Network elastic properties

If this is true, this should hold not only for polymer melts but, in the limit of long chains, also for polymer networks. In the simplest case the elastic properties of polymer networks are entirely governed by the entropic... 

Covalently crosslinked siloxane containing liquid crystalline networks with elastic properties were prepared 349). In all of the networks liquid crystalline phases of the linear precursors were retained. For low degrees of crosslinking the phase transition temperatures remained nearly unchanged, whereas higher degrees of crosslinking reduced the phase transition temperatures. 

Pearson D.S. and Graessley W.W., Elastic properties of well characterized ethylene propylene copol3Tner network. Macromolecules, 13, 1001, 1980. 

Arbabi, S Sahimi, M, Elastic Properties of Three-Dimensional Percolation Networks with Stretching and Bond-Bending Eorces, Physical Review B 38, 7173, 1988. 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Figure 4. The elastic properties of some bimodal PDMS networks. Short chains were segregated by pre-reacting them with a limited amount of (tetrafunctional)...

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

After introduction of cross-links in the strained state, the composite network retracts, upon release, to a stress-free state-of-ease (J9 ) The amount of retraction is determined by the degree of strain during cross-linking and by the ratio >i/v2. The elastic properties relative to the state-of-ease are isotropic for a Gaussian composite network ( 8, 1 9,20). 

MCA distinguishes between local and global (systemic) properties of a reaction network. Local properties are characterized by sensitivity coefficients, denoted as elasticities, of a reaction rate v,(S,p) toward a perturbation in substrate concentrations (e-elasticities) or kinetic parameters ( -elasticities). The elasticities measure the local response of a reaction in isolation and are defined as the partial derivatives at a reference state S°... 

The term non-interactive filler means that the filler does not play a role in the crosslinking of the network. Even so fillers can have a marked effect on both elastic properties and wear resistance. Filler particles are usually inorganic or organic particles with a high modulus. For example carbon is used in car tyres. 

Yamamoto M. The visco-elastic properties of network structure. 1. General formalism. J Phys Soc Jpn 1956 11 413-421. 

The kinetic theory of rubber elasticity is so well known and exhaustively discussed (17, 27, 256-257, 267) that the remarks here will be confined to questions which relate only to its application in determining the concentration of elastically effective strands. In principle, both network swelling properties and elasticity measurements can provide information on network characteristics. However, swelling measurements require the evaluation of an additional parameter, the polymer-solvent interaction coefficient. They also involve examining the network in two states, one of which differs from its as-formed state. This raises some theoretical difficulties which will be discussed later. Questions on local non-uniformity in swelling (17) also complicate the interpretation. The results described here will therefore concern elasticity measurements alone. 

Flory,P.J. Network structure and the elastic properties of vulcanized rubber. Chem. Rev. 35, 51-75 (1944). 

Even if completely homogeneous and disordered in the relaxed state, a real network differs from the ideal network, defined in Chapter I. Three types of network defects are commonly considered to be present in polymer networks unreacted functionalities, closed loops, and permanent chain entanglements. Within each group there are several possibilities dependent on the arrangement of chains the effect of defects on the elastic properties of the network is thus by no means simple, as has been stressed e.g. by Case (28). Several possible arrangements are shown in Fig. 1, where only nearest neighbour defect structures have been drawn. 

Greene, A., and A. Ciferri Elastic properties of networks formed from oriented chain molecules of fibrous natural rubber. Kolloid-Z. 186, 1 (1962). 

Jackson, J. F., and S. J. Gill Elastic properties of crosslinked poly (vinyl alcohol) gels. Network topology. J. Polymer Sci. Pt A-2, 5, 663 (1967). 

Hermans, J. 1965. Investigation of the elastic properties of the particle network in gelled solutions of hydrocolloids. I. Carboxymethyl cellulose. J. Polym. Sci. A 3 1859-1868. 

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