cyclohexane, hexa-cinnamoyl azacrown 37 self-assembles to form supramolecular columnar polymers. The periphery of photopolymerizable groups forms cross-links via photocycloaddition and allows the pre-assembled supramolecular polymer to be transferred into a rodlike covalent polymer (Figure 21). Performing the reaction on molecularly dissolved molecules gives rise to a randomly cross-linked polymer with a lower DP. 

An acetal-protected lithium initiator was used to polymerize styrene followed by linking with 1,3,5-triallyloxy-2,4,6-triazine to produce three-arm star polystyrenes.73 The protective acetal group was cleaved by weak acidic treatment in THF to give star polymers with terminal OH groups. These functional groups were coupled with toluene-2,4-diisocyanate to give randomly cross-linked products. Unfortunately, few characterization data were provided in this study. 

Gels that form from grouts normally used for field work contain 8% to 12% solids. These solids, in the gel, are in the form of long molecular chains, randomly cross-linked to each other. The rest of the grout, 88% to 92% by... 

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