Contribution Of Entanglements Research Articles

Small-Strain Modulus of Model Trifunctional Polydimethylsiloxane Networks

Abstract A number of studies to test quantitatively the molecular basis of the theory of rubber elasticity have been performed during the last few years on elastomeric networks of relatively well-known structure. Many of these studies have been done on end-linked networks, for which the number of chains between junctions, their average length, and the functionalities of the junctions could be calculated. Several studies have been with poly(dimethylsiloxane) (PDMS) networks. One of the major controversial points up to now has been the effect of topological interactions between network chains on mechanical properties. Two groups of researchers have come to quite different conclusions about the role of entanglements with respect to their contribution to the elastic modulus. The first group led by Flory considers that the entanglement contribution to the elastic equilibrium modulus is due to the restrictions that topological interactions impose on junction fluctuations among their mean equilibrium position. The second group follows the hypothesis of Langley and Graessley who argue that these interactions are also present along the chain contour. Their support of this thesis is based on the experimental observation of the rubbery plateau modulus GN0 in linear polymers, which is evidence of topological interactions between chains. These interactions would also be present during network formation, and they will be “trapped”, or prevented from relaxing, by the crosslinking process. Thus, these chain-chain interactions can contribute directly to the modulus. Recently, one of us has reviewed most of the results obtained with PDMS networks. This showed that all the experimental data to date are quite consistent and give support to the second approach. In this work, we add to these data some new experiments obtained by crosslinking trifunctional PDMS networks in different states of dilution. The results give additional evidence of the contribution of chain entanglements to the modulus.

Contribution of Entanglements to the Equilibrium Modulus of 1,2-Polybutadiene Networks at Small Strains and Estimate of the Front Factor

Contribution of Entanglements to the Equilibrium Modulus of 1,2-Polybutadiene Networks at Small Strains and Estimate of the Front Factor

Theory of the variation of relaxational properties of polymers during network formation

Recent work on the change of mechanical and dielectric relaxational properties accompanying the formation of a polymer network from reactive oligomers is reviewed. The theoretical considerations cover the essential features of the behaviour observed in different polymer systems. The theory offers new possibilities for obtaining information about the chemical kinetics, physical structure, and structure formation during crosslinking, by means of relaxation studies. Analysis of the theory of the kinetics of structure formation suggests the following picture of the process of crosslinking. Shortlv before the gel point, there appears a state of ‘kinetic entanglement’, which is completed at gel; chemical crosslinks then start to form. Beyond the gel point the contribution of entanglements to the mechanical behaviour is insignificant. However, fluctuation restrictions on crosslinks, and the topological restrictions on network chains play an important role in the reduction of the front-factor and in the increase of the Mooney-Rivlin C 2-term during network formation.

Graph-like state of matter: 12. Static and dynamic entanglements

It is shown that the contribution of chain entanglements to the equilibrium shear modulus, recently deduced theoretically and measured experimentally, cancel almost quantitatively the downward adjustment in the front-factor g of the equation of state used in such theories. This downward revision of g is contested theoretically on algebraic grounds, and the classical value of unity is recovered as a result. This classical value is supported by reinterpreting literature data on silicone rubbers by Valles and Macosko, and by new measurements (which confirm less accurate ones obtained earlier by a more difficult method) on a well-tried polyester system near its gel point. There are indications that the contributions of entanglements to the equilibrium shear modulus are all too easily overestimated by theory, and the technologist is advised to prefer the remarkably simple formulae of the graph-like-state theory of phantom chains. Dynamic entanglements can readily explain qualitatively the anelastic effects here reported, viz. frequency shifts in the plot of the real part of the dynamic shear modulus against conversion in the range α α c ⩽ 1.01 (where α c is the critical conversion at the gel point). Here too it seems as if graph-like-state theory will ultimately account for the observations, but at least certain eigenvalue problems will have to be solved first. An intriguing observation, that at the gel point of the polyester system the spectrum of relaxation frequencies approaches a block distribution, so that every finite value is equally likely, may have general validity.

Model Polystyrene Networks

Abstract Model polystyrene networks have been prepared, at different concentrations in an inert solvent, in such a way that the number of crosslinks is accurately known, and the topology of the network can be varied in a controlled way. The contribution of various network defects to the modulus of the network has been examined. A theoretical estimate of their effect has been made and compared to the experimental result. Two tentative conclusions have been made; first, that the front factor A in the equation for the free energy of deformation of the network has a value of 1/2 and not the alternative value 1; and secondly that the contribution of entanglements to the modulus of the network varies as the concentration squared rather than as the concentration to the first power.

Model polystyrene networks

Model networks have been prepared, at different concentrations in an inert solvent, in such a way that the number of crosslinks is accurately known, and the topology of the network can be varied in a controlled way. The contribution of various network defects to the modulus of the network has been examined. A theoretical estimate of their effect has been made and compared to the experimental result.Two tentative conclusions have been made; first, that the front factor A in the equation for the free energy of deformation of the network has a value of ½ and not the alternative value 1; and secondly that the contribution of entanglements to the modulus of the network varies as the concentration squared rather than as the concentration to the first power.

Influence of entanglements on viscoelastic properties of polyisoprenes

AbstractThe contribution of entanglements to the relaxation modulus of four samples of cis‐polyisoprene has been studied in detail. The average number of chain atoms between neighboring entanglements has been calculated according to the theory of Chompff et al. Relaxation spectra and modulus produced by the entanglements were also calculated from the theoretical model. Good agreement was achieved between the modulus measured experimentally and the values predicted theoretically.