Molar mass between cross-links

When a chain with M= 200,000 g/mole is linked to other chains at four points, the average molar mass between cross-links, M., amounts to 40,000. The mass of one unit is 4x12 + 6x1 =54 g/mole so the number of units between cross-links is about 740. At the glass-rubber transition no whole chains obtain free mobility, as a result of the entanglements, but chain parts of 30 to 100 monomer units. The chemical cross-links, therefore, hardly contribute to the restriction in chain mobility the increase in Tg will, therefore, be negligible. 

Mc = molar mass between cross-links (here 5 x 50 = 250)... 

Introducing density p, the average molar mass between cross-linking points A/, and flq = o Equation (34) becomes ... 

Recently, SEC/MALS measurements were used to obtain approximate measures of the average molar mass of a long-chain branch and of the average molar mass between branch points, both as a continuous fimction of the molar mass of the macromolecule. Though the particular experiments applied to the study of cross-link-induced branching well below the percolation threshold, the theory and measurements extend naturally to the study of native branching. 

Assuming a randomly cross-linked, four-functional network, and including the ionic effects in an apparent xthe swelling ratio depends on the molecular mass of polymer chain between cross-links Me, on the backbone molecular mass Mn, the molar volume Vi of the solvent, and the density po of the unswollen polymer. The volume fraction of monomer i 20 during pol5unerization influences the maximum swelling ratio through the term v i. ... 

A sample of polyisoprene (density 1300 kgm, monomer of relative molar mass 68) has a shear modulus of 4 X 10 Pa at room temperature. Calculate the average number of monomers between cross-links. 

The expression on the right-hand side depends on the molar mass M g of the chains between cross-links, since... 

The formation of intermolecular cross-links, i.e. covalent bonds between different polymer chains, causes an increase in the average molar mass and eventually combines all of the macromolecules into a three-dimensional insoluble network. Cross-linking can be accomplished in various ways. Several methods rely on reactions of electronically excited pendant groups on the polymer chains, others on reactions of various kinds of reactive species in the ground state that are photogenerated in polymeric systems. Typical of the former reaction type are [2-f-2] cycloadditions that occur in the case of linear polymers bear-... 

Average molar mass of a polymer chain segment between two adjacent cross-links (M )... 

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