Modulus of three and four functional poly(dimethylsiloxane) networks

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Networks formed from ci, w divinyl poly(dimethylsiloxane) endlinked with tnand tetrafunctional hydrosilanes are used to test several theoretical relations for the small strain modulus. The results indicate that topological interactions between chains have a large influence on the modulus, however, the suppression of junction fluctua— tion by topological interactions seems to be small for PDMS networks. Independent measurement of the topological interactions between chains, the plateau modulus G on linear PDMS, agrees well with that determined from the networks. The influence of hydrosilane side reactions on determination of structure parameters was accounted for. INTRODUCTION Recently, there has been considerable interest in testing the relation between molecular structure and the theory of rubber elasticity. Of particular concern has been the influence on mechanical properties of topological interactions between chains. Below we review the various approaches to this probLem in terms of the small strain modulus. If there are no topological interactions, i.e. if the strands can pass through each other like phantoms, then the network theories of rubber elasticity apply (1-3). For these theories the shear modulus for networks formed and tested in bulk becomes G = (v—ii)RT (1) where v and p are the concentrations of elastically active strands and junctions. A junction is elastically active if three or more of its arms are independently attached to the network. A strand is elastically active if it is attached at both ends to an active junction (4). If all strands are attached and there is only one type of junction with functionality f, then p = 2v/f. Thus for a perfect tetrafunctional Eq. 1 becomes G = 1/2 \)RT (2) which is a resilt that has rften been compared to experimental data in the past (5,6). Likewise, for a perfect trifunctional G = 1/3 VRT (3) In the phantom network, junctions can fluctuate about their mean position due to Brownian notion. This gives rise to the -p term in Eq. 1. The higher the junction functionality, f, the less will be the fluctuations. One manifestation of topological interactions may be to suppress the magnitude of these fluctuations (7,8). If all junction fluctuation is suppressed then G = VRT (4) which is also the result obtained directly from the assumption of af fine deformation. To allow for intermediate behavior Dossin and Graessley have used (9) G = (v — hp)RT (5) where h is an empirical parameter between 0 and 1. Another approach is to consider that topological interactions can not only suppress junction fluctuation but also can raise the free energy of deformation further, as if there were additional crosslinks in the network. The idea originates from the observation that linear polymers of high molecular weight behave very much like a crosslinked rubber over a wide time scale in stress relaxation and other dynamic mechanical tests (10,11). This plateau modulus, G° , appears to be characteristic of the polymer backbone independent of chain length. The pateau modulus is taken to be a measure of topological interactions or entanglements between chains. If the chains are crosslinked, it has been proposed that a