## Abstract

Recent proton n.m.r. measurements on a range of irradiated polydimethylsiloxane fluids have shown that the spin-spin relaxation (which can comprise two components $T$$_{2\text{L}}$ and $T$$_{2\text{S}}$ provides information on the density of crosslinking, which is proportional to radiation dose $r$. For material of high molecular mass it is necessary to add a virtual dose $r$$_{\text{e}}$, even in the absence of radiation-induced crosslinks. This addition is ascribed to the presence of entanglements - not induced by radiation - which on the time scale of the n.m.r. measurements can behave as crosslinks. With the slower methods of network analysis such as solubility, swelling or slow elastic deformation these entaglements, which are in a state of dynamic equilibrium, play little part. These observations have been applied to the statistical theory of network formation, in which the crosslink density $q$_{\text{o}}$r$ is replaced by the crosslink + entanglement density $q$$_{\text{o}}$($r$ + $r_{\text{e}}$). The solfraction $s$ is replaced by the quantity $f$, the non-network fraction, which is directly measurable by n.m.r. since it represents the fraction of protons relaxing with the longer spin-spin relaxation time $T$$_{2\text{L}}$. The gel fraction $g$ (= 1 - $s$) is replaced by 1-$f$, the network component, which possesses the shorter relaxation time $T$$_{2\text{S}}$. Corresponding changes are also made in the other parameters used in network theory. In the separated gel fraction $T$$_{2\text{S}}$ is found to be directly proportional to the average molecular mass $M$$_{\text{ce}}$ between crosslinked and/or entangled units. At 10 degrees C $T$$_{2\text{S}}$ $\sim $ 0.6 $\times $ 10$^{-6}$ $M$$_{\text{ce}}$, when the crosslinked or entangled unit density per molecule is changed by radiation dose or initial molecular weight respectively. For the sol fraction $T$$_{2\text{L}}$ is related to the number average molecular mass; $T$_{2\text{L}}$M$$_{n}^{0.5}$ $\approx $ 15 at 10 degrees C. This relation is derived from (a) unirradiated commercial material, (b) mixtures, (c) the residual sol fraction of a fluid irradiated to varying extents. For high molecular weight sol fractions a $T$$_{2\text{S}}$ component is also observed due to entanglements. Its magnitude, and the dose at which it disappears agree with the theory of networks, as modified to take entanglements into account. When both sol and gel fractions are present simultaneously, both $T$$_{2\text{S}}$ and $T$$_{2\text{L}}$ change, due to swelling of the network, and reduced mobility of the sol molecules. Pulsed n.m.r. promises a simple and quantitative method of studying mobile polymer networks, including the effect of short-lived entanglements whose presence affects the visco-elastic behaviour of these fluids.