The Theory of Permanent Set at Elevated Temperatures in Natural and Synthetic Rubber Vulcanizates

Abstract

A molecular theory is developed to describe quantitatively the permanent set taking place in thin samples of vulcanized natural and synthetic rubbers held at constant extension at elevated temperatures. Permanent set: is considered to be the result of the formation, through the action of molecular scission and cross-linking reactions, of a dual molecular network in the rubber sample, in which the network chains are of two types: chains which are at equilibrium when the sample is at its unstretched length, and chains which are at equilibrium when the sample is at its stretched length. According to the theory the amount of permanent set in a rubber sample is a function of only two quantities: the relative ratio of the number of chains of the two types, and the elongation at which the sample was held. Experimental data on permanent set for various rubber types and under different conditions are presented and are shown to be in good agreement with the theory.

Mechanical and Optical Behavior of Double Network Rubbers

“…This makes any analysis of the birefringence data suspect, since a prediction of the zero-stress birefringence relies on the stress calculated for each component network. Additionally, while the assumption of independent network mechanical behavior is generally accepted, 3,[22][23][24] the further assumption of additivity of the respective birefringence from the two components (eq 18) may not be correct.…”

“…20,21 Theoretical interpretations of these rubbers are based on the idea that the component networks behave independently, so that the mechanical response is the sum of the individual contributions. 3,[22][23][24] The strain energy for uniaxial deformation of a double network is thus given by where the subscripts 1 and 2 refer to the first and second networks, respectively. The stretch ratio of the composite network, λ, is referenced to the original, undeformed first network, and λ X is the stretch during the second cross-linking; hence, λ ) λ 1 and λ 2 ) λ/λ X .…”

Strength Enhancement From Heterogeneous Networks of Ethylene–propylene/Ethylene–propylene–diene

“…Since the properties of an elastomeric network depend on the orientation of the chains, double networks exhibit mechanical behavior distinct from the corresponding single (unoriented) networks. [6][7][8] Better mechanical properties have also been achieved with bimodal networks, in which a portion of the chains between cross-links is short, and the remaining network strands are very long. Bimodal networks are prepared by end-linking a large number of low Mw precursor chains with a large weight fraction of high Mw chains, yielding elastomers with good toughness.…”

Constitutive models for rubber networks undergoing simultaneous crosslinking and scission.

“…The strands formed by the new crosslinks in a deformed state have a different state-of-ease than the previously existent strands. Many years ago, Tobolsky proposed that networks crosslinked in various states of strain obey the two-network hypothesis 3 (termed the independent network hypothesis in generalizations by later researchers). The main idea is when crosslinks are added in different deformations (or stages), the resulting stress is as though separate networks are formed with states-of-ease at the deformations where the crosslinks were added.…”