Entanglement trapping probability

Figure 5. Entanglement networks cross-linked while strained in simple extension. Entanglement trapping probability plotted against log y. Points, experimental curves, standard entrapment method for uniform and most probable molecular weight distributions of original linear pol3m]er.

Langley used the mean-field percolation model to derive the entanglement trapping factor, assuming that the probability of entanglement between two network strands is proportional to the square of their concentration. The probability Vi that a randomly chosen monomer in a network strand is... 

The first term is the pure crosslink contribution and might be of a phantom nature the second is additional due to entanglements. is called the trapping factor, which accounts for the probability of trapping, probability of sliding, and other effects. is the plateau modulus for the corresponding uncrosslinked polymer melt, i.e. for the melt of same molecular weight as the strands between two crosslinks. 

Fresh natural rubber latex contains about 30-40% of rubber hydrocarbon that is normally referred to as dry rubber content (DRC). However, the total solid content (TSC) is higher than the DRC due to the presence of non-rubbers in the latex, at around 5%. The DRC and non-rubber content may change due to many factors such as clone, soil and climate conditions, season, type of fertilizers used, and tapping frequency. Most of these non-rubbers are dissolved or suspended in the aqueous serum or adsorbed on the surface of rubber particles. They become trapped, tenaciously held, or co-precipitated during coagulation of the rubber probably due to their poor solubility in the aqueous medium or strong entanglement with the rubber molecule. The major non-rubbers are lipids, proteins and amino acids, minerals, inositols and carbohydrates, as shown in Table 3.1. 

A more recent approach uses the concept of the potential entanglements that have been trapped by the cross-linking process. Langley (85) defines the quantity as the fraction (or probability) that an entanglement is trapped in this manner. 

Because of the limited usefulness of the Mooney-Rivlin equation, it is probably not worthwhile to seek a molecular interpretation of the coefficients C and C2 the deviations from neo-Hookean behavior should be examined in some other framework. However, if the deviations are expressed in terms of the ratio = C2/(C] + C2), this quantity can be correlated rather successfully with the relative numbers of trapped entanglements and cross-links in the network. It may be inferred from this and other studies that both trapped entanglements and cross-links contribute to C, but that C2 is associated with trapped entanglements only. 

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