Cross-linking index

Characteristic function of the branching probability a (Eq. IX-20) or of the cross-linking index y (Eq. IX-48). 

Cross-linking index, i.e., number of cross-linked units per primary molecule in the system as a whole (Chap. IX). 

The network chain molar mass can not only be calculated from the network density, but also from what is known as the cross-link index, y. The cross-link index gives the number of monomeric units which are cross-link points per primary polymer chain. A primary polymer chain is the linear macromolecule which existed before cross-linking. 

Descriptions of networks in terms of cross-link index and density provide no information on the internal architecture, that is, the homogeneity, of the network. Depending on how they are produced, most networks are more or less inhomogeneous, that is, the local density has a distribution. With multifunctional polycondensation, the gel point is most often reached at relatively high yields, and the network formed is quite homogeneous. In addition polymerization, the gel point occurs already at relatively low yields. The polymerization continues around the spatially fixed network structured centers, and, so, densely cross-linked centers are produced within a less densely cross-linked matrix. 

The cross-link density or the cross-link index y can be used to characterize network cross-link density, y is the number of cross-linked monomeric units per primary chain, and is given by (X is the number-average degree of polymerization)... 

As is seen from the above equations (19-22) the moles of water produced per mole melamine serve both as a measure of the degree of condensation as well as a measure of the cross-linking index. The mole ratio Lm is defined below as... 

The activation energies of the decomposition of the side-chain radical a as a depolymerization index and of the unsaturated polymer radical formation E as a cross-linking index are given in Table 8. Degradability increases with the value of ( b - Epd, which is in fair agreement with the experimental results (51). 

The major use of vinylpyrrohdinone is as a monomer in manufacture of poly(vinylpyrrohdinone) (PVP) homopolymer and in various copolymers, where it frequendy imparts hydrophilic properties. When PVP was first produced, its principal use was as a blood plasma substitute and extender, a use no longer sanctioned. These polymers are used in pharmaceutical and cosmetic appHcations, soft contact lenses, and viscosity index improvers. The monomer serves as a component in radiation-cured polymer compositions, serving as a reactive diluent that reduces viscosity and increases cross-linking rates (see... 

LDPE homopolymers in the 0.2—150 melt index or 100, 000 20,000 mPa s(= cP) viscosity range. Specialty polymers such as greases and waxes or highly cross-linked polymers are not included. 

The mineral talc is extremely soft (Mohs hardness = 1), has good sHp, a density of 2.7 to 2.8 g/cm, and a refractive index of 1.58. It is relatively inert and nonreactive with conventional acids and bases. It is soluble in hydroduoric acid. Although it has a pH in water of 9.0 to 9.5, talc has Lewis acid sites on its surface and at elevated temperatures is a mild catalyst for oxidation, depolymerization, and cross-linking of polymers. 

The commercial grades available in the 1970s used either zinc or sodium as the cross-linking ion and ranged in melt flow index from 0.4 to 14. The main application of the ionomer resins has been for packaging film. The polymer is particularly useful in composite structures to provide an outer layer with good heat sealability. The puncture resistance of film based on ionomer film has the puncture resistance of a LDPE film of twice the gauge. 

The gel content (toluene insoluble per cent) of the rubber and the swelling index of the gel (the ratio of the volume of a swollen gel to its unswollen volume). The former is a measure of the amount of cross-linked material and the second a measure of the intensity of cross-linking. It has been found that a sample of medium gel content (5-20%) and a medium swelling index (10-20) gives the best impact strength in the blend. 

Mechanical properties, such as elastic modulus and yield point, that depend on crystallinity per se are not seriously affected by low to moderate doses of ionizing radiation. On the other hand, those mechanical properties that are sensitive to interlamellar activity are most dramatically affected by the low to moderate radiation doses. This is seen in the ultimate tensile strength and elongation at failure of the polyolefins. It is also reflected in the large change in melt index between 0 and 18 Mrad, which indicates formation of cross-links that increase with increasing... 

In an alternate synthesis, the formation of thermoplastic vulcanizate (TPV) is accomplished with two polymers, wherein one polymer is grafted with a carboxylic acid anhydride, which then is reacted with an aminosilane, which reacts with the acid anhydride and then cross-links with moismre. The vulcanizates exhibit good mechanical properties and lower melt-flow index than the starting polymers. 

The orthogonal projection of the epitaxial poly(DMDA) could not be indexed using the unit cell data for the bulk polymerized crystal (8). However, poly(DMDA) cannot usually be polymerized to completion or to high crystallinity in the bulk due to cross-linking. The use of an epitaxial substrate may have controlled the polymerization process that led to oriented single crystals. 

PVA has also been extensively used for immobilization of biocatalysts in a membranous form. As compared to PAAm, PVA is more hydrophilic and having adhesive property with better tensile strength in dry conditions. But it has high swelling index and dissolves readily in water when not cross-linked. PVA can be cross-linked using a variety of reagents including... 

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... 

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