Crosslink index

Fig. 1. Schematic of cluster growth during crosslinking. At p = 0, only the monomer is present. With increasing crosslinking index, p, the connectivity increases and the molecular clusters (radius R) grow in size. In the solid state, the network spans the entire sample, 2R > H...

Crosslink index, fraction of mers participating in crosslinks multiplied by DPn of primary chains (Part 7). 

The number of crosslinked units per primary molecule denoted by crosslinking index y is equal to qP (jP is the number average). At... 

After a series of operations and introducing the crosslinking index y, one gets finally... 

The corresponding critical value of crosslinking index yc at gel point is given by... 

The crosslinking index is usually expressed as moles of crosslinking agent per mole of repeating unit, X, or moles of crosslinked units per g of polymer, 1/MC (Mc = molecular weight per crosslinked unit), whereas the crosslink density px corresponds to p = l/vMc (v = specific volume of the polymer). 

Thus, from the value of G the sol fraction w can be calculated and, subsequently, the average crosslinking index y. 

If Mw and are known, then a can be calculated with the aid of Eq. (13 thereupon from the equilibrium shear modulus, Ge, the sol fraction, w, can be calculated with the aid of Eqs. (14)-(17) provide the crosslink functionality, f, is known. Subsequently the we t average crosslinking index in the system as a whole, and the number average crosslinking index in the networic fraction,... 

If the crosslink functionality is unknown, then from additional, independent measurements, e.g. small angle X-ray scattering, the number of crosslinks might be calculated, and subsequently the weight average crosslinking index, y -Thereupon the functionality of the crosslinks can be calculated with the aid of Eqs. (14)-(17). 

F%. 7. Schematic views of the weight average crosslinking index, % (----------), and... 

Fig. 50. Logarithm of weight average crosslinking index calculated from the rubber storage modulus of PYA/borate gels, plotted vs reciprocal temperature O measurements by Beltman (PVA concentration 4 wt% borate concentration 0.275 mr [7]) A OKasurements Sdinltz aid M rs (PVA concentration 4.4 wt% borate concentration 8.7 x 10 md/l) [185]...

In a paper published in 1959 [26] Charlesby and Pinner developed the Charlesby-Pinner equation which allows the experimentalist to determine the G(S) and G(X) ratios. The derivation of the equation is based on an initial random molecular weight distribution and relates to the sol firaction, s, to the crosslinking index, y, when both main chain scission and crosslinking occur. 

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