Elasticity of entangled polymer loops: Olympic gels

Abstract

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto \lambda^{5/2}$ where $\lambda$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.Comment: latex, no figures, accepted in PRE Rapid Communicatio

Topological Interaction between Loop Structures in Polymer Networks and the Nonlinear Rubber Elasticity

“…where λ is the strain ratio in the stretched direction and the incompressibility of a sample is assumed. This stress (5) is correct only in the very small extension regime as shown below. Figure 1 shows the relation between the normalized uniaxial stress versus the inverse of the strain ratio (which we refer to as the Mooney-Rivlin plot hereinafter) obtained from experimental data of end-linking poly (dimethylsiloxane) PDMS network.…”

“…The topological effect in polymer systems has been attracting considerable attention in fundamental studies as well as in applications. [1][2][3][4][5] The topologically constrained systems such as ring polymers have been intensively studied. 1,2,[4][5][6][7][8] Recent studies [9][10][11][12] have evidenced that several familiar polycondensated polymer systems, e.g., polyesters, polycarbonates, poly (ether-sulfon)s and polyamides, also contain large amounts of cyclic polymers.…”

“…[1][2][3][4][5] The topologically constrained systems such as ring polymers have been intensively studied. 1,2,[4][5][6][7][8] Recent studies [9][10][11][12] have evidenced that several familiar polycondensated polymer systems, e.g., polyesters, polycarbonates, poly (ether-sulfon)s and polyamides, also contain large amounts of cyclic polymers. Such topology of polymer chains have great influences on the systems.…”

Modification of statistical threading in two-component pseudorotaxane melts using the amphiphilic approach and variations in the confinement geometry

“…Mechanically interlocked molecules, such as knots, catenanes, and especially rotaxanes, have been of significant interest in recent years, due to their potential application as building blocks in artificial molecular machines [33][34][35][36][37][38][39][40][41] and because they display very different properties from their components. 2,16,43 A rotaxane consists of a linear molecule threaded by one or more macrocyclic rings. 1 The linear chain usually has bulky stoppers at the ends, which prevent the macrocycle from slipping out of the chain.…”

The Formation and Structure of Olympic Gels

“…Instead, the permanent entanglement between concatenated rings establishes a three dimensional network structure similar to the structure of the Olympic rings. Due to the lack of cross-links, these samples were considered to be ideal model networks that might allow for an unperturbed analysis of the effect of entanglements in a polymer network [2]. Recently [3], it was shown by computer simulations that OGs show unusual swelling properties, since networks of longer strands swell less than networks made of short cyclic molecules at otherwise identical preparation conditions.…”