Crosslinking 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. 

The non-Newtonian index is plotted against the blend ratio in Fig. 2. There are three distinct stages of the change of value with %NBR in the preblend. First, a decrease of up to 40% of NBR, a rapid rise of up to 60% of NBR, and beyond this ratio a further decrease are observed. Heating of blends shows the only minimum at 50 50 ratio. It is obvious that 60-50% of Hypalon in the NBR-Hypalon blend is an optimum range where maximum extent of interchain crosslinking reaction is expected, and this blend is supposed to be more pseudoplastic. 

The non-Newtonian index is plotted against the blend ratio in Fig. 8. We see that for both the preblends and the preheated blends, the w value increases with NBR content up to about 50% of NBR. Beyond this while the preblend shows a continued increase in n value at a slower rate, the preheated blends seem to show a saturation in n value. The low values of may be attributed to the interchain crosslinking at higher levels of NBR in the blends. 

The properties and applications are very variable according to the nature and the ratio of the substituents, the crosslinking reaction and the formulation but one always finds a good fire resistance resulting in a high oxygen index, a ... 

Aryloxyphosphazene copolymers can also confer fireproof properties to flammable materials when blended. Dieck [591] have used the copolymers III, and IV containing small amounts of reactive unsaturated groups to prepare blends with compatible organic polymers crosslinkable by the same mechanism which crosslinks the polyphosphazene, e.g. ethylene-propylene and butadiene-acrylonitrile copolymers, poly(vinyl chloride), unsaturated urethane rubber. These blends were used to prepare foams exhibiting excellent fire retardance and producing low smoke levels or no smoke when heated in an open flame. Oxygen index values of 27-56 were obtained. 

Fig. 2. Relaxation modulus G(t) of a set of polydimethylsiloxane samples with increasing extent of crosslinking plotted against time of crosslinking. The linear PDMS chains (Mn 10 000, polydis-persity index 2) were endlinked with a four-functional silane crosslinker catalyzed by a platinum compound. Samples with different extent of reaction were prepared by poisoning the reaction at different times. The actual extent of reaction was not determined. Two of the samples are clearly before the gel point (LST) and two beyond. The third sample is very close to the gel point. Data of Chambon and Winter [5] evaluated by Baumgartel and Winter [8]...

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